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Sinha A. Development of research network on Quantum Annealing Computation and Information using Google Scholar data. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2023; 381:20210413. [PMID: 36463919 DOI: 10.1098/rsta.2021.0413] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/05/2022] [Accepted: 09/08/2022] [Indexed: 06/17/2023]
Abstract
We build and analyse the network of 100 top-cited nodes (research papers and books from Google Scholar; the strength or citation of the nodes range from about 44 000 up to 100) starting in early 1980 until last year. These searched publications (papers and books) are based on Quantum Annealing Computation and Information categorized into four different sets: (A) Quantum/Transverse Field Spin Glass Model, (B) Quantum Annealing, (C) Quantum Adiabatic Computation and (D) Quantum Computation Information in the title or abstract of the searched publications. We fitted the growth in the annual number of publication ([Formula: see text]) in each of these four categories, A-D, to the form [Formula: see text] where [Formula: see text] denotes the time in years. We found the scaling time [Formula: see text] to be of the order of about 10 years for categories A and C, whereas [Formula: see text] is of the order of about 5 years for categories B and D. This article is part of the theme issue 'Quantum annealing and computation: challenges and perspectives'.
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Affiliation(s)
- Antika Sinha
- Department of Computer Science, Asutosh College, Kolkata, West Bengal 700026, India
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2
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Okuyama M, Ohki K, Ohzeki M. Threshold theorem in isolated quantum dynamics with stochastic control errors. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2023; 381:20210412. [PMID: 36463918 PMCID: PMC9719793 DOI: 10.1098/rsta.2021.0412] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2022] [Accepted: 10/06/2022] [Indexed: 06/17/2023]
Abstract
We investigate the effect of stochastic control errors in the time-dependent Hamiltonian on isolated quantum dynamics. The control errors are formulated as time-dependent stochastic noise in the Schrödinger equation. For a class of stochastic control errors, we establish a threshold theorem that provides a sufficient condition to obtain the target state, which should be determined in noiseless isolated quantum dynamics, as a relation between the number of measurements and noise strength. The theorem guarantees that if the sum of the noise strengths is less than the inverse of computational time, the target state can be obtained through a constant-order number of measurements. If the opposite is true, the number of measurements to guarantee obtaining the target state increases exponentially with computational time. Our threshold theorem can be applied to any isolated quantum dynamics such as quantum annealing and adiabatic quantum computation. This article is part of the theme issue 'Quantum annealing and computation: challenges and perspectives'.
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Affiliation(s)
- Manaka Okuyama
- Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan
| | - Kentaro Ohki
- Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan
| | - Masayuki Ohzeki
- Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan
- Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan
- Sigma-i Co., Ltd., Tokyo 108-0075, Japan
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3
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Ayanzadeh R, Dorband J, Halem M, Finin T. Multi-qubit correction for quantum annealers. Sci Rep 2021; 11:16119. [PMID: 34373515 PMCID: PMC8352911 DOI: 10.1038/s41598-021-95482-w] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2021] [Accepted: 07/08/2021] [Indexed: 11/09/2022] Open
Abstract
We present multi-qubit correction (MQC) as a novel postprocessing method for quantum annealers that views the evolution in an open-system as a Gibbs sampler and reduces a set of excited states to a new synthetic state with lower energy value. After sampling from the ground state of a given (Ising) Hamiltonian, MQC compares pairs of excited states to recognize virtual tunnels-i.e., a group of qubits that changing their states simultaneously can result in a new state with lower energy value-and successively converges to the ground state. Experimental results using D-Wave 2000Q quantum annealers demonstrate that MQC finds samples with notably lower energy values and improves the reproducibility of results when compared to recent hardware/software advances in the realm of quantum annealing, such as spin-reversal transforms, classical postprocessing techniques, and increased inter-sample delay between successive measurements.
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Affiliation(s)
- Ramin Ayanzadeh
- College of Computing, Georgia Institute of Technology, Atlanta, GA, 30332, USA.
| | - John Dorband
- Computer Science and Electrical Engineering, University of Maryland, Baltimore County, Baltimore, MD, 21250, USA
| | - Milton Halem
- Computer Science and Electrical Engineering, University of Maryland, Baltimore County, Baltimore, MD, 21250, USA
| | - Tim Finin
- Computer Science and Electrical Engineering, University of Maryland, Baltimore County, Baltimore, MD, 21250, USA
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4
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Abstract
Quantum computation by the adiabatic theorem requires a slowly-varying Hamiltonian with respect to the spectral gap. We show that the Landau–Zener–Stückelberg oscillation phenomenon, which naturally occurs in quantum two-level systems under non-adiabatic periodic drive, can be exploited to find the ground state of an N-dimensional Grover Hamiltonian. The total runtime of this method is O(2n), which is equal to the computational time of the Grover algorithm in the quantum circuit model. An additional periodic drive can suppress a large subset of Hamiltonian control errors by using coherent destruction of tunneling, thus outperforming previous algorithms.
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5
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Marvian M, Lidar DA. Error Suppression for Hamiltonian-Based Quantum Computation Using Subsystem Codes. PHYSICAL REVIEW LETTERS 2017; 118:030504. [PMID: 28157358 DOI: 10.1103/physrevlett.118.030504] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2016] [Indexed: 06/06/2023]
Abstract
We present general conditions for quantum error suppression for Hamiltonian-based quantum computation using subsystem codes. This involves encoding the Hamiltonian performing the computation using an error detecting subsystem code and the addition of a penalty term that commutes with the encoded Hamiltonian. The scheme is general and includes the stabilizer formalism of both subspace and subsystem codes as special cases. We derive performance bounds and show that complete error suppression results in the large penalty limit. To illustrate the power of subsystem-based error suppression, we introduce fully two-local constructions for protection against local errors of the swap gate of adiabatic gate teleportation and the Ising chain in a transverse field.
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Affiliation(s)
- Milad Marvian
- Department of Electrical Engineering, University of Southern California, Los Angeles, California 90089, USA
- Center for Quantum Information Science & Technology, University of Southern California, Los Angeles, California 90089, USA
| | - Daniel A Lidar
- Department of Electrical Engineering, University of Southern California, Los Angeles, California 90089, USA
- Center for Quantum Information Science & Technology, University of Southern California, Los Angeles, California 90089, USA
- Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089, USA
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA
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6
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Nishimura K, Nishimori H, Ochoa AJ, Katzgraber HG. Retrieving the ground state of spin glasses using thermal noise: Performance of quantum annealing at finite temperatures. Phys Rev E 2016; 94:032105. [PMID: 27739776 DOI: 10.1103/physreve.94.032105] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2016] [Indexed: 11/07/2022]
Abstract
We study the problem to infer the ground state of a spin-glass Hamiltonian using data from another Hamiltonian with interactions disturbed by noise from the original Hamiltonian, motivated by the ground-state inference in quantum annealing on a noisy device. It is shown that the average Hamming distance between the inferred spin configuration and the true ground state is minimized when the temperature of the noisy system is kept at a finite value, and not at zero temperature. We present a spin-glass generalization of a well-established result that the ground state of a purely ferromagnetic Hamiltonian is best inferred at a finite temperature in the sense of smallest Hamming distance when the original ferromagnetic interactions are disturbed by noise. We use the numerical transfer-matrix method to establish the existence of an optimal finite temperature in one- and two-dimensional systems. Our numerical results are supported by mean-field calculations, which give an explicit expression of the optimal temperature to infer the spin-glass ground state as a function of variances of the distributions of the original interactions and the noise. The mean-field prediction is in qualitative agreement with numerical data. Implications on postprocessing of quantum annealing on a noisy device are discussed.
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Affiliation(s)
- Kohji Nishimura
- Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan
| | - Hidetoshi Nishimori
- Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan
| | - Andrew J Ochoa
- Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843-4242, USA
| | - Helmut G Katzgraber
- Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843-4242, USA.,Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA
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Wild DS, Gopalakrishnan S, Knap M, Yao NY, Lukin MD. Adiabatic Quantum Search in Open Systems. PHYSICAL REVIEW LETTERS 2016; 117:150501. [PMID: 27768379 DOI: 10.1103/physrevlett.117.150501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2016] [Indexed: 06/06/2023]
Abstract
Adiabatic quantum algorithms represent a promising approach to universal quantum computation. In isolated systems, a key limitation to such algorithms is the presence of avoided level crossings, where gaps become extremely small. In open quantum systems, the fundamental robustness of adiabatic algorithms remains unresolved. Here, we study the dynamics near an avoided level crossing associated with the adiabatic quantum search algorithm, when the system is coupled to a generic environment. At zero temperature, we find that the algorithm remains scalable provided the noise spectral density of the environment decays sufficiently fast at low frequencies. By contrast, higher order scattering processes render the algorithm inefficient at any finite temperature regardless of the spectral density, implying that no quantum speedup can be achieved. Extensions and implications for other adiabatic quantum algorithms will be discussed.
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Affiliation(s)
- Dominik S Wild
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Sarang Gopalakrishnan
- Department of Physics and Walter Burke Institute, California Institute of Technology, Pasadena, California 91125, USA
- Department of Engineering Science and Physics, CUNY College of Staten Island, Staten Island, New York 10134, USA
| | - Michael Knap
- Department of Physics, Walter Schottky Institute, and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany
| | - Norman Y Yao
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Mikhail D Lukin
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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Matsuura S, Nishimori H, Albash T, Lidar DA. Mean Field Analysis of Quantum Annealing Correction. PHYSICAL REVIEW LETTERS 2016; 116:220501. [PMID: 27314705 DOI: 10.1103/physrevlett.116.220501] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/03/2015] [Indexed: 06/06/2023]
Abstract
Quantum annealing correction (QAC) is a method that combines encoding with energy penalties and decoding to suppress and correct errors that degrade the performance of quantum annealers in solving optimization problems. While QAC has been experimentally demonstrated to successfully error correct a range of optimization problems, a clear understanding of its operating mechanism has been lacking. Here we bridge this gap using tools from quantum statistical mechanics. We study analytically tractable models using a mean-field analysis, specifically the p-body ferromagnetic infinite-range transverse-field Ising model as well as the quantum Hopfield model. We demonstrate that for p=2, where the phase transition is of second order, QAC pushes the transition to increasingly larger transverse field strengths. For p≥3, where the phase transition is of first order, QAC softens the closing of the gap for small energy penalty values and prevents its closure for sufficiently large energy penalty values. Thus QAC provides protection from excitations that occur near the quantum critical point. We find similar results for the Hopfield model, thus demonstrating that our conclusions hold in the presence of disorder.
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Affiliation(s)
- Shunji Matsuura
- Niels Bohr International Academy and Center for Quantum Devices, Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, 2100 Copenhagen, Denmark
- Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
| | - Hidetoshi Nishimori
- Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan
| | - Tameem Albash
- Information Sciences Institute, University of Southern California, Marina del Rey, California 90292, USA
- Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089, USA
- Center for Quantum Information Science & Technology, University of Southern California, Los Angeles, California 90089, USA
| | - Daniel A Lidar
- Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089, USA
- Center for Quantum Information Science & Technology, University of Southern California, Los Angeles, California 90089, USA
- Department of Electrical Engineering, University of Southern California, Los Angeles, California 90089, USA
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA
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9
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Sun C, Wang G, Wu C, Liu H, Feng XL, Chen JL, Xue K. Non-adiabatic holonomic quantum computation in linear system-bath coupling. Sci Rep 2016; 6:20292. [PMID: 26846444 PMCID: PMC4742878 DOI: 10.1038/srep20292] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2015] [Accepted: 12/30/2015] [Indexed: 11/09/2022] Open
Abstract
Non-adiabatic holonomic quantum computation in decoherence-free subspaces protects quantum information from control imprecisions and decoherence. For the non-collective decoherence that each qubit has its own bath, we show the implementations of two non-commutable holonomic single-qubit gates and one holonomic nontrivial two-qubit gate that compose a universal set of non-adiabatic holonomic quantum gates in decoherence-free-subspaces of the decoupling group, with an encoding rate of (N - 2)/N. The proposed scheme is robust against control imprecisions and the non-collective decoherence, and its non-adiabatic property ensures less operation time. We demonstrate that our proposed scheme can be realized by utilizing only two-qubit interactions rather than many-qubit interactions. Our results reduce the complexity of practical implementation of holonomic quantum computation in experiments. We also discuss the physical implementation of our scheme in coupled microcavities.
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Affiliation(s)
- Chunfang Sun
- School of Physics, Northeast Normal University, Changchun 130024, People's Republic of China
| | - Gangcheng Wang
- School of Physics, Northeast Normal University, Changchun 130024, People's Republic of China
| | - Chunfeng Wu
- Pillar of Engineering Product Development, Singapore University of Technology and Design, 8 Somapah Road, Singapore 487372
| | - Haodi Liu
- School of Physics, Northeast Normal University, Changchun 130024, People's Republic of China
| | - Xun-Li Feng
- Department of Physcis, Shanghai Normal University, Shanghai 200234, People's Republic of China
| | - Jing-Ling Chen
- Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071, People's Republic of China.,Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543
| | - Kang Xue
- School of Physics, Northeast Normal University, Changchun 130024, People's Republic of China
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10
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Marvian I, Lidar DA. Quantum error suppression with commuting Hamiltonians: two local is too local. PHYSICAL REVIEW LETTERS 2014; 113:260504. [PMID: 25615294 DOI: 10.1103/physrevlett.113.260504] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/30/2014] [Indexed: 06/04/2023]
Abstract
We consider error suppression schemes in which quantum information is encoded into the ground subspace of a Hamiltonian comprising a sum of commuting terms. Since such Hamiltonians are gapped, they are considered natural candidates for protection of quantum information and topological or adiabatic quantum computation. However, we prove that they cannot be used to this end in the two-local case. By making the favorable assumption that the gap is infinite, we show that single-site perturbations can generate a degeneracy splitting in the ground subspace of this type of Hamiltonian which is of the same order as the magnitude of the perturbation, and is independent of the number of interacting sites and their Hilbert space dimensions, just as in the absence of the protecting Hamiltonian. This splitting results in decoherence of the ground subspace, and we demonstrate that for natural noise models the coherence time is proportional to the inverse of the degeneracy splitting. Our proof involves a new version of the no-hiding theorem which shows that quantum information cannot be approximately hidden in the correlations between two quantum systems. The main reason that two-local commuting Hamiltonians cannot be used for quantum error suppression is that their ground subspaces have only short-range (two-body) entanglement.
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Affiliation(s)
- Iman Marvian
- Center for Quantum Information Science and and Technology, University of Southern California, Los Angeles, California 90089, USA and Department of Physics, University of Southern California, Los Angeles, California 90089, USA
| | - Daniel A Lidar
- Center for Quantum Information Science and and Technology, University of Southern California, Los Angeles, California 90089, USA and Department of Physics, University of Southern California, Los Angeles, California 90089, USA and Department of Electrical Engineering, University of Southern California, Los Angeles, California 90089, USA and Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA
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11
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Lidar DA. Review of Decoherence-Free Subspaces, Noiseless Subsystems, and Dynamical Decoupling. ADVANCES IN CHEMICAL PHYSICS 2014. [DOI: 10.1002/9781118742631.ch11] [Citation(s) in RCA: 42] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
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12
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Error-corrected quantum annealing with hundreds of qubits. Nat Commun 2014; 5:3243. [DOI: 10.1038/ncomms4243] [Citation(s) in RCA: 120] [Impact Index Per Article: 12.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2013] [Accepted: 01/10/2014] [Indexed: 11/08/2022] Open
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13
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Deng Q, Averin DV, Amin MH, Smith P. Decoherence induced deformation of the ground state in adiabatic quantum computation. Sci Rep 2013; 3:1479. [PMID: 23528821 PMCID: PMC3608076 DOI: 10.1038/srep01479] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2012] [Accepted: 03/04/2013] [Indexed: 11/16/2022] Open
Abstract
Despite more than a decade of research on adiabatic quantum computation (AQC), its decoherence properties are still poorly understood. Many theoretical works have suggested that AQC is more robust against decoherence, but a quantitative relation between its performance and the qubits' coherence properties, such as decoherence time, is still lacking. While the thermal excitations are known to be important sources of errors, they are predominantly dependent on temperature but rather insensitive to the qubits' coherence. Less understood is the role of virtual excitations, which can also reduce the ground state probability even at zero temperature. Here, we introduce normalized ground state fidelity as a measure of the decoherence-induced deformation of the ground state due to virtual transitions. We calculate the normalized fidelity perturbatively at finite temperatures and discuss its relation to the qubits' relaxation and dephasing times, as well as its projected scaling properties.
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Affiliation(s)
- Qiang Deng
- Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, NY 11794-3800
| | - Dmitri V. Averin
- Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, NY 11794-3800
| | - Mohammad H. Amin
- D-Wave Systems Inc., 100-4401 Still Creek Drive, Burnaby, B.C., Canada V5C 6G9
- Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
| | - Peter Smith
- D-Wave Systems Inc., 100-4401 Still Creek Drive, Burnaby, B.C., Canada V5C 6G9
- Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
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14
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West JR, Lidar DA, Fong BH, Gyure MF. High fidelity quantum gates via dynamical decoupling. PHYSICAL REVIEW LETTERS 2010; 105:230503. [PMID: 21231440 DOI: 10.1103/physrevlett.105.230503] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2010] [Indexed: 05/30/2023]
Abstract
Realizing the theoretical promise of quantum computers will require overcoming decoherence. Here we demonstrate numerically that high fidelity quantum gates are possible within a framework of quantum dynamical decoupling. Orders of magnitude improvement in the fidelities of a universal set of quantum gates, relative to unprotected evolution, is achieved over a broad range of system-environment coupling strengths, using recursively constructed (concatenated) dynamical decoupling pulse sequences.
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Affiliation(s)
- Jacob R West
- HRL Laboratories, LLC, 3011 Malibu Canyon Road, Malibu, California 90265, USA
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15
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Crosson IJ, Bacon D, Brown KR. Making classical ground-state spin computing fault-tolerant. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:031106. [PMID: 21230024 DOI: 10.1103/physreve.82.031106] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2010] [Indexed: 05/30/2023]
Abstract
We examine a model of classical deterministic computing in which the ground state of the classical system is a spatial history of the computation. This model is relevant to quantum dot cellular automata as well as to recent universal adiabatic quantum computing constructions. In its most primitive form, systems constructed in this model cannot compute in an error-free manner when working at nonzero temperature. However, by exploiting a mapping between the partition function for this model and probabilistic classical circuits we are able to show that it is possible to make this model effectively error-free. We achieve this by using techniques in fault-tolerant classical computing and the result is that the system can compute effectively error-free if the temperature is below a critical temperature. We further link this model to computational complexity and show that a certain problem concerning finite temperature classical spin systems is complete for the complexity class Merlin-Arthur. This provides an interesting connection between the physical behavior of certain many-body spin systems and computational complexity.
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Affiliation(s)
- I J Crosson
- Department of Physics, University of Washington, Seattle, Washington 98195, USA
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16
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Rezakhani AT, Kuo WJ, Hamma A, Lidar DA, Zanardi P. Quantum adiabatic brachistochrone. PHYSICAL REVIEW LETTERS 2009; 103:080502. [PMID: 19792702 DOI: 10.1103/physrevlett.103.080502] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/14/2009] [Indexed: 05/28/2023]
Abstract
We formulate a time-optimal approach to adiabatic quantum computation (AQC). A corresponding natural Riemannian metric is also derived, through which AQC can be understood as the problem of finding a geodesic on the manifold of control parameters. This geometrization of AQC is demonstrated through two examples, where we show that it leads to improved performance of AQC, and sheds light on the roles of entanglement and curvature of the control manifold in algorithmic performance.
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Affiliation(s)
- A T Rezakhani
- Department of Chemistry, and Center for Quantum Information Science & Technology, University of Southern California, Los Angeles, California 90089, USA
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