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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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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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3
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Jheng SD, Chen TW, Cheng SC. Spontaneous giant vortices and circular supercurrents in a trapped exciton-polariton condensate. OPTICS EXPRESS 2022; 30:35325-35337. [PMID: 36258486 DOI: 10.1364/oe.468330] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2022] [Accepted: 08/23/2022] [Indexed: 06/16/2023]
Abstract
We theoretically study an exciton-polariton condensate trapped in a harmonic potential with an annular pump. With a circular pump, predictions were made for a spontaneous rotating vortex lattice packed by singly quantized vortices. If the circular pump is replaced by an annular pump, singly quantized vortices are absorbed into the central hole and form a multiply quantized vortex. For a sufficiently narrow annular width, all vortices are absorbed into the central hole, ultimately forming a giant vortex with supersonic circular supercurrents flowing around it. Vortex-antivortex pairs can be generated if a defect is present in these supersonic circular supercurrents. We further discover that the motion of the vortex-antivortex pairs depends on the position at which they were generated. We suggest that this property can be used to control whether the velocity of the circular supercurrents is above or below the sound velocity.
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4
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Yarkoni S, Raponi E, Bäck T, Schmitt S. Quantum annealing for industry applications: introduction and review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2022; 85:104001. [PMID: 36001953 DOI: 10.1088/1361-6633/ac8c54] [Citation(s) in RCA: 13] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2021] [Accepted: 08/24/2022] [Indexed: 06/15/2023]
Abstract
Quantum annealing (QA) is a heuristic quantum optimization algorithm that can be used to solve combinatorial optimization problems. In recent years, advances in quantum technologies have enabled the development of small- and intermediate-scale quantum processors that implement the QA algorithm for programmable use. Specifically, QA processors produced by D-Wave systems have been studied and tested extensively in both research and industrial settings across different disciplines. In this paper we provide a literature review of the theoretical motivations for QA as a heuristic quantum optimization algorithm, the software and hardware that is required to use such quantum processors, and the state-of-the-art applications and proofs-of-concepts that have been demonstrated using them. The goal of our review is to provide a centralized and condensed source regarding applications of QA technology. We identify the advantages, limitations, and potential of QA for both researchers and practitioners from various fields.
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5
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Gray HM. Quantum pattern recognition algorithms for charged particle tracking. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20210103. [PMID: 34923843 PMCID: PMC8685607 DOI: 10.1098/rsta.2021.0103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/01/2021] [Accepted: 10/07/2021] [Indexed: 06/14/2023]
Abstract
High-energy physics is facing a daunting computing challenge with the large datasets expected from the upcoming High-Luminosity Large Hadron Collider in the next decade and even more so at future colliders. A key challenge in the reconstruction of events of simulated data and collision data is the pattern recognition algorithms used to determine the trajectories of charged particles. The field of quantum computing shows promise for transformative capabilities and is going through a cycle of rapid development and hence might provide a solution to this challenge. This article reviews current studies of quantum computers for charged particle pattern recognition in high-energy physics. This article is part of the theme issue 'Quantum technologies in particle physics'.
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Affiliation(s)
- H. M. Gray
- Physics Department, University of California, Berkeley, CA 947200, USA
- Physics Division, Lawrence Berkeley Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA
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6
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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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7
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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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8
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Bulmer JFF, Jones JA, Walmsley IA. Drive-noise tolerant optical switching inspired by composite pulses. OPTICS EXPRESS 2020; 28:8646-8657. [PMID: 32225485 DOI: 10.1364/oe.378469] [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] [Accepted: 01/27/2020] [Indexed: 06/10/2023]
Abstract
Electro-optic modulators within Mach-Zehnder interferometers are a common construction for optical switches in integrated photonics. A challenge faced when operating at high switching speeds is that noise from the electronic drive signals will effect switching performance. Inspired by the Mach-Zehnder lattice switching devices of Van Campenhout et al. [Opt. Express17(26), 23793 (2009).] and techniques from the field of Nuclear Magnetic Resonance known as composite pulses, we present switches which offer protection against drive-noise in both the on and off state of the switch for both the phase and intensity information encoded in the switched optical mode.
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9
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Zhang ZY, Liu JM, Hu Z, Wang Y. Optical control of entanglement and coherence for polar molecules in pendular states. OPTICS EXPRESS 2019; 27:26588-26599. [PMID: 31674537 DOI: 10.1364/oe.27.026588] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2019] [Accepted: 08/15/2019] [Indexed: 06/10/2023]
Abstract
Quantum entanglement and coherence are both essential physical resources in quantum theory. Cold polar molecules have long coherence time and strong dipole-dipole interaction and thus have been suggested as a platform for quantum information processing. In this paper, we employ the pendular states of the polar molecules trapped in static electric fields as the qubits, and put forward several theoretical schemes to generate the entanglement and coherence for two coupled dipoles by using optimal control theory. Through the designs of appropriate laser pulses, the transitions from the ground state to the Bell state and maximally coherent state can be realized with high fidelities 0.9906 and 0.9943 in the two-dipole system, respectively. Meanwhile, we show that the degrees of entanglement and coherence between the two pendular qubits are effectively enhanced with the help of optimized control fields. Furthermore, our schemes are generalized to the preparation of the Hardy state and even to the creation of arbitrary two-qubit states. Our findings can shed some light on the implementation of quantum information tasks with the molecular pendular states.
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10
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Li H, Gao X, Xin T, Yung MH, Long G. Experimental study of Forrelation in nuclear spins. Sci Bull (Beijing) 2017; 62:497-502. [PMID: 36659259 DOI: 10.1016/j.scib.2017.03.006] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2017] [Revised: 03/02/2017] [Accepted: 03/03/2017] [Indexed: 01/21/2023]
Abstract
Correlation functions are often employed to quantify the relationships among interdependent variables or sets of data. Recently, a new class of correlation functions, called Forrelation, has been introduced by Aaronson and Ambainis for studying the query complexity of quantum devices. It was found that there exists a quantum query algorithm solving 2-fold Forrelation problems with an exponential quantum speedup over all possible classical means, which represents essentially the largest possible separation between quantum and classical query complexities. Here we report an experimental study probing the 2-fold and 3-fold Forrelations encoded in nuclear spins. The major experimental challenge is to control the spin fluctuation to within a threshold value, which is achieved by developing a set of optimized GRAPE pulse sequences. Overall, our small-scale implementation indicates that the quantum query algorithm is capable of determining the values of Forrelations within an acceptable accuracy required for demonstrating quantum supremacy, given the current technology and in the presence of experimental noise.
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Affiliation(s)
- Hang Li
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China; Collaborative Innovation Centre of Quantum Matter, Beijing 100084, China
| | - Xun Gao
- Centre for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Tao Xin
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China; Collaborative Innovation Centre of Quantum Matter, Beijing 100084, China
| | - Man-Hong Yung
- Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China; Centre for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China.
| | - Guilu Long
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China; Collaborative Innovation Centre of Quantum Matter, Beijing 100084, China.
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11
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Wei Q, Cao Y, Kais S, Friedrich B, Herschbach D. Quantum Computation using Arrays of N Polar Molecules in Pendular States. Chemphyschem 2016; 17:3714-3722. [PMID: 27767247 DOI: 10.1002/cphc.201600781] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2016] [Revised: 10/10/2016] [Indexed: 11/07/2022]
Abstract
We investigate several aspects of realizing quantum computation using entangled polar molecules in pendular states. Quantum algorithms typically start from a product state |00⋯0⟩ and we show that up to a negligible error, the ground states of polar molecule arrays can be considered as the unentangled qubit basis state |00⋯0⟩ . This state can be prepared by simply allowing the system to reach thermal equilibrium at low temperature (<1 mK). We also evaluate entanglement, characterized by concurrence of pendular state qubits in dipole arrays as governed by the external electric field, dipole-dipole coupling and number N of molecules in the array. In the parameter regime that we consider for quantum computing, we find that qubit entanglement is modest, typically no greater than 10-4 , confirming the negligible entanglement in the ground state. We discuss methods for realizing quantum computation in the gate model, measurement-based model, instantaneous quantum polynomial time circuits and the adiabatic model using polar molecules in pendular states.
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Affiliation(s)
- Qi Wei
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai, 200062, China
| | - Yudong Cao
- Department of Computer Science, Purdue University, West Lafayette, IN, 47907, USA
| | - Sabre Kais
- Department of Chemistry and Physics, Purdue University, West Lafayette, IN, 47907, USA.,Qatar Environment and Energy Research Institute, HBKU, Qatar Foundation, Doha, Qatar
| | - Bretislav Friedrich
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195, Berlin, Germany
| | - Dudley Herschbach
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts, 02138, USA
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12
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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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13
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von den Hoff P, Thallmair S, Kowalewski M, Siemering R, de Vivie-Riedle R. Optimal control theory--closing the gap between theory and experiment. Phys Chem Chem Phys 2012; 14:14460-85. [PMID: 23019574 DOI: 10.1039/c2cp41838j] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Optimal control theory and optimal control experiments are state-of-the-art tools to control quantum systems. Both methods have been demonstrated successfully for numerous applications in molecular physics, chemistry and biology. Modulated light pulses could be realized, driving these various control processes. Next to the control efficiency, a key issue is the understanding of the control mechanism. An obvious way is to seek support from theory. However, the underlying search strategies in theory and experiment towards the optimal laser field differ. While the optimal control theory operates in the time domain, optimal control experiments optimize the laser fields in the frequency domain. This also implies that both search procedures experience a different bias and follow different pathways on the search landscape. In this perspective we review our recent developments in optimal control theory and their applications. Especially, we focus on approaches, which close the gap between theory and experiment. To this extent we followed two ways. One uses sophisticated optimization algorithms, which enhance the capabilities of optimal control experiments. The other is to extend and modify the optimal control theory formalism in order to mimic the experimental conditions.
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Affiliation(s)
- Philipp von den Hoff
- Department of Chemistry, Ludwig-Maximilians-Universität München, München, Germany
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14
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Zaari RR, Brown A. Effect of laser pulse shaping parameters on the fidelity of quantum logic gates. J Chem Phys 2012; 137:104306. [PMID: 22979858 DOI: 10.1063/1.4747703] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The effect of varying parameters specific to laser pulse shaping instruments on resulting fidelities for the ACNOT(1), NOT(2), and Hadamard(2) quantum logic gates are studied for the diatomic molecule (12)C(16)O. These parameters include varying the frequency resolution, adjusting the number of frequency components and also varying the amplitude and phase at each frequency component. A time domain analytic form of the original discretized frequency domain laser pulse function is derived, providing a useful means to infer the resulting pulse shape through variations to the aforementioned parameters. We show that amplitude variation at each frequency component is a crucial requirement for optimal laser pulse shaping, whereas phase variation provides minimal contribution. We also show that high fidelity laser pulses are dependent upon the frequency resolution and increasing the number of frequency components provides only a small incremental improvement to quantum gate fidelity. Analysis through use of the pulse area theorem confirms the resulting population dynamics for one or two frequency high fidelity laser pulses and implies similar dynamics for more complex laser pulse shapes. The ability to produce high fidelity laser pulses that provide both population control and global phase alignment is attributed greatly to the natural evolution phase alignment of the qubits involved within the quantum logic gate operation.
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Affiliation(s)
- Ryan R Zaari
- Department of Chemistry, University of Alberta, Edmonton, Alberta T6G 2G2, Canada
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15
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Wei Q, Kais S, Friedrich B, Herschbach D. Entanglement of polar symmetric top molecules as candidate qubits. J Chem Phys 2011; 135:154102. [DOI: 10.1063/1.3649949] [Citation(s) in RCA: 44] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Qi Wei
- Department of Physics, Texas A & M University, College Station, Texas 77843, USA
| | - Sabre Kais
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, USA
| | - Bretislav Friedrich
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany
| | - Dudley Herschbach
- Department of Physics, Texas A & M University, College Station, Texas 77843, USA
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16
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Jones JA. Quantum computing with NMR. PROGRESS IN NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY 2011; 59:91-120. [PMID: 21742157 DOI: 10.1016/j.pnmrs.2010.11.001] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2010] [Accepted: 11/02/2010] [Indexed: 05/31/2023]
Affiliation(s)
- Jonathan A Jones
- Centre for Quantum Computation, Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK.
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17
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Zaari RR, Brown A. Effect of diatomic molecular properties on binary laser pulse optimizations of quantum gate operations. J Chem Phys 2011; 135:044317. [DOI: 10.1063/1.3617248] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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18
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Optical switching of nuclear spin-spin couplings in semiconductors. Nat Commun 2011; 2:378. [PMID: 21730962 PMCID: PMC3144591 DOI: 10.1038/ncomms1378] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2011] [Accepted: 06/08/2011] [Indexed: 11/15/2022] Open
Abstract
Two-qubit operation is an essential part of quantum computation. However, solid-state nuclear magnetic resonance quantum computing has not been able to fully implement this functionality, because it requires a switchable inter-qubit coupling that controls the time evolutions of entanglements. Nuclear dipolar coupling is beneficial in that it is present whenever nuclear–spin qubits are close to each other, while it complicates two-qubit operation because the qubits must remain decoupled to prevent unwanted couplings. Here we introduce optically controllable internuclear coupling in semiconductors. The coupling strength can be adjusted externally through light power and even allows on/off switching. This feature provides a simple way of switching inter-qubit couplings in semiconductor-based quantum computers. In addition, its long reach compared with nuclear dipolar couplings allows a variety of options for arranging qubits, as they need not be next to each other to secure couplings. Two-qubit operation is an essential part of quantum computation, but implementation has been difficult. Goto et al. introduce optically controllable internuclear coupling in semiconductors providing a simple way of switching inter-qubit couplings in semiconductor-based quantum computers.
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19
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The operations of quantum logic gates with pure and mixed initial states. J Chem Phys 2011; 134:134103. [DOI: 10.1063/1.3571597] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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20
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Wei Q, Kais S, Friedrich B, Herschbach D. Entanglement of polar molecules in pendular states. J Chem Phys 2011; 134:124107. [PMID: 21456645 DOI: 10.1063/1.3567486] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Qi Wei
- Department of Physics, Texas A & M University, College Station, Texas 77843, USA
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21
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Miura T, Wasielewski MR. Manipulating Photogenerated Radical Ion Pair Lifetimes in Wirelike Molecules Using Microwave Pulses: Molecular Spintronic Gates. J Am Chem Soc 2011; 133:2844-7. [DOI: 10.1021/ja110789q] [Citation(s) in RCA: 44] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Tomoaki Miura
- Department of Chemistry and Argonne-Northwestern Solar Energy Research (ANSER) Center, Northwestern University, Evanston, Illinois 60208-3113, United States
| | - Michael R. Wasielewski
- Department of Chemistry and Argonne-Northwestern Solar Energy Research (ANSER) Center, Northwestern University, Evanston, Illinois 60208-3113, United States
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22
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Chen A. Implementation of Deutsch-Jozsa algorithm and determination of value of function via Rydberg blockade. OPTICS EXPRESS 2011; 19:2037-2045. [PMID: 21369020 DOI: 10.1364/oe.19.002037] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We propose an efficient scheme in which the Deutsch-Jozsa algorithm can be realized via Rydberg blockade interaction. Deutsch-Jozsa algorithm can fast determine whether function is constant or balanced, but this algorithm does not give the concrete value of function. Using the Rydberg blockade, value of function may be determined in our scheme. According to the quantitative calculation of Rydberg blockade, we discuss the experimental feasibility of our scheme.
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Affiliation(s)
- Aixi Chen
- Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne university of Technology, Melbourne 3122, Australia.
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Mishima K, Yamashita K. Quantum computing using molecular vibrational and rotational modes of the open-shell 14N16O molecule. Chem Phys 2010. [DOI: 10.1016/j.chemphys.2009.11.007] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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24
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Gopinath T, Kumar A. Implementation of controlled phase shift gates and Collins version of Deutsch-Jozsa algorithm on a quadrupolar spin-7/2 nucleus using non-adiabatic geometric phases. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2008; 193:168-176. [PMID: 18514557 DOI: 10.1016/j.jmr.2008.04.018] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/20/2007] [Revised: 04/12/2008] [Accepted: 04/14/2008] [Indexed: 05/26/2023]
Abstract
In this work controlled phase shift gates are implemented on a qaudrupolar system, by using non-adiabatic geometric phases. A general procedure is given, for implementing controlled phase shift gates in an 'N' level system. The utility of such controlled phase shift gates, is demonstrated here by implementing 3-qubit Deutsch-Jozsa algorithm on a spin-7/2 quadrupolar nucleus oriented in a liquid crystal matrix.
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Affiliation(s)
- T Gopinath
- NMR Quantum Computing and Quantum Information Group, Department of Physics, and NMR Research Centre, Indian Institute of Science, Yeshwanthpur, Bangalore, Karnataka 560012, India.
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26
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Auccaise R, Teles J, Sarthour RS, Bonagamba TJ, Oliveira IS, deAzevedo ER. A study of the relaxation dynamics in a quadrupolar NMR system using Quantum State Tomography. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2008; 192:17-26. [PMID: 18295520 DOI: 10.1016/j.jmr.2008.01.009] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/29/2007] [Revised: 01/11/2008] [Accepted: 01/13/2008] [Indexed: 05/25/2023]
Abstract
This article reports a relaxation study in an oriented system containing spin 3/2 nuclei using quantum state tomography (QST). The use of QST allowed evaluating the time evolution of all density matrix elements starting from several initial states. Using an appropriated treatment based on the Redfield theory, the relaxation rate of each density matrix element was measured and the reduced spectral densities that describe the system relaxation were determined. All the experimental data could be well described assuming pure quadrupolar relaxation and reduced spectral densities corresponding to a superposition of slow and fast motions. The data were also analyzed in the context of Quantum Information Processing, where the coherence loss of each qubit of the system was determined using the partial trace operation.
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Affiliation(s)
- R Auccaise
- Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, Rio de Janeiro 22290-180, RJ, Brazil.
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27
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Mitra A, Mahesh TS, Kumar A. NMR implementation of adiabatic SAT algorithm using strongly modulated pulses. J Chem Phys 2008; 128:124110. [DOI: 10.1063/1.2835542] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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28
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Scherer W, Mehring M. Entangled electron and nuclear spin states in N15@C60: Density matrix tomography. J Chem Phys 2008; 128:052305. [DOI: 10.1063/1.2819310] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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29
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Mishima K, Tokumo K, Yamashita K. Quantum computing using molecular electronic and vibrational states. Chem Phys 2008. [DOI: 10.1016/j.chemphys.2007.10.027] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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30
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de Vivie-Riedle R, Troppmann U. Femtosecond Lasers for Quantum Information Technology. Chem Rev 2007; 107:5082-100. [DOI: 10.1021/cr040094l] [Citation(s) in RCA: 77] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Affiliation(s)
- Regina de Vivie-Riedle
- Department Chemie, Ludwig Maximilians Universität, Butenandtstrasse 11, 81377 München, Germany
| | - Ulrike Troppmann
- Department Chemie, Ludwig Maximilians Universität, Butenandtstrasse 11, 81377 München, Germany
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31
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Schneider B, Gollub C, Kompa KL, de Vivie-Riedle R. Robustness of quantum gates operating on the high frequency modes of MnBr(CO)5. Chem Phys 2007. [DOI: 10.1016/j.chemphys.2007.05.027] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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32
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Mitra A, Sivapriya K, Kumar A. Experimental implementation of a three qubit quantum game with corrupt source using nuclear magnetic resonance quantum information processor. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2007; 187:306-13. [PMID: 17581766 DOI: 10.1016/j.jmr.2007.05.013] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2007] [Revised: 05/16/2007] [Accepted: 05/24/2007] [Indexed: 05/15/2023]
Abstract
In a three player quantum 'Dilemma' game each player takes independent decisions to maximize his/her individual gain. The optimal strategy in the quantum version of this game has a higher payoff compared to its classical counterpart. However, this advantage is lost if the initial qubits provided to the players are from a noisy source. We have experimentally implemented the three player quantum version of the 'Dilemma' game as described by Johnson, [N.F. Johnson, Phys. Rev. A 63 (2001) 020302(R)] using nuclear magnetic resonance quantum information processor and have experimentally verified that the payoff of the quantum game for various levels of corruption matches the theoretical payoff.
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Affiliation(s)
- Avik Mitra
- NMR Quantum Computation and Quantum Information Group, Department of Physics and NMR Research Centre, Indian Institute of Science, Bangalore 560012, India
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33
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Cheng T, Brown A. Quantum computing based on vibrational eigenstates: pulse area theorem analysis. J Chem Phys 2007; 124:034111. [PMID: 16438571 DOI: 10.1063/1.2164457] [Citation(s) in RCA: 72] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In a recent paper [D. Babikov, J. Chem. Phys. 121, 7577 (2004)], quantum optimal control theory was applied to analyze the accuracy of quantum gates in a quantum computer based on molecular vibrational eigenstates. The effects of the anharmonicity parameter of the molecule, the target time of the pulse, and the penalty function on the accuracy of the qubit transformations were investigated. We demonstrate that the effects of all the molecular and laser-pulse parameters can be explained utilizing the analytical pulse area theorem, which originates from the standard two-level model. Moreover, by analyzing the difference between the optimal control theory results and those obtained using the pulse area theorem, it is shown that extremely high quantum gate fidelity can be achieved for a qubit system based on vibrational eigenstates.
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Affiliation(s)
- Taiwang Cheng
- Department of Chemistry, University of Alberta, Edmonton, Alberta T6G 2G2, Canada
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34
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Fitzsimons J, Xiao L, Benjamin SC, Jones JA. Quantum information processing with delocalized qubits under global control. PHYSICAL REVIEW LETTERS 2007; 99:030501. [PMID: 17678274 DOI: 10.1103/physrevlett.99.030501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2006] [Indexed: 05/16/2023]
Abstract
Conventional quantum computing schemes are incompatible with nanometer-scale "hardware," where the closely packed spins cannot be individually controlled. We report the first experimental demonstration of a global control paradigm: logical qubits delocalize along a spin chain and are addressed via the two terminal spins. Using NMR studies on a three-spin molecule, we implement a globally clocked quantum mirror that outperforms the equivalent swap network. We then extend the protocol to support dense qubit storage and demonstrate this experimentally via Deutsch and Deutsch-Jozsa algorithms.
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Affiliation(s)
- Joseph Fitzsimons
- Department of Materials, Oxford University, Oxford OX1 3PH, United Kingdom.
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35
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Shioya K, Mishima K, Yamashita K. Quantum computing using molecular vibrational and rotational modes. Mol Phys 2007. [DOI: 10.1080/00268970701439573] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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36
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Tesch CM, de Vivie-Riedle R. Vibrational molecular quantum computing: basis set independence and theoretical realization of the Deutsch-Jozsa algorithm. J Chem Phys 2006; 121:12158-68. [PMID: 15606234 DOI: 10.1063/1.1818131] [Citation(s) in RCA: 91] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The phase of quantum gates is one key issue for the implementation of quantum algorithms. In this paper we first investigate the phase evolution of global molecular quantum gates, which are realized by optimally shaped femtosecond laser pulses. The specific laser fields are calculated using the multitarget optimal control algorithm, our modification of the optimal control theory relevant for application in quantum computing. As qubit system we use vibrational modes of polyatomic molecules, here the two IR-active modes of acetylene. Exemplarily, we present our results for a Pi gate, which shows a strong dependence on the phase, leading to a significant decrease in quantum yield. To correct for this unwanted behavior we include pressure on the quantum phase in our multitarget approach. In addition the accuracy of these phase corrected global quantum gates is enhanced. Furthermore we could show that in our molecular approach phase corrected quantum gates and basis set independence are directly linked. Basis set independence is also another property highly required for the performance of quantum algorithms. By realizing the Deutsch-Jozsa algorithm in our two qubit molecular model system, we demonstrate the good performance of our phase corrected and basis set independent quantum gates.
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37
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Abstract
Pseudopure states of a system of twelve interacting spins are experimentally demonstrated. The system is a cluster of dipolar-coupled nuclear spins of fully labeled (13)C(6)-benzene in a liquid crystalline matrix. At present, this is the largest and the most complex composite system where individual quantum states have been addressed.
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Affiliation(s)
- Jae-Seung Lee
- Department of Chemistry, Kent State University, Kent, OH 44242-0001, USA
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38
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Scholz M, Aichele T, Ramelow S, Benson O. Deutsch-jozsa algorithm using triggered single photons from a single quantum dot. PHYSICAL REVIEW LETTERS 2006; 96:180501. [PMID: 16712351 DOI: 10.1103/physrevlett.96.180501] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2005] [Indexed: 05/09/2023]
Abstract
We demonstrate a two-qubit Deutsch-Jozsa algorithm with single photons from a single InP quantum dot. The qubits are implemented via the spatial mode and the polarization of a single photon. Our photon source is operated both under continuous and pulsed excitation, the latter allowing deterministic quantum logic by generating photons on demand with a strong suppression of two-photon events. The computation reached a success probability of up to 79%. We also exploit the concept of decoherence-free subspaces that helps to make our experimental setup robust against sources of phase noise.
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Affiliation(s)
- M Scholz
- Physics Department, Nano-Optics, Humboldt-University Berlin, Hausvogteiplatz 5-7, D-10117 Berlin, Germany
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39
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Heidebrecht A, Mende J, Mehring M. Indirect detection of selective nuclear spin-spin interactions in a hostile environment. SOLID STATE NUCLEAR MAGNETIC RESONANCE 2006; 29:90-4. [PMID: 16256317 DOI: 10.1016/j.ssnmr.2005.09.015] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2005] [Revised: 09/06/2005] [Indexed: 05/05/2023]
Abstract
We present a number of techniques which may be used to obtain precise values of selective spin-spin interactions between two nuclear spins in a hostile environment. Such an environment may be characterized by very fast relaxation and decoherence, e.g. due to the strong coupling of the two spins of interest to electron spins in their vicinity as well as other nuclei. Here, we used dilute paramagnetic Ce(3+) centers hosted in a single crystal of CaF(2). Selected (19)F internuclear interactions were measured indirectly by applying different electron nuclear double resonance (ENDOR) pulse sequences.
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Affiliation(s)
- A Heidebrecht
- Univesität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
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40
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Korff BMR, Troppmann U, Kompa KL, de Vivie-Riedle R. Manganese pentacarbonyl bromide as candidate for a molecular qubit system operated in the infrared regime. J Chem Phys 2005; 123:244509. [PMID: 16396551 DOI: 10.1063/1.2141615] [Citation(s) in RCA: 64] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Our concept for a quantum computational system is based on qubits encoded in vibrational normal modes of polyatomic molecules. The quantum gates are implemented by shaped femtosecond laser pulses. We adopt this concept to the new species manganese pentacarbonyl bromide [MnBr(CO)5] and show that it is a promising candidate in the mid-infrared (IR) frequency range to connect theory and experiment. As direct reference for the ab initio calculations we evaluated experimentally the absorption bands of MnBr(CO)5 in the mid-IR as well as the related transition dipole moments. The two-dimensional potential-energy surface spanned by the two strongest IR active modes and the dipole vector surfaces are calculated with density-functional theory. The vibrational eigenstates representing the qubit system are determined. Laser pulses are optimized by multitarget optimal control theory to form a set of global quantum gates: NOT, CNOT, Pi, and Hadamard. For all of them simply structured pulses with low pulse energies around 1 microJ could be obtained. Exemplarily for the CNOT gate we investigated the possible transfer to experimental shaping, based on the mask function for pulse shaping in the frequency regime as well as decomposition into a train of subpulses.
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Affiliation(s)
- B M R Korff
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, 85748 Garching, Germany.
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41
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Das R, Kumar SKK, Kumar A. Use of non-adiabatic geometric phase for quantum computing by NMR. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2005; 177:318-28. [PMID: 16182577 DOI: 10.1016/j.jmr.2005.07.025] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2005] [Revised: 06/22/2005] [Accepted: 07/17/2005] [Indexed: 05/04/2023]
Abstract
Geometric phases have stimulated researchers for its potential applications in many areas of science. One of them is fault-tolerant quantum computation. A preliminary requisite of quantum computation is the implementation of controlled dynamics of qubits. In controlled dynamics, one qubit undergoes coherent evolution and acquires appropriate phase, depending on the state of other qubits. If the evolution is geometric, then the phase acquired depend only on the geometry of the path executed, and is robust against certain types of error. This phenomenon leads to an inherently fault-tolerant quantum computation. Here we suggest a technique of using non-adiabatic geometric phase for quantum computation, using selective excitation. In a two-qubit system, we selectively evolve a suitable subsystem where the control qubit is in state |1, through a closed circuit. By this evolution, the target qubit gains a phase controlled by the state of the control qubit. Using the non-adiabatic geometric phase we demonstrate implementation of Deutsch-Jozsa algorithm and Grover's search algorithm in a two-qubit system.
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Affiliation(s)
- Ranabir Das
- NMR Quantum Computation and Quantum Information Group, Department of Physics and NMR Research Centre, Indian Institute of Science, Bangalore 560012, India.
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42
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Mitra A, Ghosh A, Das R, Patel A, Kumar A. Experimental implementation of local adiabatic evolution algorithms by an NMR quantum information processor. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2005; 177:285-98. [PMID: 16172009 DOI: 10.1016/j.jmr.2005.08.004] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2005] [Revised: 08/24/2005] [Accepted: 08/11/2005] [Indexed: 05/04/2023]
Abstract
Quantum adiabatic algorithm is a method of solving computational problems by evolving the ground state of a slowly varying Hamiltonian. The technique uses evolution of the ground state of a slowly varying Hamiltonian to reach the required output state. In some cases, such as the adiabatic versions of Grover's search algorithm and Deutsch-Jozsa algorithm, applying the global adiabatic evolution yields a complexity similar to their classical algorithms. However, using the local adiabatic evolution, the algorithms given by J. Roland and N.J. Cerf for Grover's search [J. Roland, N.J. Cerf, Quantum search by local adiabatic evolution, Phys. Rev. A 65 (2002) 042308] and by Saurya Das, Randy Kobes, and Gabor Kunstatter for the Deutsch-Jozsa algorithm [S. Das, R. Kobes, G. Kunstatter, Adiabatic quantum computation and Deutsh's algorithm, Phys. Rev. A 65 (2002) 062301], yield a complexity of order N (where N=2(n) and n is the number of qubits). In this paper, we report the experimental implementation of these local adiabatic evolution algorithms on a 2-qubit quantum information processor, by Nuclear Magnetic Resonance.
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Affiliation(s)
- Avik Mitra
- NMR Quantum Computation and Quantum Information Group, Department of Physics and NMR Research Centre, Indian Institute of Science, Bangalore 560012, India
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43
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Troppmann U, de Vivie-Riedle R. Mechanisms of local and global molecular quantum gates and their implementation prospects. J Chem Phys 2005; 122:154105. [PMID: 15945623 DOI: 10.1063/1.1881112] [Citation(s) in RCA: 49] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We explore how the globality of quantum logic operations is ensured in the context of optimal control theory when qubits are encoded in vibrational eigenstates of different normal modes and specially shaped laser fields act as quantum logic operations. In a two-qubit model system, transition mechanisms for optimized laser fields generating single qubit flips, local NOT and global NOT and controlled-NOT (CNOT) gates are investigated and compared. We evaluate the participation of vibrational eigenstates beyond the qubit basis in the global gate mechanisms and how different features of CNOT and NOT gates relate to the characteristics of the vibrational manifold. When a non-qubit normal mode interacting via anharmonic resonances is introduced, neither the global gate mechanisms nor the optimized laser fields show a significant increase in complexity. Similar features of the global quantum gates in both model systems indicate a generality of the deduced principles. Finally, a primary concept for a realization of global quantum gates in an actual experiment referring to state-of-the-art techniques is presented. The possible reconstruction of optimized laser fields with sequences of simple Gaussian subpulses is demonstrated and some critical parameters are deduced.
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Affiliation(s)
- Ulrike Troppmann
- Department Chemie, Ludwig-Maximilians-Universität München, Butenandt-Strasse 11, München D 81277, Germany
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44
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Implementing Grover’s quantum search on a para-hydrogen based pure state NMR quantum computer. Chem Phys Lett 2004. [DOI: 10.1016/j.cplett.2004.10.078] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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45
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Mehring M, Scherer W, Weidinger A. Pseudoentanglement of spin states in the multilevel 15N@C60 system. PHYSICAL REVIEW LETTERS 2004; 93:206603. [PMID: 15600950 DOI: 10.1103/physrevlett.93.206603] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2004] [Indexed: 05/22/2023]
Abstract
We have prepared combined electron and nuclear spin pseudoentangled states Psi+/-27 and Phi+/-18 out of the total number of eight quantum states in the multilevel quantum system of a nitrogen atom with electron spin 3/2 and nuclear spin 1/2 encaged in the endohedral fullerene (15)N@C(60). Density matrix tomography was applied to verify the degree of entanglement.
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Affiliation(s)
- M Mehring
- Physikalisches Institut, Universität Stuttgart, D-70550 Stuttgart, Germany
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46
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Das R, Bhattacharyya R, Kumar A. Quantum information processing by NMR using a 5-qubit system formed by dipolar coupled spins in an oriented molecule. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2004; 170:310-321. [PMID: 15388095 DOI: 10.1016/j.jmr.2004.07.008] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2004] [Revised: 07/09/2004] [Indexed: 05/24/2023]
Abstract
Quantum information processing by NMR with small number of qubits is well established. Scaling to higher number of qubits is hindered by two major requirements (i) mutual coupling among qubits and (ii) qubit addressability. It has been demonstrated that mutual coupling can be increased by using residual dipolar couplings among spins by orienting the spin system in a liquid crystalline matrix. In such a case, the heteronuclear spins are weakly coupled, but the homonuclear spins often become strongly coupled. In such circumstances, the strongly coupled spins, which yield second order spectra, can no longer be individually treated as qubits. However, it has been demonstrated elsewhere, that the 2(N) energy levels of a strongly coupled N spin-1/2 system can be treated as an N-qubit system. For this purpose the various transitions have to be identified to well defined energy levels. This paper consists of two parts. In the first part, the energy level diagram of a heteronuclear 5-spin system is obtained by using a newly developed heteronuclear z-cosy (HET-Z-COSY) experiment. In the second part, implementation of logic gates, preparation of pseudopure states, creation of entanglement, and entanglement transfer is demonstrated, validating the use of such systems for quantum information processing.
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Affiliation(s)
- Ranabir Das
- Department of Physics, Indian Institute of Science, Bangalore, India
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47
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Wei D, Yang X, Luo J, Sun X, Zeng X. Realization of the new summing algorithm on an NMR ensemble quantum computer. Chem Phys Lett 2004. [DOI: 10.1016/j.cplett.2004.08.009] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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48
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Course 5 Quantum information processing in ion traps I. ACTA ACUST UNITED AC 2004. [DOI: 10.1016/s0924-8099(03)80029-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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49
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Das R, Kumar A. Spectral implementation of some quantum algorithms by one- and two-dimensional nuclear magnetic resonance. J Chem Phys 2004; 121:7601-13. [PMID: 15485220 DOI: 10.1063/1.1795674] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Quantum information processing has been effectively demonstrated on a small number of qubits by nuclear magnetic resonance. An important subroutine in any computing is the readout of the output. "Spectral implementation" originally suggested by Z. L. Madi, R. Bruschweiler, and R. R. Ernst [J. Chem. Phys. 109, 10603 (1999)], provides an elegant method of readout with the use of an extra "observer" qubit. At the end of computation, detection of the observer qubit provides the output via the multiplet structure of its spectrum. In spectral implementation by two-dimensional experiment the observer qubit retains the memory of input state during computation, thereby providing correlated information on input and output, in the same spectrum. Spectral implementation of Grover's search algorithm, approximate quantum counting, a modified version of Berstein-Vazirani problem, and Hogg's algorithm are demonstrated here in three- and four-qubit systems.
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Affiliation(s)
- Ranabir Das
- Department of Physics, Indian Institute of Science, Bangalore-560012, India
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50
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Babikov D. Accuracy of gates in a quantum computer based on vibrational eigenstates. J Chem Phys 2004; 121:7577-85. [PMID: 15485217 DOI: 10.1063/1.1791635] [Citation(s) in RCA: 103] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A model is developed to study the properties of a quantum computer that uses vibrational eigenstates of molecules to implement the quantum information bits and shaped laser pulses to apply the quantum logic gates. Particular emphasis of this study is on understanding how the different factors, such as properties of the molecule and of the pulse, can be used to affect the accuracy of quantum gates in such a system. Optimal control theory and numerical time-propagation of vibrational wave packets are employed to obtain the shaped pulses for the gates NOT and Hadamard transform. The effects of the anharmonicity parameter of the molecule, the target time of the pulse and of the penalty function are investigated. Influence of all these parameters on the accuracy of qubit transformations is observed and explained. It is shown that when all these parameters are carefully chosen the accuracy of quantum gates reaches 99.9%.
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Affiliation(s)
- Dmitri Babikov
- Chemistry Department, Marquette University, Wehr Chemistry Building, Milwaukee, WI 53201-1881, USA
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