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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Chae E, Choi J, Kim J. An elementary review on basic principles and developments of qubits for quantum computing. NANO CONVERGENCE 2024; 11:11. [PMID: 38498068 PMCID: PMC10948723 DOI: 10.1186/s40580-024-00418-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2023] [Accepted: 03/04/2024] [Indexed: 03/19/2024]
Abstract
An elementary review on principles of qubits and their prospects for quantum computing is provided. Due to its rapid development, quantum computing has attracted considerable attention as a core technology for the next generation and has demonstrated its potential in simulations of exotic materials, molecular structures, and theoretical computer science. To achieve fully error-corrected quantum computers, building a logical qubit from multiple physical qubits is crucial. The number of physical qubits needed depends on their error rates, making error reduction in physical qubits vital. Numerous efforts to reduce errors are ongoing in both existing and emerging quantum systems. Here, the principle and development of qubits, as well as the current status of the field, are reviewed to provide information to researchers from various fields and give insights into this promising technology.
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Affiliation(s)
- Eunmi Chae
- Department of Physics, Korea University, Seoul , 02841, Republic of Korea.
| | - Joonhee Choi
- Department of Electrical Engineering, Stanford University, Stanford, CA, 94305, USA.
| | - Junki Kim
- SKKU Advanced Institute of Nanotechnology (SAINT) & Department of Nano Science and Technology, Sungkyunkwan University, Suwon, 16419, Republic of Korea.
- Department of Nano Engineering, Sungkyunkwan University, Suwon, 16419, Republic of Korea.
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3
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Zhang C, Shen LT, Song J, Xia Y, Shi ZC. Three-state coherent control using narrowband and passband sequences. OPTICS EXPRESS 2024; 32:1188-1206. [PMID: 38297676 DOI: 10.1364/oe.506297] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2023] [Accepted: 11/23/2023] [Indexed: 02/02/2024]
Abstract
In this work, we propose a comprehensive design for narrowband and passband composite pulse sequences by involving the dynamics of all states in the three-state system. The design is quite universal as all pulse parameters can be freely employed to modify the coefficients of error terms. Two modulation techniques, the strength and phase modulations, are used to achieve arbitrary population transfer with a desired excitation profile, while the system keeps minimal leakage to the third state. Furthermore, the current sequences are capable of tolerating inaccurate waveforms, detuning errors, and work well when rotating wave approximation is not strictly justified. Therefore, this work provides versatile adaptability for shaping various excitation profiles in both narrowband and passband sequences.
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4
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Ji L, He Y, Cai Q, Fang Z, Wang Y, Qiu L, Zhou L, Wu S, Grava S, Chang DE. Superradiant Detection of Microscopic Optical Dipolar Interactions. PHYSICAL REVIEW LETTERS 2023; 131:253602. [PMID: 38181370 DOI: 10.1103/physrevlett.131.253602] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2021] [Revised: 08/16/2023] [Accepted: 10/31/2023] [Indexed: 01/07/2024]
Abstract
The interaction between light and cold atoms is a complex phenomenon potentially featuring many-body resonant dipole interactions. A major obstacle toward exploring these quantum resources of the system is macroscopic light propagation effects, which not only limit the available time for the microscopic correlations to locally build up, but also create a directional, superradiant emission background whose variations can overwhelm the microscopic effects. In this Letter, we demonstrate a method to perform "background-free" detection of the microscopic optical dynamics in a laser-cooled atomic ensemble. This is made possible by transiently suppressing the macroscopic optical propagation over a substantial time, before a recall of superradiance that imprints the effect of the accumulated microscopic dynamics onto an efficiently detectable outgoing field. We apply this technique to unveil and precisely characterize a density-dependent, microscopic dipolar dephasing effect that generally limits the lifetime of optical spin-wave order in ensemble-based atom-light interfaces.
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Affiliation(s)
- Lingjing Ji
- Department of Physics, State Key Laboratory of Surface Physics and Key Laboratory of Micro and Nano Photonic Structures (Ministry of Education), Fudan University, Shanghai 200433, China
| | - Yizun He
- Department of Physics, State Key Laboratory of Surface Physics and Key Laboratory of Micro and Nano Photonic Structures (Ministry of Education), Fudan University, Shanghai 200433, China
| | - Qingnan Cai
- Department of Physics, State Key Laboratory of Surface Physics and Key Laboratory of Micro and Nano Photonic Structures (Ministry of Education), Fudan University, Shanghai 200433, China
| | - Zhening Fang
- Department of Physics, State Key Laboratory of Surface Physics and Key Laboratory of Micro and Nano Photonic Structures (Ministry of Education), Fudan University, Shanghai 200433, China
| | - Yuzhuo Wang
- Department of Physics, State Key Laboratory of Surface Physics and Key Laboratory of Micro and Nano Photonic Structures (Ministry of Education), Fudan University, Shanghai 200433, China
| | - Liyang Qiu
- Department of Physics, State Key Laboratory of Surface Physics and Key Laboratory of Micro and Nano Photonic Structures (Ministry of Education), Fudan University, Shanghai 200433, China
| | - Lei Zhou
- Department of Physics, State Key Laboratory of Surface Physics and Key Laboratory of Micro and Nano Photonic Structures (Ministry of Education), Fudan University, Shanghai 200433, China
| | - Saijun Wu
- Department of Physics, State Key Laboratory of Surface Physics and Key Laboratory of Micro and Nano Photonic Structures (Ministry of Education), Fudan University, Shanghai 200433, China
| | - Stefano Grava
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain and ICREA-Institució Catalana de Recerca i Estudis Avançats, 08015 Barcelona, Spain
| | - Darrick E Chang
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain and ICREA-Institució Catalana de Recerca i Estudis Avançats, 08015 Barcelona, Spain
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5
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Little EJ, Mrozek J, Rogers CJ, Liu J, McInnes EJL, Bowen AM, Ardavan A, Winpenny REP. Title: experimental realisation of multi-qubit gates using electron paramagnetic resonance. Nat Commun 2023; 14:7029. [PMID: 37919283 PMCID: PMC10622571 DOI: 10.1038/s41467-023-42169-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2023] [Accepted: 09/28/2023] [Indexed: 11/04/2023] Open
Abstract
Quantum information processing promises to revolutionise computing; quantum algorithms have been discovered that address common tasks significantly more efficiently than their classical counterparts. For a physical system to be a viable quantum computer it must be possible to initialise its quantum state, to realise a set of universal quantum logic gates, including at least one multi-qubit gate, and to make measurements of qubit states. Molecular Electron Spin Qubits (MESQs) have been proposed to fulfil these criteria, as their bottom-up synthesis should facilitate tuning properties as desired and the reproducible production of multi-MESQ structures. Here we explore how to perform a two-qubit entangling gate on a multi-MESQ system, and how to readout the state via quantum state tomography. We propose methods of accomplishing both procedures using multifrequency pulse Electron Paramagnetic Resonance (EPR) and apply them to a model MESQ structure consisting of two nitroxide spin centres. Our results confirm the methodological principles and shed light on the experimental hurdles which must be overcome to realise a demonstration of controlled entanglement on this system.
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Affiliation(s)
- Edmund J Little
- Photon Science Institute and School of Chemistry, The University of Manchester, Oxford Road, M13 9PL, Manchester, UK
| | - Jacob Mrozek
- Clarendon Laboratory, University of Oxford, Parks Road, OX1 3PU, Oxford, UK
| | - Ciarán J Rogers
- Photon Science Institute and School of Chemistry, The University of Manchester, Oxford Road, M13 9PL, Manchester, UK
| | - Junjie Liu
- Clarendon Laboratory, University of Oxford, Parks Road, OX1 3PU, Oxford, UK
| | - Eric J L McInnes
- Photon Science Institute and School of Chemistry, The University of Manchester, Oxford Road, M13 9PL, Manchester, UK
| | - Alice M Bowen
- Photon Science Institute and School of Chemistry, The University of Manchester, Oxford Road, M13 9PL, Manchester, UK.
| | - Arzhang Ardavan
- Clarendon Laboratory, University of Oxford, Parks Road, OX1 3PU, Oxford, UK.
| | - Richard E P Winpenny
- Photon Science Institute and School of Chemistry, The University of Manchester, Oxford Road, M13 9PL, Manchester, UK.
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6
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Extending NMR Quantum Computation Systems by Employing Compounds with Several Heavy Metals as Qubits. MAGNETOCHEMISTRY 2022. [DOI: 10.3390/magnetochemistry8050047] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
Nuclear magnetic resonance (NMR) is a spectroscopic method that can be applied to several areas. Currently, this technique is also being used as an experimental quantum simulator, where nuclear spins are employed as quantum bits or qubits. The present work is devoted to studying heavy metal complexes as possible candidates to act as qubit molecules. Nuclei such 113Cd, 199Hg, 125Te, and 77Se assembled with the most common employed nuclei in NMR-QIP implementations (1H, 13C, 19F, 29Si, and 31P) could potentially be used in heteronuclear systems for NMR-QIP implementations. Hence, aiming to contribute to the development of future scalable heteronuclear spin systems, we specially designed four complexes, based on the auspicious qubit systems proposed in our previous work, which will be explored by quantum chemical calculations of their NMR parameters and proposed as suitable qubit molecules. Chemical shifts and spin–spin coupling constants in four complexes were examined using the spin–orbit zeroth-order regular approximation (ZORA) at the density functional theory (DFT) level, as well as the relaxation parameters (T1 and T2). Examining the required spectral properties of NMR-QIP, all the designed complexes were found to be promising candidates for qubit molecules.
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7
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von Kugelgen S, Krzyaniak MD, Gu M, Puggioni D, Rondinelli JM, Wasielewski MR, Freedman DE. Spectral Addressability in a Modular Two Qubit System. J Am Chem Soc 2021; 143:8069-8077. [PMID: 34014650 DOI: 10.1021/jacs.1c02417] [Citation(s) in RCA: 24] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Abstract
The combination of structural precision and reproducibility of synthetic chemistry is perfectly suited for the creation of chemical qubits, the core units of a quantum information science (QIS) system. By exploiting the atomistic control inherent to synthetic chemistry, we address a fundamental question of how the spin-spin distance between two qubits impacts electronic spin coherence. To achieve this goal, we designed a series of molecules featuring two spectrally distinct qubits, an early transition metal, Ti3+, and a late transition metal, Cu2+ with increasing separation between the two metals. Crucially, we also synthesized the monometallic congeners to serve as controls. The spectral separation between the two metals enables us to probe each metal individually in the bimetallic species and compare it with the monometallic control samples. Across a range of 1.2-2.5 nm, we find that electron spins have a negligible effect on coherence times, a finding we attribute to the distinct resonance frequencies. Coherence times are governed, instead, by the distance to nuclear spins on the other qubit's ligand framework. This finding offers guidance for the design of spectrally addressable molecular qubits.
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Affiliation(s)
- Stephen von Kugelgen
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States
| | - Matthew D Krzyaniak
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States.,The Institute for Sustainability and Energy at Northwestern, Northwestern University, Evanston, Illinois 60208, United States
| | - Mingqiang Gu
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States
| | - Danilo Puggioni
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States
| | - James M Rondinelli
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States
| | - Michael R Wasielewski
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States.,The Institute for Sustainability and Energy at Northwestern, Northwestern University, Evanston, Illinois 60208, United States
| | - Danna E Freedman
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States.,Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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8
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Buch CD, Hansen SH, Mitcov D, Tram CM, Nichol GS, Brechin EK, Piligkos S. Design of pure heterodinuclear lanthanoid cryptate complexes. Chem Sci 2021; 12:6983-6991. [PMID: 34123326 PMCID: PMC8153240 DOI: 10.1039/d1sc00987g] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2021] [Accepted: 04/14/2021] [Indexed: 01/01/2023] Open
Abstract
Heterolanthanide complexes are difficult to synthesize owing to the similar chemistry of the lanthanide ions. Consequently, very few purely heterolanthanide complexes have been synthesized. This is despite the fact that such complexes hold interesting optical and magnetic properties. To fine-tune these properties, it is important that one can choose complexes with any given combination of lanthanides. Herein we report a synthetic procedure which yields pure heterodinuclear lanthanide cryptates LnLn*LX3 (X = NO3 - or OTf-) based on the cryptand H3L = N[(CH2)2N[double bond, length as m-dash]CH-R-CH[double bond, length as m-dash]N-(CH2)2]3N (R = m-C6H2OH-2-Me-5). In the synthesis the choice of counter ion and solvent proves crucial in controlling the Ln-Ln* composition. Choosing the optimal solvent and counter ion afford pure heterodinuclear complexes with any given combination of Gd(iii)-Lu(iii) including Y(iii). To demonstrate the versatility of the synthesis all dinuclear combinations of Y(iii), Gd(iii), Yb(iii) and Lu(iii) were synthesized resulting in 10 novel complexes of the form LnLn*L(OTf)3 with LnLn* = YbGd 1, YbY 2, YbLu 3, YbYb 4, LuGd 5, LuY 6, LuLu 7, YGd 8, YY 9 and GdGd 10. Through the use of 1H, 13C NMR and mass spectrometry the heterodinuclear nature of YbGd, YbY, YbLu, LuGd, LuY and YGd was confirmed. Crystal structures of LnLn*L(NO3)3 reveal short Ln-Ln distances of ∼3.5 Å. Using SQUID magnetometry the exchange coupling between the lanthanide ions was found to be anti-ferromagnetic for GdGd and YbYb while ferromagnetic for YbGd.
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Affiliation(s)
- Christian D Buch
- Department of Chemistry, University of Copenhagen Universitetsparken 5 DK-2100 Copenhagen Denmark
| | - Steen H Hansen
- Department of Chemistry, University of Copenhagen Universitetsparken 5 DK-2100 Copenhagen Denmark
| | - Dmitri Mitcov
- Department of Chemistry, University of Copenhagen Universitetsparken 5 DK-2100 Copenhagen Denmark
| | - Camilla M Tram
- Department of Chemistry, University of Copenhagen Universitetsparken 5 DK-2100 Copenhagen Denmark
| | - Gary S Nichol
- EaStCHEM School of Chemistry, University of Edinburgh Edinburgh UK
| | - Euan K Brechin
- EaStCHEM School of Chemistry, University of Edinburgh Edinburgh UK
| | - Stergios Piligkos
- Department of Chemistry, University of Copenhagen Universitetsparken 5 DK-2100 Copenhagen Denmark
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9
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Appelt S, Lehmkuhl S, Fleischer S, Joalland B, Ariyasingha NM, Chekmenev EY, Theis T. SABRE and PHIP pumped RASER and the route to chaos. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2021; 322:106815. [PMID: 33423756 PMCID: PMC8026265 DOI: 10.1016/j.jmr.2020.106815] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2020] [Revised: 08/21/2020] [Accepted: 08/24/2020] [Indexed: 05/27/2023]
Abstract
In a RASER (Radio-frequency Amplification by Stimulated Emission of Radiation), the fast relaxing electromagnetic modes of an LC resonator are enslaved by the slow nuclear spin motion, whose coherence decays with the transverse relaxation rate γm=1/T2∗. Such a system obeys the slaving principle, mathematically identical with the adiabatic elimination procedure, leading to multi-mode RASER equations. If the pumping rate of nuclear spin polarization Γ>>γm, a second adiabatic elimination process applies and the spectral properties of the RASER can be predicted. The resulting model is similar to the model of two non-linear coupled oscillators and predicts the observed RASER phenomena, including frequency combs and mode collapse. If the second adiabatic elimination is not applicable, mode collapse is completely absent and successive period doubling processes and chaos occur at very high population inversions. We compare these theoretical predictions with experimental results from a PHIP (Para-Hydrogen Induced Polarization) pumped 1H RASER. Moreover, in SABRE (Signal Amplification By Reversible Exchange) pumped 1H experiments, RASER revivals are observed long after the parahydrogen pumping source has been switched off. All these findings shed light onto the links between NMR spectroscopy, RASER physics, synergetics and chaos theory. Several new applications are envisioned in the fields of quantum sensor technology, structure investigation or magnetic resonance imaging (MRI).
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Affiliation(s)
- Stephan Appelt
- Central Institute for Engineering, Electronics and Analytics - Electronic Systems (ZEA-2), Forschungszentrum Jülich GmbH, D-52425 Jülich, Germany; Institut für Technische und Makromolekulare Chemie, RWTH Aachen University, D-52056 Aachen, Germany.
| | - Sören Lehmkuhl
- Department of Chemistry, North Carolina State University Raleigh, NC 27695-8204, USA.
| | - Simon Fleischer
- Institut für Technische und Makromolekulare Chemie, RWTH Aachen University, D-52056 Aachen, Germany
| | - Baptiste Joalland
- Department of Chemistry, Integrative Biosciences (Ibio), Karmanos Cancer Institute (KCI), Wayne State University Detroit, MI 48202, USA
| | - Nuwandi M Ariyasingha
- Department of Chemistry, Integrative Biosciences (Ibio), Karmanos Cancer Institute (KCI), Wayne State University Detroit, MI 48202, USA
| | - Eduard Y Chekmenev
- Department of Chemistry, Integrative Biosciences (Ibio), Karmanos Cancer Institute (KCI), Wayne State University Detroit, MI 48202, USA; Russian Academy of Sciences, Leninskiy Prospekt 14, Moscow 119991, Russia
| | - Thomas Theis
- Department of Chemistry, North Carolina State University Raleigh, NC 27695-8204, USA; Department of Physics, North Carolina State University Raleigh, NC 27695, USA; Joint Department of Biomedical Engineering, University of North Carolina at Chapel Hill & North Carolina State University, Raleigh, NC 27695, USA
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10
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Chekhovich EA, da Silva SFC, Rastelli A. Nuclear spin quantum register in an optically active semiconductor quantum dot. NATURE NANOTECHNOLOGY 2020; 15:999-1004. [PMID: 32989238 DOI: 10.1038/s41565-020-0769-3] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2020] [Accepted: 08/26/2020] [Indexed: 05/25/2023]
Abstract
Epitaxial quantum dots (QDs) have long been identified as promising charge spin qubits offering an efficient interface to quantum light and advanced semiconductor nanofabrication technologies. However, charge spin coherence is limited by interaction with the nanoscale ensemble of atomic nuclear spins, which is particularly problematic in strained self-assembled dots. Here, we use strain-free GaAs/AlGaAs QDs, demonstrating a fully functioning two-qubit quantum register using the nanoscale ensemble of arsenic quadrupolar nuclear spins as its hardware. Tailored radio-frequency pulses allow quantum state storage for up to 20 ms, and are used for few-microsecond single-qubit and two-qubit control gates with fidelities exceeding 97%. Combining long coherence and high-fidelity control with optical initialization and readout, we implement benchmark quantum computations such as Grover's search and the Deutsch-Jozsa algorithm. Our results identify QD nuclei as a potential quantum information resource, which can complement charge spins and light particles in future QD circuits.
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Affiliation(s)
- Evgeny A Chekhovich
- Department of Physics and Astronomy, University of Sheffield, Sheffield, UK.
| | - Saimon F Covre da Silva
- Institute of Semiconductor and Solid State Physics, Johannes Kepler University Linz, Linz, Austria
| | - Armando Rastelli
- Institute of Semiconductor and Solid State Physics, Johannes Kepler University Linz, Linz, Austria
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11
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Lino JBDR, Sauer SPA, Ramalho TC. Enhancing NMR Quantum Computation by Exploring Heavy Metal Complexes as Multiqubit Systems: A Theoretical Investigation. J Phys Chem A 2020; 124:4946-4955. [PMID: 32463687 DOI: 10.1021/acs.jpca.0c01607] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Assembled together with the most common qubits used in nuclear resonance magnetic (NMR) quantum computation experiments, spin-1/2 nuclei, such as 113Cd, 199Hg, 125Te, and 77Se, could leverage the prospective scalable quantum computer architectures, enabling many and heteronuclear qubits for NMR quantum information processing (QIP) implementations. A computational design strategy for prescreening recently synthesized complexes of cadmium, mercury, tellurium, selenium, and phosphorus (called MRE complexes) as suitable qubit molecules for NMR QIP is reported. Chemical shifts and spin-spin coupling constants (SSCCs) in five MRE complexes were examined using the spin-orbit zeroth order regular approximation (ZORA) at the density functional theory level and the four-component relativistic Dirac-Kohn-Sham approach. In particular, the influence of different conformers, basis sets, exchange-correlation functionals, and methods to treat the relativistic as well as solvent effects were studied. The differences in the chemical shifts and SSCCs between different low energy conformers of the studied complexes were found to be very small. The TZ2P basis set was found to be the optimum choice for the studied chemical shifts, while the TZ2P-J basis set was the best for the couplings studied in this work. The PBE0 exchange-correlation functional exhibited the best performance for the studied MRE complexes. The addition of solvent effects has not improved on the gas phase results in comparison to the experiment, with the exception of the phosphorus chemical shift. The use of MRE complexes as qubit molecules for NMR QIP could face the challenges in single qubit control and multiqubit operations. They exhibit chemical shifts appropriately dispersed, allowing qubit addressability and exceptionally large spin-spin couplings, which could reduce the time of quantum gate operations and likely preserve the coherence.
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Affiliation(s)
| | - Stephan P A Sauer
- Department of Chemistry, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark
| | - Teodorico Castro Ramalho
- Department of Chemistry, Federal University of Lavras, 37200-000 Lavras, Minas Gerais, Brazil.,Center for Basic and Applied Research, Faculty of Informatics and Management, University Hradec Kralove, 50003 Hradec Kralove, Czech Republic
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12
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Xu Y, Hua Z, Chen T, Pan X, Li X, Han J, Cai W, Ma Y, Wang H, Song YP, Xue ZY, Sun L. Experimental Implementation of Universal Nonadiabatic Geometric Quantum Gates in a Superconducting Circuit. PHYSICAL REVIEW LETTERS 2020; 124:230503. [PMID: 32603172 DOI: 10.1103/physrevlett.124.230503] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/27/2019] [Accepted: 05/18/2020] [Indexed: 06/11/2023]
Abstract
Using geometric phases to realize noise-resilient quantum computing is an important method to enhance the control fidelity. In this work, we experimentally realize a universal nonadiabatic geometric quantum gate set in a superconducting qubit chain. We characterize the realized single- and two-qubit geometric gates with both quantum process tomography and randomized benchmarking methods. The measured average fidelities for the single-qubit rotation gates and two-qubit controlled-Z gate are 0.9977(1) and 0.977(9), respectively. Besides, we also experimentally demonstrate the noise-resilient feature of the realized single-qubit geometric gates by comparing their performance with the conventional dynamical gates with different types of errors in the control field. Thus, our experiment proves a way to achieve high-fidelity geometric quantum gates for robust quantum computation.
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Affiliation(s)
- 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
| | - Tao Chen
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement, and School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
| | - X Pan
- 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
| | - W Cai
- 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
| | - 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
| | - Zheng-Yuan Xue
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement, and School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
| | - L Sun
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
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13
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Rodin BA, Bengs C, Kiryutin AS, Sheberstov KF, Brown LJ, Brown RCD, Yurkovskaya AV, Ivanov KL, Levitt MH. Algorithmic cooling of nuclear spins using long-lived singlet order. J Chem Phys 2020; 152:164201. [PMID: 32357786 DOI: 10.1063/5.0006742] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023] Open
Abstract
Algorithmic cooling methods manipulate an open quantum system in order to lower its temperature below that of the environment. We achieve significant cooling of an ensemble of nuclear spin-pair systems by exploiting the long-lived nuclear singlet state, which is an antisymmetric quantum superposition of the "up" and "down" Zeeman states. The effect is demonstrated by nuclear magnetic resonance experiments on a molecular system containing a coupled pair of near-equivalent 13C nuclei. The populations of the system are subjected to a repeating sequence of cyclic permutations separated by relaxation intervals. The long-lived nuclear singlet order is pumped well beyond the unitary limit. The pumped singlet order is converted into nuclear magnetization which is enhanced by 21% relative to its thermal equilibrium value.
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Affiliation(s)
- Bogdan A Rodin
- International Tomography Center SB RAS, Novosibirsk, Russia
| | - Christian Bengs
- Department of Chemistry, Southampton University, Southampton SO17 1BJ, United Kingdom
| | | | - Kirill F Sheberstov
- Johannes Gutenberg-Universität, Helmholtz Institute Mainz, Mainz 55099, Germany
| | - Lynda J Brown
- Department of Chemistry, Southampton University, Southampton SO17 1BJ, United Kingdom
| | - Richard C D Brown
- Department of Chemistry, Southampton University, Southampton SO17 1BJ, United Kingdom
| | | | | | - Malcolm H Levitt
- Department of Chemistry, Southampton University, Southampton SO17 1BJ, United Kingdom
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14
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Concatenated Composite Pulses Applied to Liquid-State Nuclear Magnetic Resonance Spectroscopy. Sci Rep 2020; 10:2126. [PMID: 32034182 PMCID: PMC7005697 DOI: 10.1038/s41598-020-58823-9] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2019] [Accepted: 01/20/2020] [Indexed: 11/28/2022] Open
Abstract
The error-robust and short composite operations named ConCatenated Composite Pulses (CCCPs), developed as high-precision unitary operations in quantum information processing (QIP), are derived from composite pulses widely employed in nuclear magnetic resonance (NMR). CCCPs simultaneously compensate for two types of systematic errors, which was not possible with the known composite pulses in NMR. Our experiments demonstrate that CCCPs are powerful and versatile tools not only in QIP but also in NMR.
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15
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Appelt S, Kentner A, Lehmkuhl S, Blümich B. From LASER physics to the para-hydrogen pumped RASER. PROGRESS IN NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY 2019; 114-115:1-32. [PMID: 31779878 DOI: 10.1016/j.pnmrs.2019.05.003] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2018] [Accepted: 05/18/2019] [Indexed: 06/10/2023]
Abstract
The properties of the LASER with respect to self-organization are compared with the key features of the p-H2 pumped RASER. According to LASER theory the equations of motion for the LASER can be derived from the enslaving principle, i.e. the slowest-changing order parameter (the light field in the resonator) enslaves the rapidly relaxing atomic degrees of freedom. Likewise, it is shown here that the equations of motion for the p-H2 pumped RASER result from a set of order parameters, where the transverse magnetization of the RASER-active spin states enslaves the electromagnetic modes. The consequences are striking for nuclear magnetic resonance (NMR) spectroscopy, since long-lasting multi-mode RASER oscillations enable unprecedented spectroscopic resolution down to the micro-Hertz regime. Based on the theory for multi-mode RASER operation we analyze the conditions that reveal either the collapse of the entire NMR spectrum, the occurrence of self-organized frequency-combs, or RASER spectra which reflect the J-coupled network of the molecule. Certain RASER experiments involving the protons of 15N pyridine or 3-picoline molecules pumped with p-H2 via SABRE (Signal Amplification By Reversible Exchange) show either a single RASER oscillation in the time domain, giant RASER pulses or a complex RASER beat pattern. The corresponding 1H spectra consist of one narrow line, equidistant narrow lines (frequency-comb), or highly resolved lines reporting NMR properties, respectively. Numerous applications in the areas of material sciences, fundamental physics and medicine involving high precision sensors for magnetic fields, rotational motions or molecular structures become feasible.
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Affiliation(s)
- S Appelt
- Central Institute for Engineering, Electronics and Analytics - Electronic Systems (ZEA-2), Forschungszentrum Jülich GmbH, D-52425 Jülich, Germany.
| | - A Kentner
- Central Institute for Engineering, Electronics and Analytics - Electronic Systems (ZEA-2), Forschungszentrum Jülich GmbH, D-52425 Jülich, Germany
| | - S Lehmkuhl
- Institut für Technische und Makromolekulare Chemie, RWTH Aachen University, D-52056 Aachen, Germany
| | - B Blümich
- Institut für Technische und Makromolekulare Chemie, RWTH Aachen University, D-52056 Aachen, Germany
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16
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Lino JBDR, Ramalho TC. Exploring Through-Space Spin-Spin Couplings for Quantum Information Processing: Facing the Challenge of Coherence Time and Control Quantum States. J Phys Chem A 2019; 123:1372-1379. [PMID: 30673241 DOI: 10.1021/acs.jpca.8b09425] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Nuclear magnetic resonance (NMR) is a powerful tool for studying quantum information processing (QIP). Recently quantum technologies have been proposed to overcome the challenges in large-scale NMR QIP. Furthermore, computational chemistry can promote its improvement. Nuclear spins-1/2 are natural qubits and have been used in most NMR quantum computation experiments. However, molecules that enable many qubits NMR QIP implementations should meet some requirements regarding their spectroscopic properties. Exceptionally large through-space (TS) P-P spin-spin coupling constants (SSCC or J) observed in 1,8-diphosphanaphthalenes (PPN) and in naphtho[1,8- cd]-1,2-dithiole phenylphosphines (NTP) were proposed and investigated to provide more accurate control within large-scale NMR QIP. Spectroscopic properties of PPN and NTP derivatives were explored by theoretical strategies using locally dense basis sets (LDBS). 31P chemical shifts (δ) calculated at the B3LYP/aug-cc-pVTZ-J level and TS P-P SSCCs at the PBE1PBE/pcJ-2 (LDBS-1) level are very close to the experimental data for the PPN molecule. Differently, for the NTP dimer, PBE1PBE/pcJ-2 (LDBS-2) predicts more accurate 31P δ, whereas PBE1PBE/Def2-TZVP (LDBS-1) forecasts more accurate TS P-P SSCCs. From our results, PPNo-F, PPNo-ethyl, and PPNo-NH2 were the best candidates for NMR QIP, in which the large TS SSCCS could face the need of long-time quantum gates implementations. Therefore, it could overcome natural limitations concerning the development of large-scale NMR.
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Affiliation(s)
| | - Teodorico Castro Ramalho
- Chemistry Department , Federal University of Lavras , 37200-000 Lavras , MG Brazil.,Center for Basic and Applied Research, Faculty of Informatics and Management , University Hradec Kralove , 50003 Hradec Kralove , Czech Republic
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17
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Dynamical coupling between a nuclear spin ensemble and electromechanical phonons. Nat Commun 2018; 9:2993. [PMID: 30154466 PMCID: PMC6113237 DOI: 10.1038/s41467-018-05463-3] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/25/2017] [Accepted: 07/09/2018] [Indexed: 11/08/2022] Open
Abstract
Dynamical coupling with high-quality factor resonators is essential in a wide variety of hybrid quantum systems such as circuit quantum electrodynamics and opto/electromechanical systems. Nuclear spins in solids have a long relaxation time and thus have the potential to be implemented into quantum memories and sensors. However, state manipulation of nuclear spins requires high-magnetic fields, which is incompatible with state-of-the-art quantum hybrid systems based on superconducting microwave resonators. Here we investigate an electromechanical resonator whose electrically tunable phonon state imparts a dynamically oscillating strain field to the nuclear spin ensemble located within it. As a consequence of the dynamical strain, we observe both nuclear magnetic resonance (NMR) frequency shifts and NMR sidebands generated by the electromechanical phonons. This prototype system potentially opens up quantum state engineering for nuclear spins, such as coherent coupling between sound and nuclei, and mechanical cooling of solid-state nuclei. Nuclear spins in solids can be implemented into quantum devices but their manipulation usually requires microwave irradiation. Here instead the authors show that they can shift the NMR frequency and drive the nuclear spins into the resolved-sideband regime by using the tunable phonon states from an electromechanical resonator.
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18
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Hussain R, Allodi G, Chiesa A, Garlatti E, Mitcov D, Konstantatos A, Pedersen KS, De Renzi R, Piligkos S, Carretta S. Coherent Manipulation of a Molecular Ln-Based Nuclear Qudit Coupled to an Electron Qubit. J Am Chem Soc 2018; 140:9814-9818. [PMID: 30040890 DOI: 10.1021/jacs.8b05934] [Citation(s) in RCA: 63] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
Abstract
We demonstrate that the [Yb(trensal)] molecule is a prototypical coupled electronic qubit-nuclear qudit system. The combination of noise-resilient nuclear degrees of freedom and large reduction of nutation time induced by electron-nuclear mixing enables coherent manipulation of this qudit by radio frequency pulses. Moreover, the multilevel structure of the qudit is exploited to encode and operate a qubit with embedded basic quantum error correction.
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Affiliation(s)
- Riaz Hussain
- Dipartimento di Scienze Matematiche , Fisiche e Informatiche, Università di Parma , I-43124 Parma , Italy
| | - Giuseppe Allodi
- Dipartimento di Scienze Matematiche , Fisiche e Informatiche, Università di Parma , I-43124 Parma , Italy
| | - Alessandro Chiesa
- Dipartimento di Scienze Matematiche , Fisiche e Informatiche, Università di Parma , I-43124 Parma , Italy
| | - Elena Garlatti
- Dipartimento di Scienze Matematiche , Fisiche e Informatiche, Università di Parma , I-43124 Parma , Italy.,ISIS Facility, Rutherford Appleton Laboratory , OX11 0QX Didcot , United Kingdom
| | - Dmitri Mitcov
- Department of Chemistry , University of Copenhagen , DK-2100 Copenhagen , Denmark
| | - Andreas Konstantatos
- Department of Chemistry , University of Copenhagen , DK-2100 Copenhagen , Denmark
| | - Kasper S Pedersen
- Department of Chemistry , University of Copenhagen , DK-2100 Copenhagen , Denmark.,Department of Chemistry , Technical University of Denmark , DK-2800 Kgs. Lyngby , Denmark
| | - Roberto De Renzi
- Dipartimento di Scienze Matematiche , Fisiche e Informatiche, Università di Parma , I-43124 Parma , Italy
| | - Stergios Piligkos
- Department of Chemistry , University of Copenhagen , DK-2100 Copenhagen , Denmark
| | - Stefano Carretta
- Dipartimento di Scienze Matematiche , Fisiche e Informatiche, Università di Parma , I-43124 Parma , Italy.,UdR Parma, INSTM , I-43124 Parma , Italy
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19
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Atzori M, Chiesa A, Morra E, Chiesa M, Sorace L, Carretta S, Sessoli R. A two-qubit molecular architecture for electron-mediated nuclear quantum simulation. Chem Sci 2018; 9:6183-6192. [PMID: 30090305 PMCID: PMC6062844 DOI: 10.1039/c8sc01695j] [Citation(s) in RCA: 53] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2018] [Accepted: 06/13/2018] [Indexed: 01/02/2023] Open
Abstract
A molecular architecture where two vanadyl-based qubits are linked together is herein described and investigated as a platform for quantum simulation.
A switchable interaction between pairs of highly coherent qubits is a crucial ingredient for the physical realization of quantum information processing. One promising route to enable quantum logic operations involves the use of nuclear spins as protected elementary units of information, qubits. Here we propose a simple way to use fast electronic spin excitations to switch the effective interaction between nuclear spin qubits and the realization of a two-qubit molecular architecture based on highly coherent vanadyl moieties to implement quantum logic operations. Controlled generation of entanglement between qubits is possible here through chemically tuned magnetic coupling between electronic spins, which is clearly evidenced by the splitting of the vanadium(iv) hyperfine lines in the continuous-wave electron paramagnetic resonance spectrum. The system has been further characterized by pulsed electron paramagnetic resonance spectroscopy, evidencing remarkably long coherence times. The experimentally derived spin Hamiltonian parameters have been used to simulate the system dynamics under the sequence of pulses required to implement quantum gates in a realistic description that includes also the harmful effect of decoherence. This demonstrates the possibility of using this molecular complex to implement a control-Z (CZ) gate and simple quantum simulations. Indeed, we also propose a proof-of-principle experiment based on the simulation of the quantum tunneling of the magnetization in a S = 1 spin system.
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Affiliation(s)
- Matteo Atzori
- Dipartimento di Chimica "Ugo Schiff" & INSTM , Università Degli Studi di Firenze , I-50019 Sesto Fiorentino , Italy . ;
| | - Alessandro Chiesa
- Dipartimento di Scienze Matematiche , Fisiche e Informatiche , Università di Parma , I-43124 Parma , Italy . .,Institute for Advanced Simulation , Forschungszentrum Jülich , D-52425 Jülich , Germany
| | - Elena Morra
- Dipartimento di Chimica & NIS Centre , Università di Torino , Via P. Giuria 7 , I-10125 Torino , Italy
| | - Mario Chiesa
- Dipartimento di Chimica & NIS Centre , Università di Torino , Via P. Giuria 7 , I-10125 Torino , Italy
| | - Lorenzo Sorace
- Dipartimento di Chimica "Ugo Schiff" & INSTM , Università Degli Studi di Firenze , I-50019 Sesto Fiorentino , Italy . ;
| | - Stefano Carretta
- Dipartimento di Scienze Matematiche , Fisiche e Informatiche , Università di Parma , I-43124 Parma , Italy .
| | - Roberta Sessoli
- Dipartimento di Chimica "Ugo Schiff" & INSTM , Università Degli Studi di Firenze , I-50019 Sesto Fiorentino , Italy . ;
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20
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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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21
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Wu C, Qi B, Chen C, Dong D. Robust Learning Control Design for Quantum Unitary Transformations. IEEE TRANSACTIONS ON CYBERNETICS 2017; 47:4405-4417. [PMID: 27705875 DOI: 10.1109/tcyb.2016.2610979] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Robust control design for quantum unitary transformations has been recognized as a fundamental and challenging task in the development of quantum information processing due to unavoidable decoherence or operational errors in the experimental implementation of quantum operations. In this paper, we extend the systematic methodology of sampling-based learning control (SLC) approach with a gradient flow algorithm for the design of robust quantum unitary transformations. The SLC approach first uses a "training" process to find an optimal control strategy robust against certain ranges of uncertainties. Then a number of randomly selected samples are tested and the performance is evaluated according to their average fidelity. The approach is applied to three typical examples of robust quantum transformation problems including robust quantum transformations in a three-level quantum system, in a superconducting quantum circuit, and in a spin chain system. Numerical results demonstrate the effectiveness of the SLC approach and show its potential applications in various implementation of quantum unitary transformations.
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22
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Lino JBR, Rocha EP, Ramalho TC. Value of NMR Parameters and DFT Calculations for Quantum Information Processing Utilizing Phosphorus Heterocycles. J Phys Chem A 2017; 121:4486-4495. [PMID: 28441482 DOI: 10.1021/acs.jpca.6b12728] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Quantum computing is the field of science that uses quantum-mechanical phenomena, such as superposition and entanglement, to perform operations on data. The fundamental information unit used in quantum computing is the quantum bit or qubit. It is well-known that quantum computers could theoretically be able to solve problems much more quickly than any classical computers. Currently, the first and still the most successful implementations of quantum information processing (QIP) have been based on nuclear spins in liquids. However, molecules that enable many qubits NMR QIP implementations should meet some conditions: have large chemical shifts and be appropriately dispersed for qubit addressability, appreciable spin-spin coupling between any pair of spins, and a long relaxation time. In this line, benzyldene-2,3-dihydro-1H-[1,3]diphosphole (BDF) derivatives have been theoretically tested for maximizing large chemical shifts, spin-spin coupling, and minimizing the hyperfine coupling constant. Thus, the structures were optimized at the B3LYP/6-311G(d,p) level and showed a significant similarity with the experimental geometrical parameters. The NMR spectroscopic parameters (δ and J) were calculated with six different DFT functionals. The τ-HCTH/6-31G(2d) level is in better agreement with the experimental data of 31P and 13C chemical shifts, while PCM-B3LYP/cc-pVDZ level shows a decrease on deviation between calculated and experimental values for P-P and P-C SSCC. The surface response technique was employed to rationalize how the hyperfine constant varies with the chemical shifts and coupling constants values. From our findings, BDF-NO2 was the best candidate for NMR quantum computations (NMR-QC) among the studied series.
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Affiliation(s)
- Jéssica B R Lino
- Department of Chemistry, Federal University of Lavras , P.O. Box 3037, 37200-000, Lavras, MG, Brazil
| | - Eduardo P Rocha
- Federal Institute of Science, Education and Technology of Southwest MG , Campus Rio, Pomba, MG, Brazil
| | - Teodorico C Ramalho
- Department of Chemistry, Federal University of Lavras , P.O. Box 3037, 37200-000, Lavras, MG, Brazil.,Center for Basic and Applied Research, Faculty of Informatics and Management, University of Hradec Kralove , Hradec Kralove, Czech Republic
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23
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Calderon-Vargas FA, Kestner JP. Dynamically Correcting a CNOT Gate for any Systematic Logical Error. PHYSICAL REVIEW LETTERS 2017; 118:150502. [PMID: 28452552 DOI: 10.1103/physrevlett.118.150502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2016] [Indexed: 06/07/2023]
Abstract
We derive a set of composite pulse sequences that generates cnot gates and correct all systematic errors within the logical subspace to arbitrary order. These sequences are applicable for any two-qubit interaction Hamiltonian and make no assumptions about the underlying noise mechanism except that it is constant on the time scale of the operation. We do assume access to high-fidelity single-qubit gates, so single-qubit gate imperfections eventually limit the achievable fidelity. However, since single-qubit gates generally have much higher fidelities than two-qubit gates in practice, these pulse sequences offer useful dynamical correction for a wide range of coupled qubit systems.
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Affiliation(s)
- F A Calderon-Vargas
- Department of Physics, University of Maryland Baltimore County, Baltimore, Maryland 21250, USA
| | - J P Kestner
- Department of Physics, University of Maryland Baltimore County, Baltimore, Maryland 21250, USA
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24
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Camati PA, Peterson JPS, Batalhão TB, Micadei K, Souza AM, Sarthour RS, Oliveira IS, Serra RM. Experimental Rectification of Entropy Production by Maxwell's Demon in a Quantum System. PHYSICAL REVIEW LETTERS 2016; 117:240502. [PMID: 28009191 DOI: 10.1103/physrevlett.117.240502] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/26/2016] [Indexed: 06/06/2023]
Abstract
Maxwell's demon explores the role of information in physical processes. Employing information about microscopic degrees of freedom, this "intelligent observer" is capable of compensating entropy production (or extracting work), apparently challenging the second law of thermodynamics. In a modern standpoint, it is regarded as a feedback control mechanism and the limits of thermodynamics are recast incorporating information-to-energy conversion. We derive a trade-off relation between information-theoretic quantities empowering the design of an efficient Maxwell's demon in a quantum system. The demon is experimentally implemented as a spin-1/2 quantum memory that acquires information, and employs it to control the dynamics of another spin-1/2 system, through a natural interaction. Noise and imperfections in this protocol are investigated by the assessment of its effectiveness. This realization provides experimental evidence that the irreversibility in a nonequilibrium dynamics can be mitigated by assessing microscopic information and applying a feed-forward strategy at the quantum scale.
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Affiliation(s)
- Patrice A Camati
- Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, Avenida dos Estados 5001, 09210-580 Santo André, São Paulo, Brazil
| | - John P S Peterson
- Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, Rio de Janeiro, Brazil
| | - Tiago B Batalhão
- Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, Avenida dos Estados 5001, 09210-580 Santo André, São Paulo, Brazil
| | - Kaonan Micadei
- Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, Avenida dos Estados 5001, 09210-580 Santo André, São Paulo, Brazil
| | - Alexandre M Souza
- Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, Rio de Janeiro, Brazil
| | - Roberto S Sarthour
- Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, Rio de Janeiro, Brazil
| | - Ivan S Oliveira
- Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, Rio de Janeiro, Brazil
| | - Roberto M Serra
- Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, Avenida dos Estados 5001, 09210-580 Santo André, São Paulo, Brazil
- Department of Physics, University of York, York YO10 5DD, United Kingdom
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25
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Ferrando-Soria J, Moreno Pineda E, Chiesa A, Fernandez A, Magee SA, Carretta S, Santini P, Vitorica-Yrezabal IJ, Tuna F, Timco GA, McInnes EJL, Winpenny REP. A modular design of molecular qubits to implement universal quantum gates. Nat Commun 2016; 7:11377. [PMID: 27109358 PMCID: PMC4848482 DOI: 10.1038/ncomms11377] [Citation(s) in RCA: 131] [Impact Index Per Article: 16.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2015] [Accepted: 03/21/2016] [Indexed: 12/26/2022] Open
Abstract
The physical implementation of quantum information processing relies on individual modules—qubits—and operations that modify such modules either individually or in groups—quantum gates. Two examples of gates that entangle pairs of qubits are the controlled NOT-gate (CNOT) gate, which flips the state of one qubit depending on the state of another, and the gate that brings a two-qubit product state into a superposition involving partially swapping the qubit states. Here we show that through supramolecular chemistry a single simple module, molecular {Cr7Ni} rings, which act as the qubits, can be assembled into structures suitable for either the CNOT or gate by choice of linker, and we characterize these structures by electron spin resonance spectroscopy. We introduce two schemes for implementing such gates with these supramolecular assemblies and perform detailed simulations, based on the measured parameters including decoherence, to demonstrate how the gates would operate. The physical implementation of quantum information processing requires individual qubits and entangling gates. Here, the authors demonstrate a modular implementation through chemistry, assembling molecular {Cr7Ni} rings acting as qubits, with supramolecular structures realizing gates by choice of the linker.
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Affiliation(s)
- Jesús Ferrando-Soria
- School of Chemistry and Photon Science Institute, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
| | - Eufemio Moreno Pineda
- School of Chemistry and Photon Science Institute, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
| | - Alessandro Chiesa
- Dipartimento di Fisica e Scienze della Terra, Università di Parma, viale delle Scienze 7/a, Parma 43123, Italy
| | - Antonio Fernandez
- School of Chemistry and Photon Science Institute, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
| | - Samantha A Magee
- School of Chemistry and Photon Science Institute, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
| | - Stefano Carretta
- Dipartimento di Fisica e Scienze della Terra, Università di Parma, viale delle Scienze 7/a, Parma 43123, Italy
| | - Paolo Santini
- Dipartimento di Fisica e Scienze della Terra, Università di Parma, viale delle Scienze 7/a, Parma 43123, Italy
| | - Iñigo J Vitorica-Yrezabal
- School of Chemistry and Photon Science Institute, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
| | - Floriana Tuna
- School of Chemistry and Photon Science Institute, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
| | - Grigore A Timco
- School of Chemistry and Photon Science Institute, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
| | - Eric J L McInnes
- School of Chemistry and Photon Science Institute, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
| | - Richard E P Winpenny
- School of Chemistry and Photon Science Institute, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
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26
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Abstract
In ordinary, non-relativistic, quantum physics, time enters only as a parameter and not as an observable: a state of a physical system is specified at a given time and then evolved according to the prescribed dynamics. While the state can, and usually does, extend across all space, it is only defined at one instant of time. Here we ask what would happen if we defined the notion of the quantum density matrix for multiple spatial and temporal measurements. We introduce the concept of a pseudo-density matrix (PDM) which treats space and time indiscriminately. This matrix in general fails to be positive for measurement events which do not occur simultaneously, motivating us to define a measure of causality that discriminates between spatial and temporal correlations. Important properties of this measure, such as monotonicity under local operations, are proved. Two qubit NMR experiments are presented that illustrate how a temporal pseudo-density matrix approaches a genuinely allowed density matrix as the amount of decoherence is increased between two consecutive measurements.
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27
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Abstract
Quantum algorithms are known for providing more efficient solutions to certain computational tasks than any corresponding classical algorithm. Here we show that a single qudit is sufficient to implement an oracle based quantum algorithm, which can solve a black-box problem faster than any classical algorithm. For 2d permutation functions defined on a set of d elements, deciding whether a given permutation is even or odd, requires evaluation of the function for at least two elements. We demonstrate that a quantum circuit with a single qudit can determine the parity of the permutation with only one evaluation of the function. Our algorithm provides an example for quantum computation without entanglement since it makes use of the pure state of a qudit. We also present an experimental realization of the proposed quantum algorithm with a quadrupolar nuclear magnetic resonance using a single four-level quantum system, i.e., a ququart.
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28
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Kendon V, Sebald A, Stepney S. Heterotic computing: past, present and future. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2015; 373:rsta.2014.0225. [PMID: 26078342 DOI: 10.1098/rsta.2014.0225] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 04/10/2015] [Indexed: 06/04/2023]
Abstract
We introduce and define 'heterotic computing' as a combination of two or more computational systems such that they provide an advantage over either substrate used separately. This first requires a definition of physical computation. We take the framework in Horsman et al. (Horsman et al. 2014 Proc. R. Soc. A 470, 20140182. (doi:10.1098/rspa.2014.0182)), now known as abstract-representation theory, then outline how to compose such computational systems. We use examples to illustrate the ubiquity of heterotic computing, and to discuss the issues raised when one or more of the substrates is not a conventional silicon-based computer. We briefly outline the requirements for a proper theoretical treatment of heterotic computational systems, and the advantages such a theory would provide.
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Affiliation(s)
- Viv Kendon
- Department of Physics, Durham University, Durham DH1 3LE, UK
| | - Angelika Sebald
- Department of Chemistry, University of York, York YO10 5DD, UK York Centre for Complex Systems Analysis, University of York, York YO10 5DD, UK
| | - Susan Stepney
- Department of Computer Science, University of York, York YO10 5DD, UK York Centre for Complex Systems Analysis, University of York, York YO10 5DD, UK
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29
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Mattei TA, Rehman AA. Technological developments and future perspectives on graphene-based metamaterials: a primer for neurosurgeons. Neurosurgery 2014; 74:499-516; discussion 516. [PMID: 24476906 DOI: 10.1227/neu.0000000000000302] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
Abstract
Graphene, a monolayer atomic-scale honeycomb lattice of carbon atoms, has been considered the greatest revolution in metamaterials research in the past 5 years. Its developers were awarded the Nobel Prize in Physics in 2010, and massive funding has been directed to graphene-based experimental research in the last years. For instance, an international scientific collaboration has recently received a €1 billion grant from the European Flagship Initiative, the largest amount of financial resources ever granted for a single research project in the history of modern science. Because of graphene's unique optical, thermal, mechanical, electronic, and quantum properties, the incorporation of graphene-based metamaterials to biomedical applications is expected to lead to major technological breakthroughs in the next few decades. Current frontline research in graphene technology includes the development of high-performance, lightweight, and malleable electronic devices, new optical modulators, ultracapacitors, molecular biodevices, organic photovoltaic cells, lithium-ion microbatteries, frequency multipliers, quantum dots, and integrated circuits, just to mention a few. With such advances, graphene technology is expected to significantly impact several areas of neurosurgery, including neuro-oncology, neurointensive care, neuroregeneration research, peripheral nerve surgery, functional neurosurgery, and spine surgery. In this topic review, the authors provide a basic introduction to the main electrophysical properties of graphene. Additionally, future perspectives of ongoing frontline investigations on this new metamaterial are discussed, with special emphasis on those research fields that are expected to most substantially impact experimental and clinical neurosurgery in the near future.
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Affiliation(s)
- Tobias A Mattei
- *Invision Health Brain and Spine Center, Williamsville, New York; ‡University of Illinois College of Medicine at Peoria, Peoria, Illinois
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Batalhão TB, Souza AM, Mazzola L, Auccaise R, Sarthour RS, Oliveira IS, Goold J, De Chiara G, Paternostro M, Serra RM. Experimental reconstruction of work distribution and study of fluctuation relations in a closed quantum system. PHYSICAL REVIEW LETTERS 2014; 113:140601. [PMID: 25325627 DOI: 10.1103/physrevlett.113.140601] [Citation(s) in RCA: 105] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/01/2014] [Indexed: 06/04/2023]
Abstract
We report the experimental reconstruction of the nonequilibrium work probability distribution in a closed quantum system, and the study of the corresponding quantum fluctuation relations. The experiment uses a liquid-state nuclear magnetic resonance platform that offers full control on the preparation and dynamics of the system. Our endeavors enable the characterization of the out-of-equilibrium dynamics of a quantum spin from a finite-time thermodynamics viewpoint.
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Affiliation(s)
- Tiago B Batalhão
- Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, R. Santa Adélia 166, 09210-170 Santo André, São Paulo, Brazil
| | - Alexandre M Souza
- Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, Rio de Janeiro, Brazil
| | - Laura Mazzola
- Centre for Theoretical Atomic, Molecular and Optical Physics, School of Mathematics and Physics, Queen's University, Belfast BT7 1NN, United Kingdom
| | - Ruben Auccaise
- Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, Rio de Janeiro, Brazil
| | - Roberto S Sarthour
- Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, Rio de Janeiro, Brazil
| | - Ivan S Oliveira
- Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, Rio de Janeiro, Brazil
| | - John Goold
- The Abdus Salam International Centre for Theoretical Physics, 34014 Trieste, Italy
| | - Gabriele De Chiara
- Centre for Theoretical Atomic, Molecular and Optical Physics, School of Mathematics and Physics, Queen's University, Belfast BT7 1NN, United Kingdom
| | - Mauro Paternostro
- Centre for Theoretical Atomic, Molecular and Optical Physics, School of Mathematics and Physics, Queen's University, Belfast BT7 1NN, United Kingdom and Institut für Theoretische Physik, Albert-Einstein-Allee 11, Universität Ulm, D-89069 Ulm, Germany
| | - Roberto M Serra
- Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, R. Santa Adélia 166, 09210-170 Santo André, São Paulo, Brazil
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Wei D, Spörl A, Chang Y, Khaneja N, Yang X, Glaser SJ. Time-optimized quantum gates on linear three-qubit systems with indirect Ising coupling. Chem Phys Lett 2014. [DOI: 10.1016/j.cplett.2014.08.007] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Merrill JT, Brown KR. Progress in Compensating Pulse Sequences for Quantum Computation. ADVANCES IN CHEMICAL PHYSICS 2014. [DOI: 10.1002/9781118742631.ch10] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
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Yung MH, Whitfield JD, Boixo S, Tempel DG, Aspuru-Guzik A. Introduction to Quantum Algorithms for Physics and Chemistry. ADVANCES IN CHEMICAL PHYSICS 2014. [DOI: 10.1002/9781118742631.ch03] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/04/2022]
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Shim JH, Lee SJ, Yu KK, Hwang SM, Kim K. Strong pulsed excitations using circularly polarized fields for ultra-low field NMR. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2014; 239:87-90. [PMID: 24463634 DOI: 10.1016/j.jmr.2013.12.007] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/29/2013] [Revised: 12/06/2013] [Accepted: 12/08/2013] [Indexed: 06/03/2023]
Abstract
A pulse, which is produced by a single coil and thereby has a linear polarization, cannot coherently drive nuclear spins if the pulse is stronger than the static field B0. The inaccuracy of the pulse, which arises from the failure of the rotating wave approximation, has been an obstacle in adopting multiple pulse techniques in ultra-low field NMR where B0 is less than a few μT. Here, we show that such a limitation can be overcome by applying pulses of circular polarization using two orthogonal coils. The sinusoidal nutation of the nuclear spins was experimentally obtained, which indicates that coherent and precise controls of the nuclear spins can be achieved with circularly polarized pulses. Additional demonstration of the Carl-Purcell-Meiboom-Gill sequence verifies the feasibility of adopting multiple pulse sequences to ultra-low field NMR studies.
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Affiliation(s)
- Jeong Hyun Shim
- Center for Brain and Cognition Measurement, Korea Research Institute of Standards and Science, Daejeon 350-340, Republic of Korea.
| | - Seong-Joo Lee
- Center for Brain and Cognition Measurement, Korea Research Institute of Standards and Science, Daejeon 350-340, Republic of Korea
| | - Kwon-Kyu Yu
- Center for Brain and Cognition Measurement, Korea Research Institute of Standards and Science, Daejeon 350-340, Republic of Korea
| | - Seong-Min Hwang
- Center for Brain and Cognition Measurement, Korea Research Institute of Standards and Science, Daejeon 350-340, Republic of Korea
| | - Kiwoong Kim
- Center for Brain and Cognition Measurement, Korea Research Institute of Standards and Science, Daejeon 350-340, Republic of Korea
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Husain S, Kawamura M, Jones JA. Further analysis of some symmetric and antisymmetric composite pulses for tackling pulse strength errors. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2013; 230:145-154. [PMID: 23500528 DOI: 10.1016/j.jmr.2013.02.007] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/20/2012] [Revised: 01/30/2013] [Accepted: 02/03/2013] [Indexed: 06/01/2023]
Abstract
Composite pulses have found widespread use in both conventional Nuclear Magnetic Resonance experiments and in experimental quantum information processing to reduce the effects of systematic errors. Here we describe several families of time symmetric and antisymmetric fully compensating composite pulses, inspired by the previous Fn, Gn and BB1 families family developed by Wimperis. We describe families of composite 180° pulses (not gates) which exhibit unprecedented tolerance of pulse strength errors without unreasonable sensitivity to off-resonance errors, and related families with more exotic tailored responses. Next we address the problem of extending these methods to other rotation angles, and discuss numerical results for 90° pulses. Finally we demonstrate the performance of some 90° and 180° pulses in NMR experiments.
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Affiliation(s)
- Sami Husain
- Centre for Quantum Computation, Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
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36
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Odedra S, Thrippleton MJ, Wimperis S. Dual-compensated antisymmetric composite refocusing pulses for NMR. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2012; 225:81-92. [PMID: 23147399 DOI: 10.1016/j.jmr.2012.10.003] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2012] [Revised: 09/29/2012] [Accepted: 10/07/2012] [Indexed: 06/01/2023]
Abstract
Novel antisymmetric composite 180° pulses are designed for use in nuclear magnetic resonance (NMR) and verified experimentally. The pulses are simultaneously broadband with respect to both inhomogeneity of the radiofrequency (B(1)) field and resonance offset and, as a result of their antisymmetric phase schemes, can be used to form spin echoes without the introduction of a phase error. The new dual-compensated pulses are designed analytically, using symmetry arguments and a graphical interpretation of average Hamiltonian theory. Two families of composite refocusing pulses are presented, one (ASBO-9) consisting of sequences made up of 9 simple 180° pulses and one (ASBO-11) of sequences made up of 11 simple 180° pulses. There are an infinite number of composite pulses in each family owing to a free phase variable in the solution to the average Hamiltonian equations and this allows selection of individual composite pulses with particular properties. Finally, a comparison is made between composite pulses designed using average Hamiltonian theory and those proposed for use in quantum computing by NMR.
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Affiliation(s)
- Smita Odedra
- School of Chemistry and WestCHEM, University of Glasgow, Glasgow G12 8QQ, United Kingdom
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Rowland B, Jones JA. Implementing quantum logic gates with gradient ascent pulse engineering: principles and practicalities. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2012; 370:4636-50. [PMID: 22946033 DOI: 10.1098/rsta.2011.0361] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/17/2023]
Abstract
We briefly describe the use of gradient ascent pulse engineering (GRAPE) pulses to implement quantum logic gates in nuclear magnetic resonance quantum computers, and discuss a range of simple extensions to the core technique. We then consider a range of difficulties that can arise in practical implementations of GRAPE sequences, reflecting non-idealities in the experimental systems used.
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Affiliation(s)
- Benjamin Rowland
- Oxford Centre for Quantum Computation, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK
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Ichikawa T, Bando M, Kondo Y, Nakahara M. Geometric aspects of composite pulses. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2012; 370:4671-4689. [PMID: 22946035 DOI: 10.1098/rsta.2011.0358] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Unitary operations acting on a quantum system must be robust against systematic errors in control parameters for reliable quantum computing. Composite pulse technique in nuclear magnetic resonance realizes such a robust operation by employing a sequence of possibly poor-quality pulses. In this study, we demonstrate that two kinds of composite pulses-one compensates for a pulse length error in a one-qubit system and the other compensates for a J-coupling error in a two-qubit system-have a vanishing dynamical phase and thereby can be seen as geometric quantum gates, which implement unitary gates by the holonomy associated with dynamics of cyclic vectors defined in the text.
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Affiliation(s)
- Tsubasa Ichikawa
- Research Center for Quantum Computing, Interdisciplinary Graduate School of Science and Engineering, 3-4-1 Kowakae, Higashi-Osaka, Osaka 577-8502, Japan
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Soares-Pinto DO, Auccaise R, Maziero J, Gavini-Viana A, Serra RM, Céleri LC. On the quantumness of correlations in nuclear magnetic resonance. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2012; 370:4821-4836. [PMID: 22946043 DOI: 10.1098/rsta.2011.0364] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Nuclear magnetic resonance (NMR) was successfully employed to test several protocols and ideas in quantum information science. In most of these implementations, the existence of entanglement was ruled out. This fact introduced concerns and questions about the quantum nature of such bench tests. In this paper, we address some issues related to the non-classical aspects of NMR systems. We discuss some experiments where the quantum aspects of this system are supported by quantum correlations of separable states. Such quantumness, beyond the entanglement-separability paradigm, is revealed via a departure between the quantum and the classical versions of information theory. In this scenario, the concept of quantum discord seems to play an important role. We also present an experimental implementation of an analogue of the single-photon Mach-Zehnder interferometer employing two nuclear spins to encode the interferometric paths. This experiment illustrates how non-classical correlations of separable states may be used to simulate quantum dynamics. The results obtained are completely equivalent to the optical scenario, where entanglement (between two field modes) may be present.
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Affiliation(s)
- D O Soares-Pinto
- Instituto de Física de São Carlos, Universidade de São Paulo, Caixa Postal 369, 13560-970 São Carlos, São Paulo, Brazil
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Odedra S, Wimperis S. Use of composite refocusing pulses to form spin echoes. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2012; 214:68-75. [PMID: 22070969 DOI: 10.1016/j.jmr.2011.10.006] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/24/2011] [Revised: 10/06/2011] [Accepted: 10/09/2011] [Indexed: 05/31/2023]
Abstract
The radiofrequency pulses used in NMR are subject to a number of imperfections such as those caused by inhomogeneity of the radiofrequency (B(1)) field and an offset of the transmitter frequency from precise resonance. The effect of these pulse imperfections upon a refocusing pulse in a spin-echo experiment can be severe. Many of the worst effects, those that distort the phase of the spin echo, can be removed completely by selecting the echo coherence pathway using either the "Exorcycle" phase cycle or magnetic field gradients. It is then tempting to go further and try to improve the amplitude of the spin-echo signal by replacing the simple refocusing pulse with a broadband composite 180° pulse that compensates for the relevant pulse imperfection. We show here that all composite pulses with a symmetric or asymmetric phase shift scheme will reintroduce phase distortions into the spin echo, despite the selection of the echo coherence pathway. In contrast, all antisymmetric composite pulses yield no phase distortion whatsoever, both on and off resonance, and are therefore the correct symmetry of composite refocusing pulse to use. These conclusions are verified using simulations and (31)P MAS NMR spin-echo experiments performed on a microporous aluminophosphate.
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Affiliation(s)
- Smita Odedra
- School of Chemistry and WestCHEM, University of Glasgow, Glasgow G12 8QQ, United Kingdom
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McKemmish LK, Kedziora DJ, White GR, Hush NS, Reimers JR. Frequency-based Quantum Computers from a Chemist's Perspective. Aust J Chem 2012. [DOI: 10.1071/ch12053] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Abstract
Quantum computer elements are often designed and tested using molecular or nanoscopic components that form registers of qubits in which memory is stored and information processed. Often such registers are probed and manipulated using frequency-based techniques such as nuclear-magnetic resonance spectroscopy. A major challenge is to design molecules to act as these registers. We provide a basis for rational molecular design through consideration of the generic spectroscopic properties required for quantum computing, bypassing the need for intricate knowledge of the way these molecules are used spectroscopically. Designs in which two-qubit gate times scale similarly to those for one-qubit gates are presented. The specified spectroscopic requirements are largely independent of the type of spectroscopy used (e.g. magnetic resonance or vibrational) and are often independent of technical details of the application (e.g. broadband or high-resolution spectroscopy). This should allow the design of much larger quantum registers than have currently been demonstrated.
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Possa D, Gaudio AC, Freitas JCC. Numerical simulation of NQR/NMR: Applications in quantum computing. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2011; 209:250-260. [PMID: 21324720 DOI: 10.1016/j.jmr.2011.01.020] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2010] [Revised: 01/18/2011] [Accepted: 01/19/2011] [Indexed: 05/30/2023]
Abstract
A numerical simulation program able to simulate nuclear quadrupole resonance (NQR) as well as nuclear magnetic resonance (NMR) experiments is presented, written using the Mathematica package, aiming especially applications in quantum computing. The program makes use of the interaction picture to compute the effect of the relevant nuclear spin interactions, without any assumption about the relative size of each interaction. This makes the program flexible and versatile, being useful in a wide range of experimental situations, going from NQR (at zero or under small applied magnetic field) to high-field NMR experiments. Some conditions specifically required for quantum computing applications are implemented in the program, such as the possibility of use of elliptically polarized radiofrequency and the inclusion of first- and second-order terms in the average Hamiltonian expansion. A number of examples dealing with simple NQR and quadrupole-perturbed NMR experiments are presented, along with the proposal of experiments to create quantum pseudopure states and logic gates using NQR. The program and the various application examples are freely available through the link http://www.profanderson.net/files/nmr_nqr.php.
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Affiliation(s)
- Denimar Possa
- Departamento de Fı´sica, Universidade Federal do Espı´rito Santo, 29075-910 Vitória, ES, Brazil
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