1
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Jones JA. Controlling NMR spin systems for quantum computation. PROGRESS IN NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY 2024; 140-141:49-85. [PMID: 38705636 DOI: 10.1016/j.pnmrs.2024.02.002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/02/2024] [Accepted: 02/05/2024] [Indexed: 05/07/2024]
Abstract
Nuclear magnetic resonance is arguably both the best available quantum technology for implementing simple quantum computing experiments and the worst technology for building large scale quantum computers that has ever been seriously put forward. After a few years of rapid growth, leading to an implementation of Shor's quantum factoring algorithm in a seven-spin system, the field started to reach its natural limits and further progress became challenging. Rather than pursuing more complex algorithms on larger systems, interest has now largely moved into developing techniques for the precise and efficient manipulation of spin states with the aim of developing methods that can be applied in other more scalable technologies and within conventional NMR. However, the user friendliness of NMR implementations means that they remain popular for proof-of-principle demonstrations of simple quantum information protocols.
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Affiliation(s)
- Jonathan A Jones
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK
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2
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Joseph D, Griesinger C. Optimal control pulses for the 1.2-GHz (28.2-T) NMR spectrometers. SCIENCE ADVANCES 2023; 9:eadj1133. [PMID: 37948513 PMCID: PMC10637738 DOI: 10.1126/sciadv.adj1133] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/07/2023] [Accepted: 10/12/2023] [Indexed: 11/12/2023]
Abstract
The ability to measure nuclear magnetic resonance (NMR) spectra with a large sample volume is crucial for concentration-limited biological samples to attain adequate signal-to-noise (S/N) ratio. The possibility to measure with a 5-mm cryoprobe is currently absent at the 1.2-GHz NMR instruments due to the exceedingly high radio frequency power demands, which is four times compared to 600-MHz instruments. Here, we overcome the high-power demands by designing optimal control (OC) pulses with up to 20 times lower power requirements than currently necessary at a 1.2-GHz spectrometer. We show that multidimensional biomolecular NMR experiments constructed using these OC pulses can bestow improvement in the S/N ratio of up to 26%. With the expected power limitations of a 5-mm cryoprobe, we observe an enhancement in the S/N ratio of more than 240% using our OC sequences. This motivates the development of a cryoprobe with a larger volume than the current 3-mm cryoprobes.
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Affiliation(s)
- David Joseph
- Max Planck Institute for Multidisciplinary Sciences, Göttingen, Niedersachsen D-37077, Germany
| | - Christian Griesinger
- Max Planck Institute for Multidisciplinary Sciences, Göttingen, Niedersachsen D-37077, Germany
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3
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Rasulov U, Acharya A, Carravetta M, Mathies G, Kuprov I. Simulation and design of shaped pulses beyond the piecewise-constant approximation. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2023; 353:107478. [PMID: 37343394 DOI: 10.1016/j.jmr.2023.107478] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/20/2023] [Revised: 05/06/2023] [Accepted: 05/09/2023] [Indexed: 06/23/2023]
Abstract
Response functions of resonant circuits create ringing artefacts if their input changes rapidly. When physical limits of electromagnetic spectroscopies are explored, this creates two types of problems. Firstly, simulation: the system must be propagated accurately through every response transient, this may be computationally expensive. Secondly, optimal control: circuit response must be taken into account; it may be advantageous to design pulses that are resilient to such distortions. At the root of both problems is the popular piecewise-constant approximation for control sequences in the rotating frame; in magnetic resonance it has persisted since the earliest days and has become entrenched in the commercially available hardware. In this paper, we report an implementation and benchmarks of recent Lie-group methods that can efficiently simulate and optimise smooth control sequences.
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Affiliation(s)
- Uluk Rasulov
- School of Chemistry, University of Southampton, United Kingdom
| | - Anupama Acharya
- School of Chemistry, University of Southampton, United Kingdom
| | | | | | - Ilya Kuprov
- School of Chemistry, University of Southampton, United Kingdom.
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4
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Goodwin DL, Singh P, Foroozandeh M. Adaptive optimal control of entangled qubits. SCIENCE ADVANCES 2022; 8:eabq4244. [PMID: 36475803 PMCID: PMC9728963 DOI: 10.1126/sciadv.abq4244] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 04/24/2022] [Accepted: 11/02/2022] [Indexed: 06/17/2023]
Abstract
Developing fast, robust, and accurate methods for optimal control of quantum systems comprising interacting particles is one of the most active areas of current science. Although a valuable repository of algorithms is available for numerical applications in quantum control, the high computational cost is somewhat overlooked. Here, we present a fast and accurate optimal control algorithm for systems of interacting qubits, QOALA (quantum optimal control by adaptive low-cost algorithm), which is predicted to offer [Formula: see text](M2) speedup for an M-qubit system, compared to the state-of-the-art exact methods, without compromising overall accuracy of the optimal solution. The method is general and compatible with diverse Hamiltonian structures. The proposed approach uses inexpensive low-accuracy approximations of propagators far from the optimum, adaptively switching to higher accuracy, higher-cost propagators when approaching the optimum. In addition, the utilization of analytical Lie algebraic derivatives that do not require computationally expensive matrix exponential brings even better performance.
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Affiliation(s)
- David L. Goodwin
- Chemistry Research Laboratory, University of Oxford, Mansfield Road, Oxford OX1 3TA, UK
| | - Pranav Singh
- Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK
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5
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Slad S, Bermel W, Kümmerle R, Mathieu D, Luy B. Band-selective universal 90° and 180° rotation pulses covering the aliphatic carbon chemical shift range for triple resonance experiments on 1.2 GHz spectrometers. JOURNAL OF BIOMOLECULAR NMR 2022; 76:185-195. [PMID: 36418752 PMCID: PMC9712393 DOI: 10.1007/s10858-022-00404-1] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/31/2022] [Accepted: 09/02/2022] [Indexed: 06/16/2023]
Abstract
Biomolecular NMR spectroscopy requires large magnetic field strengths for high spectral resolution. Today's highest fields comprise proton Larmor frequencies of 1.2 GHz and even larger field strengths are to be expected in the future. In protein triple resonance experiments, various carbon bandwidths need to be excited by selective pulses including the large aliphatic chemical shift range. When the spectrometer field strength is increased, the length of these pulses has to be decreased by the same factor, resulting in higher rf-amplitudes being necessary in order to cover the required frequency region. Currently available band-selective pulses like Q3/Q5 excite a narrow bandwidth compared to the necessary rf-amplitude. Because the maximum rf-power allowed in probeheads is limited, none of the selective universal rotation pulses reported so far is able to cover the full [Formula: see text]C aliphatic region on 1.2 GHz spectrometers. In this work, we present band-selective 90° and 180° universal rotation pulses (SURBOP90 and SURBOP180) that have a higher ratio of selective bandwidth to maximum rf-amplitude than standard pulses. Simulations show that these pulses perform better than standard pulses, e. g. Q3/Q5, especially when rf-inhomogeneity is taken into account. The theoretical and experimental performance is demonstrated in offset profiles and by implementing the SURBOP pulses in an HNCACB experiment at 1.2 GHz.
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Affiliation(s)
- Stella Slad
- Institute of Organic Chemistry and Institute for Biological Interfaces 4 - Magnetic Resonance, Karlsruhe Institute of Technology (KIT), Fritz-Haber-Weg 6, 76131, Karlsruhe, Germany
| | - Wolfgang Bermel
- Bruker BioSpin GmbH, Rudolf-Plank-Str. 23, 76275, Ettlingen, Germany
| | - Rainer Kümmerle
- Bruker BioSpin AG, Industriestr. 26, 8117, Fällanden, Switzerland
| | - Daniel Mathieu
- Bruker BioSpin GmbH, Rudolf-Plank-Str. 23, 76275, Ettlingen, Germany
| | - Burkhard Luy
- Institute of Organic Chemistry and Institute for Biological Interfaces 4 - Magnetic Resonance, Karlsruhe Institute of Technology (KIT), Fritz-Haber-Weg 6, 76131, Karlsruhe, Germany.
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6
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Quantum Optimal Control: Practical Aspects and Diverse Methods. J Indian Inst Sci 2022. [DOI: 10.1007/s41745-022-00311-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
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7
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Quantum-enhanced radiometry via approximate quantum error correction. Nat Commun 2022; 13:3214. [PMID: 35680786 PMCID: PMC9184621 DOI: 10.1038/s41467-022-30410-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2021] [Accepted: 04/29/2022] [Indexed: 11/08/2022] Open
Abstract
Quantum sensing based on exotic quantum states is appealing for practical metrology applications and fundamental studies. However, these quantum states are vulnerable to noise and the resulting quantum enhancement is weakened in practice. Here, we experimentally demonstrate a quantum-enhanced sensing scheme with a bosonic probe, by exploring the large Hilbert space of the bosonic mode and developing both the approximate quantum error correction and the quantum jump tracking approaches. In a practical radiometry scenario, we attain a 5.3 dB enhancement of sensitivity, which reaches 9.1 × 10−4 Hz−1/2 when measuring the excitation population of a receiver mode. Our results demonstrate the potential of quantum sensing with near-term quantum technologies, not only shedding new light on the quantum advantage of sensing, but also stimulating further efforts on bosonic quantum technologies. Exotic quantum states can be advantageous for sensing, but are very fragile, so that some form of quantum error correction is needed. Here, the authors show how approximate QEC helps overcoming decoherence due to noise when measuring the excitation population of a receiver mode in a superconducting circuit.
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Haller J, Goodwin D, Luy B. SORDOR pulses: expansion of the Böhlen-Bodenhausen scheme for low-power broadband magnetic resonance. MAGNETIC RESONANCE (GOTTINGEN, GERMANY) 2022; 3:53-63. [PMID: 37905174 PMCID: PMC10539771 DOI: 10.5194/mr-3-53-2022] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/12/2022] [Accepted: 03/28/2022] [Indexed: 11/02/2023]
Abstract
A novel type of efficient broadband pulse, called second-order phase dispersion by optimised rotation (SORDOR), has recently been introduced. In contrast to adiabatic excitation, SORDOR-90 pulses provide effective transverse 90∘ rotations throughout their bandwidth, with a quadratic offset dependence of the phase in the x , y plane. Together with phase-matched SORDOR-180 pulses, this enables the Böhlen-Bodenhausen broadband refocusing approach for linearly frequency-swept pulses to be extended to any type of 90∘ /180∘ pulse-delay sequence. Example pulse shapes are characterised in theory and experiment, and an example application is given with a 19 F -PROJECT experiment for measuring relaxation times with reduced distortions due to J -coupling evolution.
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Affiliation(s)
- Jens D. Haller
- Institute for Biological Interfaces 4 – Magnetic Resonance, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
| | - David L. Goodwin
- Institute for Biological Interfaces 4 – Magnetic Resonance, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
| | - Burkhard Luy
- Institute for Biological Interfaces 4 – Magnetic Resonance, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
- Institute of Organic Chemistry, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
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9
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Dalgaard M, Weidner CA, Motzoi F. Dynamical Uncertainty Propagation with Noisy Quantum Parameters. PHYSICAL REVIEW LETTERS 2022; 128:150503. [PMID: 35499880 DOI: 10.1103/physrevlett.128.150503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/2021] [Accepted: 03/25/2022] [Indexed: 06/14/2023]
Abstract
Many quantum technologies rely on high-precision dynamics, which raises the question of how these are influenced by the experimental uncertainties that are always present in real-life settings. A standard approach in the literature to assess this is Monte Carlo sampling, which suffers from two major drawbacks. First, it is computationally expensive. Second, it does not reveal the effect that each individual uncertainty parameter has on the state of the system. In this Letter, we evade both these drawbacks by incorporating propagation of uncertainty directly into simulations of quantum dynamics, thereby obtaining a method that is orders of magnitude faster than Monte Carlo simulations and directly provides information on how each uncertainty parameter influences the system dynamics. Additionally, we compare our method to experimental results obtained using the IBM quantum computers.
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Affiliation(s)
- Mogens Dalgaard
- Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, 8000 Aarhus C, Denmark
| | - Carrie A Weidner
- Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, 8000 Aarhus C, Denmark
| | - Felix Motzoi
- Forschungszentrum Jülich, Institute of Quantum Control (PGI-8), D-52425 Jülich, Germany
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10
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Ehni S, Koos MRM, Reinsperger T, Haller JD, Goodwin DL, Luy B. Concurrent J-evolving refocusing pulses. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2022; 336:107152. [PMID: 35189510 DOI: 10.1016/j.jmr.2022.107152] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/23/2021] [Revised: 01/06/2022] [Accepted: 01/25/2022] [Indexed: 06/14/2023]
Abstract
Conventional refocusing pulses are optimised for a single spin without considering any type of coupling. However, despite the fact that most couplings will result in undesired distortions, refocusing in delay-pulse-delay-type sequences with desired heteronuclear coherence transfer might be enhanced considerably by including coupling evolution into pulse design. We provide a proof of principle study for a Hydrogen-Carbon refocusing pulse sandwich with inherent J-evolution following the previously reported ICEBERG-principle with improved performance in terms of refocusing performance and/or overall effective coherence transfer time. Pulses are optimised using optimal control theory with a newly derived quality factor and z-controls as an efficient tool to speed up calculations. Pulses are characterised in theory and experiment and compared to conventional concurrent refocusing pulses, clearly showing an improvement for the J-evolving pulse sandwich. As a side-product, also efficient J-compensated resfocusing pulse sandwiches - termed BUBU pulses following the nomenclature of previous J-compensated BUBI and BEBEtr pulse sandwiches - have been optimised.
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Affiliation(s)
- Sebastian Ehni
- Institute for Biological Interfaces 4 - Magnetic Resonance, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany; Institute of Organic Chemistry, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany; Bruker Biospin GmbH, Fällanden 8117, Switzerland
| | - Martin R M Koos
- Institute for Biological Interfaces 4 - Magnetic Resonance, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany; Pfizer Inc., Groton, CT 06340, USA; Department of Chemistry, Carnegie Mellon University, Pittsburgh, USA
| | - Tony Reinsperger
- Institute for Biological Interfaces 4 - Magnetic Resonance, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany; Institute of Organic Chemistry, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany; Bruker Biospin GmbH, Ettlingen 76275, Germany
| | - Jens D Haller
- Institute for Biological Interfaces 4 - Magnetic Resonance, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany; Institute of Organic Chemistry, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
| | - David L Goodwin
- Institute for Biological Interfaces 4 - Magnetic Resonance, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany; Chemistry Research Laboratory, University of Oxford, Mansfield Road, Oxford OX1 3TA, UK.
| | - Burkhard Luy
- Institute for Biological Interfaces 4 - Magnetic Resonance, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany; Institute of Organic Chemistry, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany.
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11
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Vinding MS, Goodwin DL, Kuprov I, Lund TE. Optimal control gradient precision trade-offs: Application to fast generation of DeepControl libraries for MRI. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2021; 333:107094. [PMID: 34794089 DOI: 10.1016/j.jmr.2021.107094] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2021] [Revised: 09/21/2021] [Accepted: 10/19/2021] [Indexed: 06/13/2023]
Abstract
We have recently demonstrated supervised deep learning methods for rapid generation of radiofrequency pulses in magnetic resonance imaging (https://doi.org/10.1002/mrm.27740, https://doi.org/10.1002/mrm.28667). Unlike the previous iterative optimization approaches, deep learning methods generate a pulse using a fixed number of floating-point operations - this is important in MRI, where patient-specific pulses preferably must be produced in real time. However, deep learning requires vast training libraries, which must be generated using the traditional methods, e.g., iterative quantum optimal control methods. Those methods are usually variations of gradient descent, and the calculation of the gradient of the performance metric with respect to the pulse waveform can be the most numerically intensive step. In this communication, we explore various ways in which the calculation of gradients in quantum optimal control theory may be accelerated. Four optimization avenues are explored: truncated commutator series expansions at zeroth and first order, a novel midpoint truncation scheme at first order, and the exact complex-step method. For the spin systems relevant to MRI, the first-order midpoint truncation is found to be sufficiently accurate, but also significantly faster than the machine precision gradient. This makes the generation of training databases for the machine learning methods considerably more realistic.
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Affiliation(s)
- Mads Sloth Vinding
- Center of Functionally Integrative Neuroscience (CFIN), Department of Clinical Medicine, Faculty of Health, Aarhus University, Denmark.
| | - David L Goodwin
- Institute for Biological Interfaces 4 - Magnetic Resonance, Karlsruhe Institute for Technology (KIT), Karlsruhe, Germany; Chemistry Research Laboratory, University of Oxford, Mansfield Road, Oxford, UK.
| | - Ilya Kuprov
- School of Chemistry, University of Southampton, Southampton SO17 1BJ, UK
| | - Torben Ellegaard Lund
- Center of Functionally Integrative Neuroscience (CFIN), Department of Clinical Medicine, Faculty of Health, Aarhus University, Denmark
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12
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Tošner Z, Brandl MJ, Blahut J, Glaser SJ, Reif B. Maximizing efficiency of dipolar recoupling in solid-state NMR using optimal control sequences. SCIENCE ADVANCES 2021; 7:eabj5913. [PMID: 34644121 PMCID: PMC8514097 DOI: 10.1126/sciadv.abj5913] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/22/2021] [Accepted: 08/25/2021] [Indexed: 06/13/2023]
Abstract
Dipolar recoupling is a central concept in the nuclear magnetic resonance spectroscopy of powdered solids and is used to establish correlations between different nuclei by magnetization transfer. The efficiency of conventional cross-polarization methods is low because of the inherent radio frequency (rf) field inhomogeneity present in the magic angle spinning (MAS) experiments and the large chemical shift anisotropies at high magnetic fields. Very high transfer efficiencies can be obtained using optimal control–derived experiments. These sequences had to be optimized individually for a particular MAS frequency. We show that by adjusting the length and the rf field amplitude of the shaped pulse synchronously with sample rotation, optimal control sequences can be successfully applied over a range of MAS frequencies without the need of reoptimization. This feature greatly enhances their applicability on spectrometers operating at differing external fields where the MAS frequency needs to be adjusted to avoid detrimental resonance effects.
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Affiliation(s)
- Zdeněk Tošner
- Department of Chemistry, Faculty of Science, Charles University, Albertov 6, 12842 Prague, Czech Republic
| | - Matthias J. Brandl
- Bayerisches NMR Zentrum (BNMRZ) at Department Chemie, Technische Universität München (TUM), 85747 Garching, Germany
| | - Jan Blahut
- Department of Chemistry, Faculty of Science, Charles University, Albertov 6, 12842 Prague, Czech Republic
| | - Steffen J. Glaser
- Bayerisches NMR Zentrum (BNMRZ) at Department Chemie, Technische Universität München (TUM), 85747 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 München, Germany
| | - Bernd Reif
- Bayerisches NMR Zentrum (BNMRZ) at Department Chemie, Technische Universität München (TUM), 85747 Garching, Germany
- Helmholtz Zentrum München (HMGU), Deutsches Forschungszentrum für Gesundheit und Umwelt, 85764 Neuherberg, Germany
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13
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Ma WL, Puri S, Schoelkopf RJ, Devoret MH, Girvin SM, Jiang L. Quantum control of bosonic modes with superconducting circuits. Sci Bull (Beijing) 2021; 66:1789-1805. [PMID: 36654386 DOI: 10.1016/j.scib.2021.05.024] [Citation(s) in RCA: 21] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2021] [Revised: 05/20/2021] [Accepted: 05/24/2021] [Indexed: 01/20/2023]
Abstract
Bosonic modes have wide applications in various quantum technologies, such as optical photons for quantum communication, magnons in spin ensembles for quantum information storage and mechanical modes for reversible microwave-to-optical quantum transduction. There is emerging interest in utilizing bosonic modes for quantum information processing, with circuit quantum electrodynamics (circuit QED) as one of the leading architectures. Quantum information can be encoded into subspaces of a bosonic superconducting cavity mode with long coherence time. However, standard Gaussian operations (e.g., beam splitting and two-mode squeezing) are insufficient for universal quantum computing. The major challenge is to introduce additional nonlinear control beyond Gaussian operations without adding significant bosonic loss or decoherence. Here we review recent advances in universal control of a single bosonic code with superconducting circuits, including unitary control, quantum feedback control, driven-dissipative control and holonomic dissipative control. Various approaches to entangling different bosonic modes are also discussed.
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Affiliation(s)
- Wen-Long Ma
- State Key Laboratory for Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China; Pritzker School of Molecular Engineering, University of Chicago, Illinois 60637, USA
| | - Shruti Puri
- Department of Applied Physics and Physics, Yale University, New Haven, Connecticut 06511, USA; Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, USA
| | - Robert J Schoelkopf
- Department of Applied Physics and Physics, Yale University, New Haven, Connecticut 06511, USA; Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, USA
| | - Michel H Devoret
- Department of Applied Physics and Physics, Yale University, New Haven, Connecticut 06511, USA; Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, USA
| | - S M Girvin
- Department of Applied Physics and Physics, Yale University, New Haven, Connecticut 06511, USA; Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, USA
| | - Liang Jiang
- Pritzker School of Molecular Engineering, University of Chicago, Illinois 60637, USA.
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14
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Zhang H, Kuang Z, Puri S, Miller OD. Conservation-Law-Based Global Bounds to Quantum Optimal Control. PHYSICAL REVIEW LETTERS 2021; 127:110506. [PMID: 34558952 DOI: 10.1103/physrevlett.127.110506] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2021] [Revised: 08/07/2021] [Accepted: 08/09/2021] [Indexed: 06/13/2023]
Abstract
Active control of quantum systems enables diverse applications ranging from quantum computation to manipulation of molecular processes. Maximum speeds and related bounds have been identified from uncertainty principles and related inequalities, but such bounds utilize only coarse system information and loosen significantly in the presence of constraints and complex interaction dynamics. We show that an integral-equation-based formulation of conservation laws in quantum dynamics leads to a systematic framework for identifying fundamental limits to any quantum control scenario. We demonstrate the utility of our bounds in three scenarios-three-level driving, decoherence suppression, and maximum-fidelity gate implementations-and show that in each case our bounds are tight or nearly so. Global bounds complement local-optimization-based designs, illuminating performance levels that may be possible, as well as those that cannot be surpassed.
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Affiliation(s)
- Hanwen Zhang
- Department of Applied Physics, Yale University, New Haven, Connecticut 06511, USA
- Energy Sciences Institute, Yale University, New Haven, Connecticut 06511, USA
| | - Zeyu Kuang
- Department of Applied Physics, Yale University, New Haven, Connecticut 06511, USA
- Energy Sciences Institute, Yale University, New Haven, Connecticut 06511, USA
| | - Shruti Puri
- Department of Applied Physics, Yale University, New Haven, Connecticut 06511, USA
- Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, USA
| | - Owen D Miller
- Department of Applied Physics, Yale University, New Haven, Connecticut 06511, USA
- Energy Sciences Institute, Yale University, New Haven, Connecticut 06511, USA
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15
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Cai W, Han J, Hu L, Ma Y, Mu X, Wang W, Xu Y, Hua Z, Wang H, Song YP, Zhang JN, Zou CL, Sun L. High-Efficiency Arbitrary Quantum Operation on a High-Dimensional Quantum System. PHYSICAL REVIEW LETTERS 2021; 127:090504. [PMID: 34506165 DOI: 10.1103/physrevlett.127.090504] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/23/2021] [Accepted: 08/02/2021] [Indexed: 06/13/2023]
Abstract
The ability to manipulate quantum systems lies at the heart of the development of quantum technology. The ultimate goal of quantum control is to realize arbitrary quantum operations (AQUOs) for all possible open quantum system dynamics. However, the demanding extra physical resources impose great obstacles. Here, we experimentally demonstrate a universal approach of AQUO on a photonic qudit with the minimum physical resource of a two-level ancilla and a log_{2}d-scale circuit depth for a d-dimensional system. The AQUO is then applied in a quantum trajectory simulation for quantum subspace stabilization and quantum Zeno dynamics, as well as incoherent manipulation and generalized measurements of the qudit. Therefore, the demonstrated AQUO for complete quantum control would play an indispensable role in quantum information science.
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Affiliation(s)
- W Cai
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - J Han
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - L Hu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Y Ma
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - X Mu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - W Wang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Y Xu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Z Hua
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - H Wang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Y P Song
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - J-N Zhang
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
| | - C-L Zou
- Key Laboratory of Quantum Information, CAS, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - L Sun
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
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Han J, Cai W, Hu L, Mu X, Ma Y, Xu Y, Wang W, Wang H, Song YP, Zou CL, Sun L. Experimental Simulation of Open Quantum System Dynamics via Trotterization. PHYSICAL REVIEW LETTERS 2021; 127:020504. [PMID: 34296922 DOI: 10.1103/physrevlett.127.020504] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2020] [Revised: 04/23/2021] [Accepted: 06/14/2021] [Indexed: 06/13/2023]
Abstract
Digital quantum simulators provide a diversified tool for solving the evolution of quantum systems with complicated Hamiltonians and hold great potential for a wide range of applications. Although much attention is paid to the unitary evolution of closed quantum systems, dissipation and noise are vital in understanding the dynamics of practical quantum systems. In this work, we experimentally demonstrate a digital simulation of an open quantum system in a controllable Markovian environment with the assistance of a single ancillary qubit. By Trotterizing the quantum Liouvillians, the continuous evolution of an open quantum system is effectively realized, and its application in error mitigation is demonstrated by adjusting the simulated noise intensities. High-order Trotter for open quantum dynamics is also experimentally investigated and shows higher accuracy. Our results represent a significant step toward hardware-efficient simulation of open quantum systems and error mitigation in quantum algorithms in noisy intermediate-scale quantum systems.
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Affiliation(s)
- J Han
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - W Cai
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - L Hu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - X Mu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Y Ma
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Y Xu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - W Wang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - H Wang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Y P Song
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - C-L Zou
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - L Sun
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
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17
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Coote P, Bermel W, Arthanari H. Optimization of phase dispersion enables broadband excitation without homonuclear coupling artifacts. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2021; 325:106928. [PMID: 33652210 PMCID: PMC8012116 DOI: 10.1016/j.jmr.2021.106928] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/08/2020] [Revised: 01/19/2021] [Accepted: 01/25/2021] [Indexed: 06/12/2023]
Abstract
In NMR spectroscopy, many specialized shaped pulses are available for broadband excitation, beyond the bandwidth of conventional high-powered hard pulses. These shaped pulses typically have long duration. However, long-duration pulses are unsuitable for spectra containing significant homonuclear couplings, such as polyfluorinated compounds in 19F NMR. J-coupling evolution during the excitation pulse leads to spectral artifacts and incorrect peak integrals. Here, we report an approach to optimal control pulse design which significantly reduces the pulse length required to excite large bandwidths of chemical shift frequencies. The target state phase is not chosen beforehand but is instead only constrained to be linearly dependent on offset frequency. The first-order phase of the target state is then treated as a free-variable, to be optimized at the same time as the RF waveform itself. The resulting spectra are easily phased using standard NMR processing software. We observe that the required pulse length is significantly shorter than for currently available in-phase excitation schemes. Spectral artifacts from homonuclear couplings are avoided. We also demonstrate that pure in-phase excitation can be obtained over the same bandwidth by appending two inversion pulses, at the expense of increased overall duration.
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Affiliation(s)
- Paul Coote
- Department of Biological Chemistry and Molecular Pharmacology, Harvard Medical School, Boston, MA, USA; Dana Farber Cancer Institute, Boston, MA, USA
| | - Wolfgang Bermel
- Bruker BioSpin GmbH, Silberstreifen 4, 76287 Rheinstetten, Germany
| | - Haribabu Arthanari
- Department of Biological Chemistry and Molecular Pharmacology, Harvard Medical School, Boston, MA, USA; Dana Farber Cancer Institute, Boston, MA, USA.
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18
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Cai W, Ma Y, Wang W, Zou CL, Sun L. Bosonic quantum error correction codes in superconducting quantum circuits. FUNDAMENTAL RESEARCH 2021. [DOI: 10.1016/j.fmre.2020.12.006] [Citation(s) in RCA: 28] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022] Open
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19
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Wu X, Tomarken SL, Petersson NA, Martinez LA, Rosen YJ, DuBois JL. High-Fidelity Software-Defined Quantum Logic on a Superconducting Qudit. PHYSICAL REVIEW LETTERS 2020; 125:170502. [PMID: 33156670 DOI: 10.1103/physrevlett.125.170502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2020] [Accepted: 09/14/2020] [Indexed: 06/11/2023]
Abstract
We present an efficient approach to achieving arbitrary, high-fidelity control of a multilevel quantum system using optimal control techniques. As an demonstration, we implement a continuous, software-defined microwave pulse to realize a 0↔2 SWAP gate that achieves an average gate fidelity of 99.4%. We describe our procedure for extracting the system Hamiltonian, calibrating the quantum and classical hardware chain, and evaluating the gate fidelity. Our work represents an alternative, fully generalizable route towards achieving universal quantum control by leveraging optimal control techniques.
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Affiliation(s)
- Xian Wu
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - S L Tomarken
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - N Anders Petersson
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - L A Martinez
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Yaniv J Rosen
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Jonathan L DuBois
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
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20
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Van Damme L, Mauconduit F, Chambrion T, Boulant N, Gras V. Universal nonselective excitation and refocusing pulses with improved robustness to off-resonance for Magnetic Resonance Imaging at 7 Tesla with parallel transmission. Magn Reson Med 2020; 85:678-693. [PMID: 32755064 DOI: 10.1002/mrm.28441] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2020] [Revised: 06/25/2020] [Accepted: 07/01/2020] [Indexed: 11/07/2022]
Abstract
PURPOSE In MRI at ultra-high field, the k T -point and spiral nonselective (SPINS) pulse design techniques can be advantageously combined with the parallel transmission (pTX) and universal pulse techniques to create uniform excitation in a calibration-free manner. However, in these approaches, pulse duration is typically increased as compared to standard hard pulses, and excitation quality in regions exhibiting large resonance frequency offsets often suffer. This limitation is inherent to structure of k T -point or SPINS pulse, and likely can be mitigated using parameterization-free pulse design approaches. METHODS The Gradient Ascent Pulse Engineering (GRAPE) algorithm was used to design parameterization-free RF and magnetic field gradient (MFG) waveforms for creating 8 ∘ excitation, up to 105 ∘ scalable refocusing and inversion, nonselectively across the brain. Simulations were performed to provide flip angle normalized root-mean-squares error (FA-NRMSE) estimations for the 8 ∘ and the 180 ∘ k T -point, SPINS, and GRAPE pulses. GRAPE pulses were tested experimentally with anatomical head scans at 7T. RESULTS As compared to k T -points and SPINS, GRAPE provided substantial improvement of excitation, refocusing, and inversion quality at off-resonance while at least preserving the same global FA-NRMSE performance. As compared to k T -points, GRAPE allowed for a substantial reduction of the pulse duration for the 8 ∘ excitation and the 105 ∘ refocusing. CONCLUSIONS Parameterization-free universal nonselective pTX-pulses were successfully computed using GRAPE. Performance gains as compared to k T -points were validated numerically and experimentally for three imaging protocols. In its current implementation, the computational burden of GRAPE limits its use to applications where pulse computations are not subject to time constraints.
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Affiliation(s)
- L Van Damme
- Institut Elie Cartan, Université de Nancy, Nancy, France.,CEA, CNRS, BAOBAB, NeuroSpin, Université Paris-Saclay, Gif-sur-Yvette, France
| | - F Mauconduit
- CEA, CNRS, BAOBAB, NeuroSpin, Université Paris-Saclay, Gif-sur-Yvette, France
| | - T Chambrion
- Institut Elie Cartan, Université de Nancy, Nancy, France.,INRIA Nancy Grand Est, Vandœuvre, France
| | - N Boulant
- CEA, CNRS, BAOBAB, NeuroSpin, Université Paris-Saclay, Gif-sur-Yvette, France
| | - V Gras
- CEA, CNRS, BAOBAB, NeuroSpin, Université Paris-Saclay, Gif-sur-Yvette, France
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21
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Concilio MG. Large-scale magnetic resonance simulations: A tutorial. MAGNETIC RESONANCE IN CHEMISTRY : MRC 2020; 58:691-717. [PMID: 32173898 DOI: 10.1002/mrc.5018] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/24/2019] [Revised: 02/14/2020] [Accepted: 03/09/2020] [Indexed: 06/10/2023]
Abstract
Computational modeling is becoming an essential tool in magnetic resonance to design and optimize experiments, test the performance of theoretical models, and interpret experimental data. Recent theoretical research and software development made possible simulations of large spin systems, for example, proteins with thousands of spins, in reasonable time. In the last few years, the Fokker-Planck formalism also re-emerged due to its ability to handle spatial dynamics. The purpose of this tutorial is to describe advantages and disadvantages of the most common formalisms, the latest developments and strategies to improve the computational efficiency, and to guide users in the setting up of a simulation using the Spinach software.
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22
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Xu Y, Ma Y, Cai W, Mu X, Dai W, Wang W, Hu L, Li X, Han J, Wang H, Song YP, Yang ZB, Zheng SB, Sun L. Demonstration of Controlled-Phase Gates between Two Error-Correctable Photonic Qubits. PHYSICAL REVIEW LETTERS 2020; 124:120501. [PMID: 32281851 DOI: 10.1103/physrevlett.124.120501] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2018] [Revised: 10/09/2019] [Accepted: 02/28/2020] [Indexed: 06/11/2023]
Abstract
To realize fault-tolerant quantum computing, it is necessary to store quantum information in logical qubits with error correction functions, realized by distributing a logical state among multiple physical qubits or by encoding it in the Hilbert space of a high-dimensional system. Quantum gate operations between these error-correctable logical qubits, which are essential for implementation of any practical quantum computational task, have not been experimentally demonstrated yet. Here we demonstrate a geometric method for realizing controlled-phase gates between two logical qubits encoded in photonic fields stored in cavities. The gates are realized by dispersively coupling an ancillary superconducting qubit to these cavities and driving it to make a cyclic evolution depending on the joint photonic state of the cavities, which produces a conditional geometric phase. We first realize phase gates for photonic qubits with the logical basis states encoded in two quasiorthogonal coherent states, which have important implications for continuous-variable-based quantum computation. Then we use this geometric method to implement a controlled-phase gate between two binomially encoded logical qubits, which have an error-correctable function.
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Affiliation(s)
- Y Xu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Y Ma
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - W Cai
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - X Mu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - W Dai
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - W Wang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - L Hu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - X Li
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - J Han
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - H Wang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Y P Song
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Zhen-Biao Yang
- Fujian Key Laboratory of Quantum Information and Quantum Optics, College of Physics and Information Engineering, Fuzhou University, Fuzhou, Fujian 350108, China
| | - Shi-Biao Zheng
- Fujian Key Laboratory of Quantum Information and Quantum Optics, College of Physics and Information Engineering, Fuzhou University, Fuzhou, Fujian 350108, China
| | - L Sun
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
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23
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Sørensen JJ, Nyemann JS, Motzoi F, Sherson J, Vosegaard T. Optimization of pulses with low bandwidth for improved excitation of multiple-quantum coherences in NMR of quadrupolar nuclei. J Chem Phys 2020; 152:054104. [DOI: 10.1063/1.5141384] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jens Jakob Sørensen
- Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, 8000 Aarhus C, Denmark
| | - Jacob Søgaard Nyemann
- Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, 8000 Aarhus C, Denmark
- Interdisciplinary Nanoscience Center and Department of Chemistry, Aarhus University, Gustav Wieds Vej 14, 8000 Aarhus C, Denmark
| | - Felix Motzoi
- Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, 8000 Aarhus C, Denmark
- Forschungszentrum Jülich, Institute of Quantum Control (PGI-8), D-52425 Jülich, Germany
| | - Jacob Sherson
- Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, 8000 Aarhus C, Denmark
| | - Thomas Vosegaard
- Interdisciplinary Nanoscience Center and Department of Chemistry, Aarhus University, Gustav Wieds Vej 14, 8000 Aarhus C, Denmark
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24
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Layden D, Chen M, Cappellaro P. Efficient Quantum Error Correction of Dephasing Induced by a Common Fluctuator. PHYSICAL REVIEW LETTERS 2020; 124:020504. [PMID: 32004019 DOI: 10.1103/physrevlett.124.020504] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2019] [Indexed: 06/10/2023]
Abstract
Quantum error correction is expected to be essential in large-scale quantum technologies. However, the substantial overhead of qubits it requires is thought to greatly limit its utility in smaller, near-term devices. Here we introduce a new family of special-purpose quantum error-correcting codes that offer an exponential reduction in overhead compared to the usual repetition code. They are tailored for a common and important source of decoherence in current experiments, whereby a register of qubits is subject to phase noise through coupling to a common fluctuator, such as a resonator or a spin defect. The smallest instance encodes one logical qubit into two physical qubits, and corrects decoherence to leading-order using a constant number of one- and two-qubit operations. More generally, while the repetition code on n qubits corrects errors to order t^{O(n)}, with t the time between recoveries, our codes correct to order t^{O(2^{n})}. Moreover, they are robust to model imperfections in small- and intermediate-scale devices, where they already provide substantial gains in error suppression. As a result, these hardware-efficient codes open a potential avenue for useful quantum error correction in near-term, pre-fault tolerant devices.
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Affiliation(s)
- David Layden
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Mo Chen
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Paola Cappellaro
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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25
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Lin J, Nan J, Luo Y, Yao XC, Li X. Quantum Adiabatic Doping with Incommensurate Optical Lattices. PHYSICAL REVIEW LETTERS 2019; 123:233603. [PMID: 31868469 DOI: 10.1103/physrevlett.123.233603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2019] [Indexed: 06/10/2023]
Abstract
Quantum simulations of Fermi-Hubbard models have been attracting considerable effort in the optical lattice research, with the ultracold antiferromagnetic atomic phase reached at half filling in recent years. An unresolved issue is to dope the system while maintaining the low thermal entropy. Here we propose to achieve the low temperature phase of the doped Fermi-Hubbard model using incommensurate optical lattices through adiabatic quantum evolution. In this theoretical proposal, we find that one major problem about the adiabatic doping is atomic localization in the incommensurate lattice, potentially causing an exponential slowing down of the adiabatic procedure. We study both one- and two-dimensional incommensurate optical lattices, and find that the localization prevents efficient adiabatic doping in the strong lattice regime for both cases. With density matrix renormalization group calculation, we further show that the slowing down problem in one dimension can be circumvented by considering interaction induced many-body delocalization, which is experimentally feasible using Feshbach resonance techniques. This protocol is expected to be efficient as well in two dimensions where the localization phenomenon is less stable.
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Affiliation(s)
- Jian Lin
- State Key Laboratory of Surface Physics, Institute of Nanoelectronics and Quantum Computing, and Department of Physics, Fudan University, Shanghai 200433, China
| | - Jue Nan
- Shanghai Branch, National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Shanghai 201315, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yuchen Luo
- State Key Laboratory of Surface Physics, Institute of Nanoelectronics and Quantum Computing, and Department of Physics, Fudan University, Shanghai 200433, China
| | - Xing-Can Yao
- Shanghai Branch, National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Shanghai 201315, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xiaopeng Li
- State Key Laboratory of Surface Physics, Institute of Nanoelectronics and Quantum Computing, and Department of Physics, Fudan University, Shanghai 200433, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China
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26
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Altenhof AR, Lindquist AW, Foster LDD, Holmes ST, Schurko RW. On the use of frequency-swept pulses and pulses designed with optimal control theory for the acquisition of ultra-wideline NMR spectra. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2019; 309:106612. [PMID: 31622849 DOI: 10.1016/j.jmr.2019.106612] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2019] [Revised: 09/19/2019] [Accepted: 09/20/2019] [Indexed: 06/10/2023]
Abstract
Frequency-swept (FS) pulses, such as wideband uniform-rate smooth-truncation (WURST) pulses, have found much success for the acquisition of ultra-wideline (UW) solid-state NMR spectra. In this preliminary study, new pulses and pulse sequences are explored in simulation and experimentally for several nuclei exhibiting UWNMR powder patterns under static conditions, including 119Sn (I = 1/2), 195Pt (I = 1/2), 2H (I = 1), and 71Ga (I = 3/2). First, hyperbolic secant (HS) and tanh/tan (THT) pulses are tested and implemented as excitation and refocusing pulses in spin-echo and Carr-Purcell/Meiboom Gill (CPMG)-type sequences, and shown to have comparable performances to analogous WURST pulses. Second, optimal control theory (OCT) is utilized for the design of new Optimal Control Theory Optimized Broadband Excitation and Refocusing (OCTOBER) pulses, using carefully parameterized WURST, THT, and HS pulses as starting points. Some of the new OCTOBER pulses used in spin-echo sequences are capable of efficient broadband excitation and refocusing, in some cases resulting in spectra with increased signal enhancements over those obtained in experiments using conventional FS pulses. Finally, careful consideration of the spin dynamics of several systems, by monitoring of the time evolution of the density matrix via the Liouville-von Neumann equation and analysis of the time-resolved Fourier transforms of the pulses, lends insight into the underlying mechanisms of the FS and OCTOBER pulses. This is crucial for understanding their performance in terms of generating uniformly excited patterns of high signal intensity, and for identifying trends that may offer pathways to generalized parameterization and/or new pulse shapes.
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Affiliation(s)
- Adam R Altenhof
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, FL 32308, United States
| | - Austin W Lindquist
- Department of Chemistry and Biochemistry, University of Windsor, Windsor, ON N9B 3P4, Canada
| | - Lucas D D Foster
- Department of Chemistry and Biochemistry, University of Windsor, Windsor, ON N9B 3P4, Canada
| | - Sean T Holmes
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, FL 32308, United States
| | - Robert W Schurko
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, FL 32308, United States.
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27
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Wang W, Han J, Yadin B, Ma Y, Ma J, Cai W, Xu Y, Hu L, Wang H, Song YP, Gu M, Sun L. Witnessing Quantum Resource Conversion within Deterministic Quantum Computation Using One Pure Superconducting Qubit. PHYSICAL REVIEW LETTERS 2019; 123:220501. [PMID: 31868406 DOI: 10.1103/physrevlett.123.220501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2018] [Revised: 10/22/2019] [Indexed: 06/10/2023]
Abstract
Deterministic quantum computation with one qubit (DQC1) is iconic in highlighting that exponential quantum speedup may be achieved with negligible entanglement. Its discovery catalyzed a heated study of general quantum resources, and various conjectures regarding their role in DQC1's performance advantage. Coherence and discord are prominent candidates, respectively, characterizing nonclassicality within localized and correlated systems. Here we realize DQC1 within a superconducting system, engineered such that the dynamics of coherence and discord can be tracked throughout its execution. We experimentally confirm that DQC1 acts as a resource converter, consuming coherence to generate discord during its operation. Our results highlight superconducting circuits as a promising platform for both realizing DQC1 and related algorithms, and experimentally characterizing resource dynamics within quantum protocols.
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Affiliation(s)
- W Wang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - J Han
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - B Yadin
- Atomic and Laser Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford, OX1 3PU, United Kingdom
| | - Y Ma
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - J Ma
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - W Cai
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Y Xu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - L Hu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - H Wang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Y P Song
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Mile Gu
- School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 639673, Republic of Singapore
- Complexity Institute, Nanyang Technological University, Singapore 639673, Republic of Singapore
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Republic of Singapore
| | - L Sun
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
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28
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Lee PK, Watkins LE, Anderson TI, Buonincontri G, Hargreaves BA. Flexible and efficient optimization of quantitative sequences using automatic differentiation of Bloch simulations. Magn Reson Med 2019; 82:1438-1451. [PMID: 31131500 PMCID: PMC8057531 DOI: 10.1002/mrm.27832] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2018] [Revised: 05/06/2019] [Accepted: 05/08/2019] [Indexed: 12/21/2022]
Abstract
PURPOSE To investigate a computationally efficient method for optimizing the Cramér-Rao Lower Bound (CRLB) of quantitative sequences without using approximations or an analytical expression of the signal. METHODS Automatic differentiation was applied to Bloch simulations and used to optimize several quantitative sequences without the need for approximations or an analytical expression. The results were validated with in vivo measurements and comparisons to prior art. Multi-echo spin echo and DESPO T 1 were used as benchmarks to verify the CRLB implementation. The CRLB of the Magnetic Resonance Fingerprinting (MRF) sequence, which has a complicated analytical formulation, was also optimized using automatic differentiation. RESULTS The sequence parameters obtained for multi-echo spin echo and DESPO T 1 matched results obtained using conventional methods. In vivo, MRF scans demonstrate that the CRLB optimization obtained with automatic differentiation can improve performance in presence of white noise. For MRF, the CRLB optimization converges in 1.1 CPU hours for N TR = 400 and has O ( N TR ) asymptotic runtime scaling for the calculation of the CRLB objective and gradient. CONCLUSIONS Automatic differentiation can be used to optimize the CRLB of quantitative sequences without using approximations or analytical expressions. For MRF, the runtime is computationally efficient and can be used to investigate confounding factors as well as MRF sequences with a greater number of repetitions.
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Affiliation(s)
- Philip K. Lee
- Radiology, Stanford University, Stanford, CA, 94305, USA
- Electrical Engineering, Stanford University, Stanford, CA, 94305, USA
| | - Lauren E. Watkins
- Radiology, Stanford University, Stanford, CA, 94305, USA
- Bioengineering, Stanford University, Stanford, CA, 94305, USA
| | | | - Guido Buonincontri
- IRCCS Fondazione Stella Maris, Pisa, PI, 56128, Italy
- Fondazione Imago7, Pisa, PI, 56128, Italy
| | - Brian A. Hargreaves
- Radiology, Stanford University, Stanford, CA, 94305, USA
- Electrical Engineering, Stanford University, Stanford, CA, 94305, USA
- Bioengineering, Stanford University, Stanford, CA, 94305, USA
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29
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Heisenberg-limited single-mode quantum metrology in a superconducting circuit. Nat Commun 2019; 10:4382. [PMID: 31558721 PMCID: PMC6763470 DOI: 10.1038/s41467-019-12290-7] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2019] [Accepted: 08/27/2019] [Indexed: 11/08/2022] Open
Abstract
Two-mode interferometers lay the foundations for quantum metrology. Instead of exploring quantum entanglement in the two-mode interferometers, a single bosonic mode also promises a measurement precision beyond the shot-noise limit (SNL) by taking advantage of the infinite-dimensional Hilbert space of Fock states. Here, we demonstrate a single-mode phase estimation that approaches the Heisenberg limit (HL) unconditionally. Due to the strong dispersive nonlinearity and long coherence time of a microwave cavity, quantum states of the form [Formula: see text] can be generated, manipulated and detected with high fidelities, leading to an experimental phase estimation precision scaling as ∼N-0.94. A 9.1 dB enhancement of the precision over the SNL at N = 12 is achieved, which is only 1.7 dB away from the HL. Our experimental architecture is hardware efficient and can be combined with quantum error correction techniques to fight against decoherence, and thus promises quantum-enhanced sensing in practical applications.
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Kuprov I. Defeating the Matrix. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2019; 306:75-79. [PMID: 31326209 DOI: 10.1016/j.jmr.2019.07.031] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2019] [Revised: 04/28/2019] [Accepted: 07/08/2019] [Indexed: 05/25/2023]
Abstract
These are personal recollections and musings, written for the 50th Anniversary of the Journal of Magnetic Resonance. They are distilled from twenty years of writing simulation code, and filtered through hindsight and sarcastic intransigence. To me, the biggest recent achievements of the magnetic resonance community in the field of theory and simulation have been the successful war on the exponential scaling, the powerful and general simulation software, and the return to elegant notation. It appears that our future will be defined by computers. Three aspects are pertinent: simulation as the experiment is designed, optimal control as the experiment proceeds, and machine learning at the data processing stage.
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Affiliation(s)
- Ilya Kuprov
- School of Chemistry, University of Southampton, United Kingdom.
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31
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Assländer J, Novikov DS, Lattanzi R, Sodickson DK, Cloos MA. Hybrid-state free precession in nuclear magnetic resonance. COMMUNICATIONS PHYSICS 2019; 2:73. [PMID: 31328174 PMCID: PMC6641569 DOI: 10.1038/s42005-019-0174-0] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2018] [Accepted: 05/30/2019] [Indexed: 05/27/2023]
Abstract
The dynamics of large spin-1/2 ensembles are commonly described by the Bloch equation, which is characterized by the magnetization's non-linear response to the driving magnetic field. Consequently, most magnetic field variations result in non-intuitive spin dynamics, which are sensitive to small calibration errors. Although simplistic field variations result in robust spin dynamics, they do not explore the richness of the system's phase space. Here, we identify adiabaticity conditions that span a large experiment design space with tractable dynamics. All dynamics are trapped in a one-dimensional subspace, namely in the magnetization's absolute value, which is in a transient state, while its direction adiabatically follows the steady state. In this hybrid state, the polar angle is the effective drive of the spin dynamics. As an example, we optimize this drive for robust and efficient quantification of spin relaxation times and utilize it for magnetic resonance imaging of the human brain.
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Affiliation(s)
- Jakob Assländer
- Department of Radiology, Center for Biomedical Imaging, New York University School of Medicine, New York, NY, USA
- Center for Advanced Imaging Innovation and Research, New York University School of Medicine, New York, NY, USA
| | - Dmitry S Novikov
- Department of Radiology, Center for Biomedical Imaging, New York University School of Medicine, New York, NY, USA
- Center for Advanced Imaging Innovation and Research, New York University School of Medicine, New York, NY, USA
| | - Riccardo Lattanzi
- Department of Radiology, Center for Biomedical Imaging, New York University School of Medicine, New York, NY, USA
- Center for Advanced Imaging Innovation and Research, New York University School of Medicine, New York, NY, USA
- The Sackler Institute of Graduate Biomedical Sciences, New York University School of Medicine, New York, NY, USA
| | - Daniel K Sodickson
- Department of Radiology, Center for Biomedical Imaging, New York University School of Medicine, New York, NY, USA
- Center for Advanced Imaging Innovation and Research, New York University School of Medicine, New York, NY, USA
- The Sackler Institute of Graduate Biomedical Sciences, New York University School of Medicine, New York, NY, USA
| | - Martijn A Cloos
- Department of Radiology, Center for Biomedical Imaging, New York University School of Medicine, New York, NY, USA
- Center for Advanced Imaging Innovation and Research, New York University School of Medicine, New York, NY, USA
- The Sackler Institute of Graduate Biomedical Sciences, New York University School of Medicine, New York, NY, USA
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32
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Assländer J, Lattanzi R, Sodickson DK, Cloos MA. Optimized quantification of spin relaxation times in the hybrid state. Magn Reson Med 2019; 82:1385-1397. [PMID: 31189025 DOI: 10.1002/mrm.27819] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2018] [Revised: 04/01/2019] [Accepted: 04/29/2019] [Indexed: 01/08/2023]
Abstract
PURPOSE The optimization and analysis of spin ensemble trajectories in the hybrid state-a state in which the direction of the magnetization adiabatically follows the steady state while the magnitude remains in a transient state. METHODS Numerical optimizations were performed to find spin ensemble trajectories that minimize the Cramér-Rao bound for T 1 -encoding, T 2 -encoding, and their weighted sum, respectively, followed by a comparison between the Cramér-Rao bounds obtained with our optimized spin-trajectories, Look-Locker sequences, and multi-spin-echo methods. Finally, we experimentally tested our optimized spin trajectories with in vivo scans of the human brain. RESULTS After a nonrecurring inversion segment on the southern half of the Bloch sphere, all optimized spin trajectories pursue repetitive loops on the northern hemisphere in which the beginning of the first and the end of the last loop deviate from the others. The numerical results obtained in this work align well with intuitive insights gleaned directly from the governing equation. Our results suggest that hybrid-state sequences outperform traditional methods. Moreover, hybrid-state sequences that balance T 1 - and T 2 -encoding still result in near optimal signal-to-noise efficiency for each relaxation time. Thus, the second parameter can be encoded at virtually no extra cost. CONCLUSIONS We provided new insights into the optimal encoding processes of spin relaxation times in order to guide the design of robust and efficient pulse sequences. We found that joint acquisitions of T 1 and T 2 in the hybrid state are substantially more efficient than sequential encoding techniques.
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Affiliation(s)
- Jakob Assländer
- Center for Biomedical Imaging, Department of Radiology, New York University School of Medicine, New York, New York.,Center for Advanced Imaging Innovation and Research (CAI2R), Department of Radiology, New York University School of Medicine, New York, New York
| | - Riccardo Lattanzi
- Center for Biomedical Imaging, Department of Radiology, New York University School of Medicine, New York, New York.,Center for Advanced Imaging Innovation and Research (CAI2R), Department of Radiology, New York University School of Medicine, New York, New York.,Sackler Institute of Graduate Biomedical Sciences, New York University School of Medicine, New York, New York
| | - Daniel K Sodickson
- Center for Biomedical Imaging, Department of Radiology, New York University School of Medicine, New York, New York.,Center for Advanced Imaging Innovation and Research (CAI2R), Department of Radiology, New York University School of Medicine, New York, New York.,Sackler Institute of Graduate Biomedical Sciences, New York University School of Medicine, New York, New York
| | - Martijn A Cloos
- Center for Biomedical Imaging, Department of Radiology, New York University School of Medicine, New York, New York.,Center for Advanced Imaging Innovation and Research (CAI2R), Department of Radiology, New York University School of Medicine, New York, New York.,Sackler Institute of Graduate Biomedical Sciences, New York University School of Medicine, New York, New York
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Hu L, Wu SH, Cai W, Ma Y, Mu X, Xu Y, Wang H, Song Y, Deng DL, Zou CL, Sun L. Quantum generative adversarial learning in a superconducting quantum circuit. SCIENCE ADVANCES 2019; 5:eaav2761. [PMID: 30746476 PMCID: PMC6357722 DOI: 10.1126/sciadv.aav2761] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/31/2018] [Accepted: 12/11/2018] [Indexed: 05/25/2023]
Abstract
Generative adversarial learning is one of the most exciting recent breakthroughs in machine learning. It has shown splendid performance in a variety of challenging tasks such as image and video generation. More recently, a quantum version of generative adversarial learning has been theoretically proposed and shown to have the potential of exhibiting an exponential advantage over its classical counterpart. Here, we report the first proof-of-principle experimental demonstration of quantum generative adversarial learning in a superconducting quantum circuit. We demonstrate that, after several rounds of adversarial learning, a quantum-state generator can be trained to replicate the statistics of the quantum data output from a quantum channel simulator, with a high fidelity (98.8% on average) so that the discriminator cannot distinguish between the true and the generated data. Our results pave the way for experimentally exploring the intriguing long-sought-after quantum advantages in machine learning tasks with noisy intermediate-scale quantum devices.
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Affiliation(s)
- Ling Hu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Shu-Hao Wu
- Key Laboratory of Quantum Information, CAS, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Weizhou Cai
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Yuwei Ma
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Xianghao Mu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Yuan Xu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Haiyan Wang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Yipu Song
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Dong-Ling Deng
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Chang-Ling Zou
- Key Laboratory of Quantum Information, CAS, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Luyan Sun
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
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34
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Experimental repetitive quantum channel simulation. Sci Bull (Beijing) 2018; 63:1551-1557. [PMID: 36751075 DOI: 10.1016/j.scib.2018.11.010] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2018] [Revised: 11/17/2018] [Accepted: 11/19/2018] [Indexed: 11/22/2022]
Abstract
Universal control of quantum systems is a major goal to be achieved for quantum information processing, which demands thorough understanding of fundamental quantum mechanics and promises applications of quantum technologies. So far, most studies concentrate on ideally isolated quantum systems governed by unitary evolutions, while practical quantum systems are open and described by quantum channels due to their inevitable coupling to environment. Here, we experimentally simulate arbitrary quantum channels for an open quantum system, i.e. a single photonic qubit in a superconducting quantum circuit. The arbitrary channel simulation is achieved with minimum resource of only one ancilla qubit and measurement-based adaptive control. By repetitively implementing the quantum channel simulation, we realize an arbitrary Liouvillian for a continuous evolution of an open quantum system for the first time. Our experiment provides not only a testbed for understanding quantum noise and decoherence, but also a powerful tool for full control of practical open quantum systems.
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Goodwin DL, Myers WK, Timmel CR, Kuprov I. Feedback control optimisation of ESR experiments. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2018; 297:9-16. [PMID: 30326343 DOI: 10.1016/j.jmr.2018.09.009] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2017] [Revised: 09/20/2018] [Accepted: 09/21/2018] [Indexed: 06/08/2023]
Abstract
Numerically optimised microwave pulses are used to increase excitation efficiency and modulation depth in electron spin resonance experiments performed on a spectrometer equipped with an arbitrary waveform generator. The optimisation procedure is sample-specific and reminiscent of the magnet shimming process used in the early days of nuclear magnetic resonance - an objective function (for example, echo integral in a spin echo experiment) is defined and optimised numerically as a function of the pulse waveform vector using noise-resilient gradient-free methods. We found that the resulting shaped microwave pulses achieve higher excitation bandwidth and better echo modulation depth than the pulse shapes used as the initial guess. Although the method is theoretically less sophisticated than simulation based quantum optimal control techniques, it has the advantage of being free of the linear response approximation; rapid electron spin relaxation also means that the optimisation takes only a few seconds. This makes the procedure fast, convenient, and easy to use. An important application of this method is at the final stage of the implementation of theoretically designed pulse shapes: compensation of pulse distortions introduced by the instrument. The performance is illustrated using spin echo and out-of-phase electron spin echo envelope modulation experiments. Interface code between Bruker SpinJet arbitrary waveform generator and Matlab is included in versions 2.2 and later of the Spinach library.
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Affiliation(s)
- David L Goodwin
- School of Chemistry, University of Southampton, Highfield Campus, Southampton SO17 1BJ, UK; Institute for Biological Interfaces 4 - Magnetic Resonance, Karlsruhe Institute of Technology (KIT), Fritz-Haber-Weg 6, 76131 Karlsruhe, Germany
| | - William K Myers
- Department of Chemistry, Centre for Advanced Electron Spin Resonance, University of Oxford, South Parks Road, Oxford OX1 3QR, UK.
| | - Christiane R Timmel
- Department of Chemistry, Centre for Advanced Electron Spin Resonance, University of Oxford, South Parks Road, Oxford OX1 3QR, UK
| | - Ilya Kuprov
- School of Chemistry, University of Southampton, Highfield Campus, Southampton SO17 1BJ, UK.
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36
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Reeth EV, Ratiney H, Tse Ve Koon K, Tesch M, Grenier D, Beuf O, Glaser SJ, Sugny D. A simplified framework to optimize MRI contrast preparation. Magn Reson Med 2018; 81:424-438. [PMID: 30265759 DOI: 10.1002/mrm.27417] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2018] [Revised: 05/28/2018] [Accepted: 06/01/2018] [Indexed: 11/08/2022]
Abstract
PURPOSE This article proposes a rigorous optimal control framework for the design of preparation schemes that optimize MRI contrast based on relaxation time differences. METHODS Compared to previous optimal contrast preparation schemes, a drastic reduction of the optimization parameter number is performed. The preparation scheme is defined as a combination of several block pulses whose flip angles, phase terms and inter-pulse delays are optimized to control the magnetization evolution. RESULTS The proposed approach reduces the computation time of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>B</mml:mi> <mml:mn>0</mml:mn></mml:msub> </mml:math> -robust preparation schemes to around a minute (whereas several hours were required with previous schemes), with negligible performance loss. The chosen parameterization allows to formulate the total preparation duration as a constraint, which improves the overall compromise between contrast performance and preparation time. Simulation, in vitro and in vivo results validate this improvement, illustrate the straightforward applicability of the proposed approach, and point out its flexibility in terms of achievable contrasts. Major improvement is especially achieved for short-T2 enhancement, as shown by the acquisition of a non-trivial contrast on a rat brain, where a short-T2 white matter structure (corpus callosum) is enhanced compared to surrounding gray matter tissues (hippocampus and neocortex). CONCLUSIONS This approach proposes key advances for the design of optimal contrast preparation sequences, that emphasize their ability to generate non-standard contrasts, their potential benefit in a clinical context, and their straightforward applicability on any MR system.
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Affiliation(s)
- Eric Van Reeth
- CNRS, Inserm, CREATIS UMR 5220, U1206, Univ Lyon, INSA-Lyon, Université Claude Bernard Lyon 1, UJM-Saint Etienne, Lyon, France
| | - Hélène Ratiney
- CNRS, Inserm, CREATIS UMR 5220, U1206, Univ Lyon, INSA-Lyon, Université Claude Bernard Lyon 1, UJM-Saint Etienne, Lyon, France
| | - Kevin Tse Ve Koon
- CNRS, Inserm, CREATIS UMR 5220, U1206, Univ Lyon, INSA-Lyon, Université Claude Bernard Lyon 1, UJM-Saint Etienne, Lyon, France
| | - Michael Tesch
- Department of Chemistry, Technical University of Munich, Munich, Germany
| | - Denis Grenier
- CNRS, Inserm, CREATIS UMR 5220, U1206, Univ Lyon, INSA-Lyon, Université Claude Bernard Lyon 1, UJM-Saint Etienne, Lyon, France
| | - Olivier Beuf
- CNRS, Inserm, CREATIS UMR 5220, U1206, Univ Lyon, INSA-Lyon, Université Claude Bernard Lyon 1, UJM-Saint Etienne, Lyon, France
| | - Steffen J Glaser
- Department of Chemistry, Technical University of Munich, Munich, Germany
| | - Dominique Sugny
- ICB, CNRS UMR5209, Université de Bourgogne, France.,Institute for Advanced Study, Technical University of Munich, Garching, Germany
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37
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Van Reeth E, Lefebvre PM, Ratiney H, Lambert SA, Tesch M, Brusseau E, Grenier D, Beuf O, Glaser SJ, Sugny D, Tse-Ve-Koon K. Constant gradient elastography with optimal control RF pulses. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2018; 294:153-161. [PMID: 30053754 DOI: 10.1016/j.jmr.2018.07.013] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/2018] [Revised: 07/16/2018] [Accepted: 07/17/2018] [Indexed: 06/08/2023]
Abstract
This article presents a new motion encoding strategy to perform magnetic resonance elastography (MRE). Instead of using standard motion encoding gradients, a tailored RF pulse is designed to simultaneously perform selective excitation and motion encoding in presence of a constant gradient. The RF pulse is designed with a numerical optimal control algorithm, in order to obtain a magnetization phase distribution that depends on the displacement characteristics inside each voxel. As a consequence, no post-excitation encoding gradients are required. This offers numerous advantages, such as reducing eddy current artifacts, and relaxing the constraint on the gradients maximum switch rate. It also allows to perform MRE with ultra-short TE acquisition schemes, which limits T2 decay and optimizes signal-to-noise ratio. The pulse design strategy is developed and analytically analyzed to clarify the encoding mechanism. Finally, simulations, phantom and ex vivo experiments show that phase-to-noise ratios are improved when compared to standard MRE encoding strategies.
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Affiliation(s)
- Eric Van Reeth
- CREATIS, CNRS UMR5220, INSERM U1206, Université Lyon 1, INSA Lyon, Université Jean Monnet Saint-Etienne, France.
| | - Pauline M Lefebvre
- CREATIS, CNRS UMR5220, INSERM U1206, Université Lyon 1, INSA Lyon, Université Jean Monnet Saint-Etienne, France
| | - Hélène Ratiney
- CREATIS, CNRS UMR5220, INSERM U1206, Université Lyon 1, INSA Lyon, Université Jean Monnet Saint-Etienne, France
| | - Simon A Lambert
- CREATIS, CNRS UMR5220, INSERM U1206, Université Lyon 1, INSA Lyon, Université Jean Monnet Saint-Etienne, France
| | - Michael Tesch
- Department of Chemistry, Technische Universität München, Germany
| | - Elisabeth Brusseau
- CREATIS, CNRS UMR5220, INSERM U1206, Université Lyon 1, INSA Lyon, Université Jean Monnet Saint-Etienne, France
| | - Denis Grenier
- CREATIS, CNRS UMR5220, INSERM U1206, Université Lyon 1, INSA Lyon, Université Jean Monnet Saint-Etienne, France
| | - Olivier Beuf
- CREATIS, CNRS UMR5220, INSERM U1206, Université Lyon 1, INSA Lyon, Université Jean Monnet Saint-Etienne, France
| | - Steffen J Glaser
- Department of Chemistry, Technische Universität München, Germany
| | - Dominique Sugny
- ICB, CNRS UMR6303, Université de Bourgogne, France; Institute for Advanced Study, Technische Universität München, Lichtenbergstrasse 2a, D-85748 Garching, Germany
| | - Kevin Tse-Ve-Koon
- CREATIS, CNRS UMR5220, INSERM U1206, Université Lyon 1, INSA Lyon, Université Jean Monnet Saint-Etienne, France
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38
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Kharkov B, Strouk L, Skinner TE, Jerschow A. Optimal control RF pulses for excitation and suppression of NMR signals in a conductive medium. J Chem Phys 2018; 149:034201. [DOI: 10.1063/1.5031154] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Boris Kharkov
- Department of Chemistry, New York University, 100 Washington Sq. East, New York, New York 10003, USA
- Laboratory of Biomolecular NMR, St. Petersburg State University, St. Petersburg 199034, Russia
| | - Leonard Strouk
- Department of Chemistry, New York University, 100 Washington Sq. East, New York, New York 10003, USA
| | - Thomas E. Skinner
- Department of Physics, Wright State University, Dayton, Ohio 45435, USA
| | - Alexej Jerschow
- Department of Chemistry, New York University, 100 Washington Sq. East, New York, New York 10003, USA
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Majewski K. Rotation relaxation splitting for optimizing parallel RF excitation pulses with T 1- and T 2-relaxations in MRI. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2018; 288:43-57. [PMID: 29414063 DOI: 10.1016/j.jmr.2018.01.005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2017] [Revised: 12/18/2017] [Accepted: 01/09/2018] [Indexed: 06/08/2023]
Abstract
Exact solutions of the Bloch equations with T1- and T2-relaxation terms for piecewise constant magnetic fields are numerically challenging. We therefore investigate an approximation for the achieved magnetization in which rotations and relaxations are split into separate operations. We develop an estimate for its accuracy and explicit first and second order derivatives with respect to the complex excitation radio frequency voltages. In practice, the deviation between an exact solution of the Bloch equations and this rotation relaxation splitting approximation seems negligible. Its computation times are similar to exact solutions without relaxation terms. We apply the developed theory to numerically optimize radio frequency excitation waveforms with T1- and T2-relaxations in several examples.
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Affiliation(s)
- Kurt Majewski
- Siemens AG, CT RDA BAM ORD-DE, 80200 Munich, Germany.
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40
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NMRCloudQ: a quantum cloud experience on a nuclear magnetic resonance quantum computer. Sci Bull (Beijing) 2018; 63:17-23. [PMID: 36658912 DOI: 10.1016/j.scib.2017.12.022] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/05/2017] [Revised: 12/15/2017] [Accepted: 12/18/2017] [Indexed: 01/21/2023]
Abstract
Cloud-based quantum computing is anticipated to be the most useful and reachable form for public users to experience with the power of quantum. As initial attempts, IBM Q has launched influential cloud services on a superconducting quantum processor in 2016, but no other platforms has followed up yet. Here, we report our new cloud quantum computing service - NMRCloudQ (http://nmrcloudq.com/zh-hans/), where nuclear magnetic resonance, one of the pioneer platforms with mature techniques in experimental quantum computing, plays as the role of implementing computing tasks. Our service provides a comprehensive software environment preconfigured with a list of quantum information processing packages, and aims to be freely accessible to either amateurs that look forward to keeping pace with this quantum era or professionals that are interested in carrying out real quantum computing experiments in person. In our current version, four qubits are already usable with in average 99.10% single-qubit gate fidelity and 97.15% two-qubit fidelity via randomized benchmaking tests. Improved control precisions as well as a new seven-qubit processor are also in preparation and will be available later.
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41
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Kallies W, Glaser SJ. Cooperative broadband spin echoes through optimal control. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2018; 286:115-137. [PMID: 29241044 DOI: 10.1016/j.jmr.2017.10.011] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/29/2017] [Revised: 10/25/2017] [Accepted: 10/29/2017] [Indexed: 06/07/2023]
Abstract
The Hahn echo sequence is one of the most common building blocks in magnetic resonance, consisting of an excitation pulse and a refocusing pulse. Conventional approaches to improve the performance of echo experiments focused on the optimization of individual pulses, compensating their own imperfections. Here we present an approach to concurrently design both pulses such that they also compensate each others imperfections. The fact that for such cooperative pulses the individual pulses do not need to be perfect provides additional degrees of freedom, resulting in improved overall Hahn echo performance. Single-scan cooperative pulses are compared to conventional approaches by simulations as well as experiments.
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Affiliation(s)
- Wolfgang Kallies
- Department of Chemistry, Technical University of Munich, Lichtenbergstr. 4, 85748 Garching, Germany
| | - Steffen J Glaser
- Department of Chemistry, Technical University of Munich, Lichtenbergstr. 4, 85748 Garching, Germany.
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42
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Khurana D, Mahesh TS. Bang-bang optimal control of large spin systems: Enhancement of 13C- 13C singlet-order at natural abundance. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2017; 284:8-14. [PMID: 28938135 DOI: 10.1016/j.jmr.2017.09.006] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2017] [Revised: 09/06/2017] [Accepted: 09/13/2017] [Indexed: 06/07/2023]
Abstract
Using a bang-bang optimal control technique, we transfer polarization from a set of abundant high-γ nuclei directly to singlet order of a low-γ spin-pair. This approach is analogous to algorithmic cooling (AC) procedure used in quantum state purification. Specifically, we apply this method for enhancing the singlet order in a natural abundant 13C- 13C spin pair by exploiting nine equivalent protons of an 11-spin system. Compared to the standard method not involving polarization transfer, we find an enhancement of singlet order by about 3.4 times. In addition, since the singlet magnetization is contributed by the faster relaxing protons, the recycle delay is halved. Thus effectively we observe a reduction in the overall experimental time by a factor of 23. We also discuss a possible extension of AC, known as heat-bath algorithmic cooling (HBAC).
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Affiliation(s)
- Deepak Khurana
- Department of Physics and NMR Research center, Indian Institute of Science Education and Research, Pune 411008, India.
| | - T S Mahesh
- Department of Physics and NMR Research center, Indian Institute of Science Education and Research, Pune 411008, India; Center for Energy Sciences, Indian Institute of Science Education and Research, Pune 411008, India.
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43
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Nguyen TT, Glaser SJ. An optimal control approach to design entire relaxation dispersion experiments. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2017; 282:142-153. [PMID: 28822305 DOI: 10.1016/j.jmr.2017.07.010] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2017] [Revised: 07/21/2017] [Accepted: 07/29/2017] [Indexed: 06/07/2023]
Abstract
A general approach is introduced to optimize experiments for the analysis of spin systems in the presence of chemical exchange. Rather than optimizing individual pulse sequence elements, such as refocusing pulses, entire relaxation dispersion sequences are optimized in the form of a single shaped pulse. This is achieved by defining a performance index that is only based on the remaining signal after the relaxation dispersion sequence for a range of exchange, relaxation, offset, and rf inhomogeneity parameters. The approach is demonstrated by optimizing energy-limited broadband relaxation dispersion sequences that closely approach the overall effect of ideal CPMG sequences. As illustrated both theoretically and experimentally, significant improvements are found compared to standard amplitude or energy-limited CPMG sequences.
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Affiliation(s)
- Thoa T Nguyen
- Technical University of Munich, Department of Chemistry, Lichtenbergstr. 4, 85747 Garching, Germany
| | - Steffen J Glaser
- Technical University of Munich, Department of Chemistry, Lichtenbergstr. 4, 85747 Garching, Germany.
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Lefebvre PM, Van Reeth E, Ratiney H, Beuf O, Brusseau E, Lambert SA, Glaser SJ, Sugny D, Grenier D, Tse Ve Koon K. Active control of the spatial MRI phase distribution with optimal control theory. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2017; 281:82-93. [PMID: 28558274 DOI: 10.1016/j.jmr.2017.05.008] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2017] [Revised: 05/11/2017] [Accepted: 05/15/2017] [Indexed: 06/07/2023]
Abstract
This paper investigates the use of Optimal Control (OC) theory to design Radio-Frequency (RF) pulses that actively control the spatial distribution of the MRI magnetization phase. The RF pulses are generated through the application of the Pontryagin Maximum Principle and optimized so that the resulting transverse magnetization reproduces various non-trivial and spatial phase patterns. Two different phase patterns are defined and the resulting optimal pulses are tested both numerically with the ODIN MRI simulator and experimentally with an agar gel phantom on a 4.7T small-animal MR scanner. Phase images obtained in simulations and experiments are both consistent with the defined phase patterns. A practical application of phase control with OC-designed pulses is also presented, with the generation of RF pulses adapted for a Magnetic Resonance Elastography experiment. This study demonstrates the possibility to use OC-designed RF pulses to encode information in the magnetization phase and could have applications in MRI sequences using phase images.
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Affiliation(s)
- Pauline M Lefebvre
- Univ.Lyon, INSA-Lyon, Université Claude Bernard Lyon 1, UJM-Saint Etienne, CNRS, Inserm, CREATIS UMR 5220, U1206, 3 rue Victor Grignard, F-69616 Lyon, France.
| | - Eric Van Reeth
- Univ.Lyon, INSA-Lyon, Université Claude Bernard Lyon 1, UJM-Saint Etienne, CNRS, Inserm, CREATIS UMR 5220, U1206, 3 rue Victor Grignard, F-69616 Lyon, France.
| | - Hélène Ratiney
- Univ.Lyon, INSA-Lyon, Université Claude Bernard Lyon 1, UJM-Saint Etienne, CNRS, Inserm, CREATIS UMR 5220, U1206, 3 rue Victor Grignard, F-69616 Lyon, France.
| | - Olivier Beuf
- Univ.Lyon, INSA-Lyon, Université Claude Bernard Lyon 1, UJM-Saint Etienne, CNRS, Inserm, CREATIS UMR 5220, U1206, 3 rue Victor Grignard, F-69616 Lyon, France.
| | - Elisabeth Brusseau
- Univ.Lyon, INSA-Lyon, Université Claude Bernard Lyon 1, UJM-Saint Etienne, CNRS, Inserm, CREATIS UMR 5220, U1206, 3 rue Victor Grignard, F-69616 Lyon, France.
| | - Simon A Lambert
- Univ.Lyon, INSA-Lyon, Université Claude Bernard Lyon 1, UJM-Saint Etienne, CNRS, Inserm, CREATIS UMR 5220, U1206, 3 rue Victor Grignard, F-69616 Lyon, France.
| | - Steffen J Glaser
- Department of Chemistry, Technische Universität München, Lichtenbergstraße 4, D-85748 Garching, Germany.
| | - Dominique Sugny
- ICB, UMR 6303 CNRS-Université de Bourgogne, 9 avenue Alain Savary, F-21078 Dijon, France; Institute for Advanced Study, Technische Universität München, Lichtenbergstraße 2a, D-85748 Garching, Germany.
| | - Denis Grenier
- Univ.Lyon, INSA-Lyon, Université Claude Bernard Lyon 1, UJM-Saint Etienne, CNRS, Inserm, CREATIS UMR 5220, U1206, 3 rue Victor Grignard, F-69616 Lyon, France.
| | - Kevin Tse Ve Koon
- Univ.Lyon, INSA-Lyon, Université Claude Bernard Lyon 1, UJM-Saint Etienne, CNRS, Inserm, CREATIS UMR 5220, U1206, 3 rue Victor Grignard, F-69616 Lyon, France.
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Implementing a universal gate set on a logical qubit encoded in an oscillator. Nat Commun 2017; 8:94. [PMID: 28733580 PMCID: PMC5522494 DOI: 10.1038/s41467-017-00045-1] [Citation(s) in RCA: 39] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2016] [Accepted: 04/27/2017] [Indexed: 11/09/2022] Open
Abstract
A logical qubit is a two-dimensional subspace of a higher dimensional system, chosen such that it is possible to detect and correct the occurrence of certain errors. Manipulation of the encoded information generally requires arbitrary and precise control over the entire system. Whether based on multiple physical qubits or larger dimensional modes such as oscillators, the individual elements in realistic devices will always have residual interactions, which must be accounted for when designing logical operations. Here we demonstrate a holistic control strategy which exploits accurate knowledge of the Hamiltonian to manipulate a coupled oscillator-transmon system. We use this approach to realize high-fidelity (98.5%, inferred), decoherence-limited operations on a logical qubit encoded in a superconducting cavity resonator using four-component cat states. Our results show the power of applying numerical techniques to control linear oscillators and pave the way for utilizing their large Hilbert space as a resource in quantum information processing.A logical qubit is a two-dimensional subspace of a higher dimensional system, whose manipulation requires precise control over the whole system. Here the authors demonstrate a control strategy which exploits precise knowledge of the Hamiltonian to manipulate a coupled oscillator-transmon system.
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46
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Spindler PE, Schöps P, Kallies W, Glaser SJ, Prisner TF. Perspectives of shaped pulses for EPR spectroscopy. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2017; 280:30-45. [PMID: 28579101 DOI: 10.1016/j.jmr.2017.02.023] [Citation(s) in RCA: 42] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2016] [Revised: 02/27/2017] [Accepted: 02/28/2017] [Indexed: 06/07/2023]
Abstract
This article describes current uses of shaped pulses, generated by an arbitrary waveform generator, in the field of EPR spectroscopy. We show applications of sech/tanh and WURST pulses to dipolar spectroscopy, including new pulse schemes and procedures, and discuss the more general concept of optimum-control-based pulses for applications in EPR spectroscopy. The article also describes a procedure to correct for experimental imperfections, mostly introduced by the microwave resonator, and discusses further potential applications and limitations of such pulses.
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Affiliation(s)
- Philipp E Spindler
- Institute of Physical and Theoretical Chemistry and Center of Biomolecular Magnetic Resonance, Goethe University Frankfurt, Germany
| | - Philipp Schöps
- Institute of Physical and Theoretical Chemistry and Center of Biomolecular Magnetic Resonance, Goethe University Frankfurt, Germany
| | - Wolfgang Kallies
- Department of Chemistry, Technical University of Munich, Germany
| | - Steffen J Glaser
- Department of Chemistry, Technical University of Munich, Germany
| | - Thomas F Prisner
- Institute of Physical and Theoretical Chemistry and Center of Biomolecular Magnetic Resonance, Goethe University Frankfurt, Germany.
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47
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Van Reeth E, Ratiney H, Tesch M, Grenier D, Beuf O, Glaser SJ, Sugny D. Optimal control design of preparation pulses for contrast optimization in MRI. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2017; 279:39-50. [PMID: 28460243 DOI: 10.1016/j.jmr.2017.04.012] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/10/2017] [Revised: 04/19/2017] [Accepted: 04/20/2017] [Indexed: 06/07/2023]
Abstract
This work investigates the use of MRI radio-frequency (RF) pulses designed within the framework of optimal control theory for image contrast optimization. The magnetization evolution is modeled with Bloch equations, which defines a dynamic system that can be controlled via the application of the Pontryagin Maximum Principle (PMP). This framework allows the computation of optimal RF pulses that bring the magnetization to a given state to obtain the desired contrast after acquisition. Creating contrast through the optimal manipulation of Bloch equations is a new way of handling contrast in MRI, which can explore the theoretical limits of the system. Simulation experiments carried out on-resonance quantify the contrast improvement when compared to standard T1 or T2 weighting strategies. The use of optimal pulses is also validated for the first time in both in vitro and in vivo experiments on a small-animal 4.7T MR system. Results demonstrate their robustness to static field inhomogeneities as well as the fact that they can be embedded in standard imaging sequences without affecting standard parameters such as slice selection or echo type. In vivo results on rat and mouse brains illustrate the ability of optimal contrast pulses to create non-trivial contrasts on well-studied structures (white matter versus gray matter).
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Affiliation(s)
- Eric Van Reeth
- CREATIS, CNRS UMR5220, INSERM U1206, Université Lyon 1, INSA Lyon, Université Jean Monnet Saint-Etienne, France.
| | - Hélène Ratiney
- CREATIS, CNRS UMR5220, INSERM U1206, Université Lyon 1, INSA Lyon, Université Jean Monnet Saint-Etienne, France
| | - Michael Tesch
- Department of Chemistry, Technische Universität München, Germany
| | - Denis Grenier
- CREATIS, CNRS UMR5220, INSERM U1206, Université Lyon 1, INSA Lyon, Université Jean Monnet Saint-Etienne, France
| | - Olivier Beuf
- CREATIS, CNRS UMR5220, INSERM U1206, Université Lyon 1, INSA Lyon, Université Jean Monnet Saint-Etienne, France
| | - Steffen J Glaser
- Department of Chemistry, Technische Universität München, Germany
| | - Dominique Sugny
- ICB, CNRS UMR6303, Université de Bourgogne-Franche Comté, France; Institute for Advanced Study, Technische Universität München, Lichtenbergstrasse 2a, D-85748 Garching, Germany
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48
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Li J, Yang X, Peng X, Sun CP. Hybrid Quantum-Classical Approach to Quantum Optimal Control. PHYSICAL REVIEW LETTERS 2017; 118:150503. [PMID: 28452527 DOI: 10.1103/physrevlett.118.150503] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2016] [Indexed: 05/25/2023]
Abstract
A central challenge in quantum computing is to identify more computational problems for which utilization of quantum resources can offer significant speedup. Here, we propose a hybrid quantum-classical scheme to tackle the quantum optimal control problem. We show that the most computationally demanding part of gradient-based algorithms, namely, computing the fitness function and its gradient for a control input, can be accomplished by the process of evolution and measurement on a quantum simulator. By posing queries to and receiving answers from the quantum simulator, classical computing devices update the control parameters until an optimal control solution is found. To demonstrate the quantum-classical scheme in experiment, we use a seven-qubit nuclear magnetic resonance system, on which we have succeeded in optimizing state preparation without involving classical computation of the large Hilbert space evolution.
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Affiliation(s)
- Jun Li
- Beijing Computational Science Research Center, Beijing 100193, China
| | - Xiaodong Yang
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xinhua Peng
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Synergetic Innovation Centre of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Chang-Pu Sun
- Beijing Computational Science Research Center, Beijing 100193, China
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49
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Vinding MS, Guérin B, Vosegaard T, Nielsen NC. Local SAR, global SAR, and power-constrained large-flip-angle pulses with optimal control and virtual observation points. Magn Reson Med 2017; 77:374-384. [PMID: 26715084 PMCID: PMC4929033 DOI: 10.1002/mrm.26086] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2015] [Revised: 11/03/2015] [Accepted: 11/23/2015] [Indexed: 11/11/2022]
Abstract
PURPOSE To present a constrained optimal-control (OC) framework for designing large-flip-angle parallel-transmit (pTx) pulses satisfying hardware peak-power as well as regulatory local and global specific-absorption-rate (SAR) limits. The application is 2D and 3D spatial-selective 90° and 180° pulses. THEORY AND METHODS The OC gradient-ascent-pulse-engineering method with exact gradients and the limited-memory Broyden-Fletcher-Goldfarb-Shanno method is proposed. Local SAR is constrained by the virtual-observation-points method. Two numerical models facilitated the optimizations, a torso at 3 T and a head at 7 T, both in eight-channel pTx coils and acceleration-factors up to 4. RESULTS The proposed approach yielded excellent flip-angle distributions. Enforcing the local-SAR constraint, as opposed to peak power alone, reduced the local SAR 7 and 5-fold with the 2D torso excitation and inversion pulse, respectively. The root-mean-square errors of the magnetization profiles increased less than 5% with the acceleration factor of 4. CONCLUSION A local and global SAR, and peak-power constrained OC large-flip-angle pTx pulse design was presented, and numerically validated for 2D and 3D spatial-selective 90° and 180° pulses at 3 T and 7 T. Magn Reson Med 77:374-384, 2017. © 2015 Wiley Periodicals, Inc.
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Affiliation(s)
- Mads S. Vinding
- Center of Insoluble Protein Structures (inSPIN), Interdisciplinary Nanoscience Center (iNANO) and Department of Chemistry, Aarhus University, Aarhus C, Denmark
| | - Bastien Guérin
- A.A. Martinos Center for Biomedical Imaging, Department of Radiology, Massachusetts General Hospital, Charlestown, Massachusetts, USA
- Harvard Medical School, Boston, Massachusetts, USA
| | - Thomas Vosegaard
- Center of Insoluble Protein Structures (inSPIN), Interdisciplinary Nanoscience Center (iNANO) and Department of Chemistry, Aarhus University, Aarhus C, Denmark
| | - Niels Chr. Nielsen
- Center of Insoluble Protein Structures (inSPIN), Interdisciplinary Nanoscience Center (iNANO) and Department of Chemistry, Aarhus University, Aarhus C, Denmark
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50
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Guduff L, Allami AJ, van Heijenoort C, Dumez JN, Kuprov I. Efficient simulation of ultrafast magnetic resonance experiments. Phys Chem Chem Phys 2017; 19:17577-17586. [DOI: 10.1039/c7cp03074f] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
We present a convenient and powerful simulation formalism for ultrafast NMR spectroscopy. The formalism is based on the Fokker–Planck equation that supports systems with complicated combinations of classical spatial dynamics and quantum mechanical spin dynamics.
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Affiliation(s)
- Ludmilla Guduff
- Institut de Chimie des Substances Naturelles
- CNRS UPR2301
- Université Paris Sud
- Université Paris-Saclay
- 91190 Gif-sur-Yvette
| | | | - Carine van Heijenoort
- Institut de Chimie des Substances Naturelles
- CNRS UPR2301
- Université Paris Sud
- Université Paris-Saclay
- 91190 Gif-sur-Yvette
| | - Jean-Nicolas Dumez
- Institut de Chimie des Substances Naturelles
- CNRS UPR2301
- Université Paris Sud
- Université Paris-Saclay
- 91190 Gif-sur-Yvette
| | - Ilya Kuprov
- School of Chemistry
- University of Southampton
- Southampton
- UK
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