201
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Marty O, Cramer M, Plenio MB. Practical Entanglement Estimation for Spin-System Quantum Simulators. PHYSICAL REVIEW LETTERS 2016; 116:105301. [PMID: 27015489 DOI: 10.1103/physrevlett.116.105301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2015] [Indexed: 06/05/2023]
Abstract
We present practical methods to measure entanglement for quantum simulators that can be realized with trapped ions, cold atoms, and superconducting qubits. Focusing on long- and short-range Ising-type Hamiltonians, we introduce schemes that are applicable under realistic experimental conditions including mixedness due to, e.g., noise or temperature. In particular, we identify a single observable whose expectation value serves as a lower bound to entanglement and that may be obtained by a simple quantum circuit. As such circuits are not (yet) available for every platform, we investigate the performance of routinely measured observables as quantitative entanglement witnesses. Possible applications include experimental studies of entanglement scaling in critical systems and the reliable benchmarking of quantum simulators.
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Affiliation(s)
- O Marty
- Institut für Theoretische Physik & IQST, Albert-Einstein-Allee 11, Universität Ulm, Germany
| | - M Cramer
- Institut für Theoretische Physik & IQST, Albert-Einstein-Allee 11, Universität Ulm, Germany
| | - M B Plenio
- Institut für Theoretische Physik & IQST, Albert-Einstein-Allee 11, Universität Ulm, Germany
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202
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Chancellor N, Szoke S, Vinci W, Aeppli G, Warburton PA. Maximum-Entropy Inference with a Programmable Annealer. Sci Rep 2016; 6:22318. [PMID: 26936311 PMCID: PMC4776239 DOI: 10.1038/srep22318] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2015] [Accepted: 02/11/2016] [Indexed: 11/23/2022] Open
Abstract
Optimisation problems typically involve finding the ground state (i.e. the minimum energy configuration) of a cost function with respect to many variables. If the variables are corrupted by noise then this maximises the likelihood that the solution is correct. The maximum entropy solution on the other hand takes the form of a Boltzmann distribution over the ground and excited states of the cost function to correct for noise. Here we use a programmable annealer for the information decoding problem which we simulate as a random Ising model in a field. We show experimentally that finite temperature maximum entropy decoding can give slightly better bit-error-rates than the maximum likelihood approach, confirming that useful information can be extracted from the excited states of the annealer. Furthermore we introduce a bit-by-bit analytical method which is agnostic to the specific application and use it to show that the annealer samples from a highly Boltzmann-like distribution. Machines of this kind are therefore candidates for use in a variety of machine learning applications which exploit maximum entropy inference, including language processing and image recognition.
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Affiliation(s)
| | - Szilard Szoke
- Department of Electronic and Electrical Engineering, UCL, Torrington Place, London, WC1E 7JE, UK
| | - Walter Vinci
- University of Southern California Department of Electrical Engineering 825 Bloom, Walk Los Angeles CA, 90089, USA
- University of Southern California Center for Quantum Information Science Technology 825 Bloom Walk, Los Angeles CA, 90089, USA
| | - Gabriel Aeppli
- Department of Physics, ETH Zürich, Zürich, CH-8093, Switzerland
- Department of Physics, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, CH-1015, Switzerland
- Synchrotron and Nanotechnology Department, Paul Scherrer Institute, Villigen, CH-5232, Switzerland
| | - Paul A. Warburton
- London Centre For Nanotechnology 19 Gordon St, London, WC1H 0AH, UK
- Department of Electronic and Electrical Engineering, UCL, Torrington Place, London, WC1E 7JE, UK
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203
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Kumar KS, Vepsäläinen A, Danilin S, Paraoanu GS. Stimulated Raman adiabatic passage in a three-level superconducting circuit. Nat Commun 2016; 7:10628. [PMID: 26902454 PMCID: PMC4766393 DOI: 10.1038/ncomms10628] [Citation(s) in RCA: 107] [Impact Index Per Article: 13.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2015] [Accepted: 01/05/2016] [Indexed: 12/04/2022] Open
Abstract
The adiabatic manipulation of quantum states is a powerful technique that opened up new directions in quantum engineering—enabling tests of fundamental concepts such as geometrical phases and topological transitions, and holding the promise of alternative models of quantum computation. Here we benchmark the stimulated Raman adiabatic passage for circuit quantum electrodynamics by employing the first three levels of a transmon qubit. In this ladder configuration, we demonstrate a population transfer efficiency >80% between the ground state and the second excited state using two adiabatic Gaussian-shaped control microwave pulses. By doing quantum tomography at successive moments during the Raman pulses, we investigate the transfer of the population in time domain. Furthermore, we show that this protocol can be reversed by applying a third adiabatic pulse, we study a hybrid nondiabatic–adiabatic sequence, and we present experimental results for a quasi-degenerate intermediate level. The precise control and manipulation of the states of a multi-level quantum system are fundamental for quantum information processing. Here, the authors demonstrate the robust adiabatic manipulation of the quantum states of a superconducting circuit via stimulated Raman adiabatic passage.
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Affiliation(s)
- K S Kumar
- Low Temperature Laboratory, Department of Applied Physics, Aalto University School of Science, PO Box 15100, Aalto FI-00076, Finland
| | - A Vepsäläinen
- Low Temperature Laboratory, Department of Applied Physics, Aalto University School of Science, PO Box 15100, Aalto FI-00076, Finland
| | - S Danilin
- Low Temperature Laboratory, Department of Applied Physics, Aalto University School of Science, PO Box 15100, Aalto FI-00076, Finland
| | - G S Paraoanu
- Low Temperature Laboratory, Department of Applied Physics, Aalto University School of Science, PO Box 15100, Aalto FI-00076, Finland
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204
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Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network. Sci Rep 2016; 6:21686. [PMID: 26899997 PMCID: PMC4761947 DOI: 10.1038/srep21686] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2015] [Accepted: 01/27/2016] [Indexed: 11/08/2022] Open
Abstract
The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.
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205
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Altaisky MV, Zolnikova NN, Kaputkina NE, Krylov VA, Lozovik YE, Dattani NS. Decoherence and Entanglement Simulation in a Model of Quantum Neural Network Based on Quantum Dots. EPJ WEB OF CONFERENCES 2016. [DOI: 10.1051/epjconf/201610802006] [Citation(s) in RCA: 2] [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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206
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Yang YG, Zhao QQ. Novel pseudo-random number generator based on quantum random walks. Sci Rep 2016; 6:20362. [PMID: 26842402 PMCID: PMC4740897 DOI: 10.1038/srep20362] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2015] [Accepted: 10/14/2015] [Indexed: 11/23/2022] Open
Abstract
In this paper, we investigate the potential application of quantum computation for constructing pseudo-random number generators (PRNGs) and further construct a novel PRNG based on quantum random walks (QRWs), a famous quantum computation model. The PRNG merely relies on the equations used in the QRWs, and thus the generation algorithm is simple and the computation speed is fast. The proposed PRNG is subjected to statistical tests such as NIST and successfully passed the test. Compared with the representative PRNG based on quantum chaotic maps (QCM), the present QRWs-based PRNG has some advantages such as better statistical complexity and recurrence. For example, the normalized Shannon entropy and the statistical complexity of the QRWs-based PRNG are 0.999699456771172 and 1.799961178212329e-04 respectively given the number of 8 bits-words, say, 16Mbits. By contrast, the corresponding values of the QCM-based PRNG are 0.999448131481064 and 3.701210794388818e-04 respectively. Thus the statistical complexity and the normalized entropy of the QRWs-based PRNG are closer to 0 and 1 respectively than those of the QCM-based PRNG when the number of words of the analyzed sequence increases. It provides a new clue to construct PRNGs and also extends the applications of quantum computation.
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Affiliation(s)
- Yu-Guang Yang
- College of Computer Science and Technology, Beijing University of Technology, Beijing, 100124, China
- State Key Laboratory of Information Security (Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093), China
- Beijing Key Laboratory of Trusted Computing, Beijing, 100124, China
- National Engineering Laboratory for Critical Technologies of Information Security Classified Protection, Beijing, 100124, China
| | - Qian-Qian Zhao
- College of Computer Science and Technology, Beijing University of Technology, Beijing, 100124, China
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207
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Determination and correction of persistent biases in quantum annealers. Sci Rep 2016; 6:18628. [PMID: 26783120 PMCID: PMC4725997 DOI: 10.1038/srep18628] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2015] [Accepted: 11/10/2015] [Indexed: 11/08/2022] Open
Abstract
Calibration of quantum computers is essential to the effective utilisation of their quantum resources. Specifically, the performance of quantum annealers is likely to be significantly impaired by noise in their programmable parameters, effectively misspecification of the computational problem to be solved, often resulting in spurious suboptimal solutions. We developed a strategy to determine and correct persistent, systematic biases between the actual values of the programmable parameters and their user-specified values. We applied the recalibration strategy to two D-Wave Two quantum annealers, one at NASA Ames Research Center in Moffett Field, California, and another at D-Wave Systems in Burnaby, Canada. We show that the recalibration procedure not only reduces the magnitudes of the biases in the programmable parameters but also enhances the performance of the device on a set of random benchmark instances.
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208
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Fernandez A, Ferrando-Soria J, Pineda EM, Tuna F, Vitorica-Yrezabal IJ, Knappke C, Ujma J, Muryn CA, Timco GA, Barran PE, Ardavan A, Winpenny RE. Making hybrid [n]-rotaxanes as supramolecular arrays of molecular electron spin qubits. Nat Commun 2016; 7:10240. [PMID: 26742716 PMCID: PMC4729860 DOI: 10.1038/ncomms10240] [Citation(s) in RCA: 79] [Impact Index Per Article: 9.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2015] [Accepted: 11/17/2015] [Indexed: 02/04/2023] Open
Abstract
Quantum information processing (QIP) would require that the individual units involved--qubits--communicate to other qubits while retaining their identity. In many ways this resembles the way supramolecular chemistry brings together individual molecules into interlocked structures, where the assembly has one identity but where the individual components are still recognizable. Here a fully modular supramolecular strategy has been to link hybrid organic-inorganic [2]- and [3]-rotaxanes into still larger [4]-, [5]- and [7]-rotaxanes. The ring components are heterometallic octanuclear [Cr7NiF8(O2C(t)Bu)16](-) coordination cages and the thread components template the formation of the ring about the organic axle, and are further functionalized to act as a ligand, which leads to large supramolecular arrays of these heterometallic rings. As the rings have been proposed as qubits for QIP, the strategy provides a possible route towards scalable molecular electron spin devices for QIP. Double electron-electron resonance experiments demonstrate inter-qubit interactions suitable for mediating two-qubit quantum logic gates.
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Affiliation(s)
- Antonio Fernandez
- School of Chemistry and Photon Science Institute, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
| | - Jesus Ferrando-Soria
- School of Chemistry and Photon Science Institute, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
| | - Eufemio Moreno Pineda
- School of Chemistry and Photon Science Institute, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
| | - Floriana Tuna
- School of Chemistry and Photon Science Institute, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
| | - Iñigo J. Vitorica-Yrezabal
- School of Chemistry and Photon Science Institute, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
| | | | - Jakub Ujma
- School of Chemistry and Photon Science Institute, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
- The Michael Barber Centre for Collaborative Mass Spectrometry, Manchester Institute of Biotechnology, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
| | - Christopher A. Muryn
- School of Chemistry and Photon Science Institute, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
| | - Grigore A. Timco
- School of Chemistry and Photon Science Institute, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
| | - Perdita E. Barran
- School of Chemistry and Photon Science Institute, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
- The Michael Barber Centre for Collaborative Mass Spectrometry, Manchester Institute of Biotechnology, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
| | - Arzhang Ardavan
- Department of Physics, Centre for Advanced Electron Spin Resonance, The Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK
| | - Richard E.P. Winpenny
- School of Chemistry and Photon Science Institute, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
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209
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Computational multiqubit tunnelling in programmable quantum annealers. Nat Commun 2016; 7:10327. [PMID: 26739797 PMCID: PMC4729842 DOI: 10.1038/ncomms10327] [Citation(s) in RCA: 134] [Impact Index Per Article: 16.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2015] [Accepted: 11/26/2015] [Indexed: 11/17/2022] Open
Abstract
Quantum tunnelling is a phenomenon in which a quantum state traverses energy barriers higher than the energy of the state itself. Quantum tunnelling has been hypothesized as an advantageous physical resource for optimization in quantum annealing. However, computational multiqubit tunnelling has not yet been observed, and a theory of co-tunnelling under high- and low-frequency noises is lacking. Here we show that 8-qubit tunnelling plays a computational role in a currently available programmable quantum annealer. We devise a probe for tunnelling, a computational primitive where classical paths are trapped in a false minimum. In support of the design of quantum annealers we develop a nonperturbative theory of open quantum dynamics under realistic noise characteristics. This theory accurately predicts the rate of many-body dissipative quantum tunnelling subject to the polaron effect. Furthermore, we experimentally demonstrate that quantum tunnelling outperforms thermal hopping along classical paths for problems with up to 200 qubits containing the computational primitive. Quantum tunnelling may be advantageous for quantum annealing, but multiqubit tunnelling has not yet been observed or characterized theoretically. Here, the authors demonstrate that 8-qubit tunnelling plays a role in a D-Wave Two device through a nonperturbative theory and experimental data.
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210
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Steiger DS, Rønnow TF, Troyer M. Heavy Tails in the Distribution of Time to Solution for Classical and Quantum Annealing. PHYSICAL REVIEW LETTERS 2015; 115:230501. [PMID: 26684103 DOI: 10.1103/physrevlett.115.230501] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/21/2015] [Indexed: 06/05/2023]
Abstract
For many optimization algorithms the time to solution depends not only on the problem size but also on the specific problem instance and may vary by many orders of magnitude. It is then necessary to investigate the full distribution and especially its tail. Here, we analyze the distributions of annealing times for simulated annealing and simulated quantum annealing (by path integral quantum Monte Carlo simulation) for random Ising spin glass instances. We find power-law distributions with very heavy tails, corresponding to extremely hard instances, but far broader distributions-and thus worse performance for hard instances-for simulated quantum annealing than for simulated annealing. Fast, nonadiabatic, annealing schedules can improve the performance of simulated quantum annealing for very hard instances by many orders of magnitude.
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Affiliation(s)
| | - Troels F Rønnow
- Theoretische Physik, ETH Zurich, 8093 Zurich, Switzerland
- Nokia Technologies, Broers Building, 21 JJ Thomson Avenue, CB3 0FA Cambridge, United Kingdom
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211
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Uncertain behaviours of integrated circuits improve computational performance. Sci Rep 2015; 5:16213. [PMID: 26586362 PMCID: PMC4653651 DOI: 10.1038/srep16213] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2015] [Accepted: 10/05/2015] [Indexed: 11/29/2022] Open
Abstract
Improvements to the performance of conventional computers have mainly been achieved through semiconductor scaling; however, scaling is reaching its limitations. Natural phenomena, such as quantum superposition and stochastic resonance, have been introduced into new computing paradigms to improve performance beyond these limitations. Here, we explain that the uncertain behaviours of devices due to semiconductor scaling can improve the performance of computers. We prototyped an integrated circuit by performing a ground-state search of the Ising model. The bit errors of memory cell devices holding the current state of search occur probabilistically by inserting fluctuations into dynamic device characteristics, which will be actualised in the future to the chip. As a result, we observed more improvements in solution accuracy than that without fluctuations. Although the uncertain behaviours of devices had been intended to be eliminated in conventional devices, we demonstrate that uncertain behaviours has become the key to improving computational performance.
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212
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Inack EM, Pilati S. Simulated quantum annealing of double-well and multiwell potentials. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:053304. [PMID: 26651813 DOI: 10.1103/physreve.92.053304] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/28/2015] [Indexed: 06/05/2023]
Abstract
We analyze the performance of quantum annealing as a heuristic optimization method to find the absolute minimum of various continuous models, including landscapes with only two wells and also models with many competing minima and with disorder. The simulations performed using a projective quantum Monte Carlo (QMC) algorithm are compared with those based on the finite-temperature path-integral QMC technique and with classical annealing. We show that the projective QMC algorithm is more efficient than the finite-temperature QMC technique, and that both are inferior to classical annealing if this is performed with appropriate long-range moves. However, as the difficulty of the optimization problem increases, classical annealing loses efficiency, while the projective QMC algorithm keeps stable performance and is finally the most effective optimization tool. We discuss the implications of our results for the outstanding problem of testing the efficiency of adiabatic quantum computers using stochastic simulations performed on classical computers.
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Affiliation(s)
- E M Inack
- The Abdus Salam International Centre for Theoretical Physics, I-34151 Trieste, Italy
- SISSA, International School for Advanced Studies and INFN, Sezione di Trieste, I-34136 Trieste, Italy
| | - S Pilati
- The Abdus Salam International Centre for Theoretical Physics, I-34151 Trieste, Italy
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213
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Superadiabatic Controlled Evolutions and Universal Quantum Computation. Sci Rep 2015; 5:15775. [PMID: 26511064 PMCID: PMC4625175 DOI: 10.1038/srep15775] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2015] [Accepted: 10/05/2015] [Indexed: 11/29/2022] Open
Abstract
Adiabatic state engineering is a powerful technique in quantum information and quantum control. However, its performance is limited by the adiabatic theorem of quantum mechanics. In this scenario, shortcuts to adiabaticity, such as provided by the superadiabatic theory, constitute a valuable tool to speed up the adiabatic quantum behavior. Here, we propose a superadiabatic route to implement universal quantum computation. Our method is based on the realization of piecewise controlled superadiabatic evolutions. Remarkably, they can be obtained by simple time-independent counter-diabatic Hamiltonians. In particular, we discuss the implementation of fast rotation gates and arbitrary n-qubit controlled gates, which can be used to design different sets of universal quantum gates. Concerning the energy cost of the superadiabatic implementation, we show that it is dictated by the quantum speed limit, providing an upper bound for the corresponding adiabatic counterparts.
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214
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Li Y, Chen CY, Kaye AM, Wasserman WW. The identification of cis-regulatory elements: A review from a machine learning perspective. Biosystems 2015; 138:6-17. [PMID: 26499213 DOI: 10.1016/j.biosystems.2015.10.002] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2015] [Revised: 10/09/2015] [Accepted: 10/14/2015] [Indexed: 01/06/2023]
Abstract
The majority of the human genome consists of non-coding regions that have been called junk DNA. However, recent studies have unveiled that these regions contain cis-regulatory elements, such as promoters, enhancers, silencers, insulators, etc. These regulatory elements can play crucial roles in controlling gene expressions in specific cell types, conditions, and developmental stages. Disruption to these regions could contribute to phenotype changes. Precisely identifying regulatory elements is key to deciphering the mechanisms underlying transcriptional regulation. Cis-regulatory events are complex processes that involve chromatin accessibility, transcription factor binding, DNA methylation, histone modifications, and the interactions between them. The development of next-generation sequencing techniques has allowed us to capture these genomic features in depth. Applied analysis of genome sequences for clinical genetics has increased the urgency for detecting these regions. However, the complexity of cis-regulatory events and the deluge of sequencing data require accurate and efficient computational approaches, in particular, machine learning techniques. In this review, we describe machine learning approaches for predicting transcription factor binding sites, enhancers, and promoters, primarily driven by next-generation sequencing data. Data sources are provided in order to facilitate testing of novel methods. The purpose of this review is to attract computational experts and data scientists to advance this field.
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Affiliation(s)
- Yifeng Li
- Centre for Molecular Medicine and Therapeutics, Child and Family Research Institute, Department of Medical Genetics, University of British Columbia Vancouver, British Columbia V5Z 4H4, Canada; Information and Communications Technologies, National Research Council of Canada, Ottawa, Ontario K1A 0R6, Canada.
| | - Chih-Yu Chen
- Centre for Molecular Medicine and Therapeutics, Child and Family Research Institute, Department of Medical Genetics, University of British Columbia Vancouver, British Columbia V5Z 4H4, Canada.
| | - Alice M Kaye
- Centre for Molecular Medicine and Therapeutics, Child and Family Research Institute, Department of Medical Genetics, University of British Columbia Vancouver, British Columbia V5Z 4H4, Canada.
| | - Wyeth W Wasserman
- Centre for Molecular Medicine and Therapeutics, Child and Family Research Institute, Department of Medical Genetics, University of British Columbia Vancouver, British Columbia V5Z 4H4, Canada.
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215
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Unraveling Quantum Annealers using Classical Hardness. Sci Rep 2015; 5:15324. [PMID: 26483257 PMCID: PMC4611884 DOI: 10.1038/srep15324] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2015] [Accepted: 09/22/2015] [Indexed: 11/08/2022] Open
Abstract
Recent advances in quantum technology have led to the development and manufacturing of experimental programmable quantum annealing optimizers that contain hundreds of quantum bits. These optimizers, commonly referred to as 'D-Wave' chips, promise to solve practical optimization problems potentially faster than conventional 'classical' computers. Attempts to quantify the quantum nature of these chips have been met with both excitement and skepticism but have also brought up numerous fundamental questions pertaining to the distinguishability of experimental quantum annealers from their classical thermal counterparts. Inspired by recent results in spin-glass theory that recognize 'temperature chaos' as the underlying mechanism responsible for the computational intractability of hard optimization problems, we devise a general method to quantify the performance of quantum annealers on optimization problems suffering from varying degrees of temperature chaos: A superior performance of quantum annealers over classical algorithms on these may allude to the role that quantum effects play in providing speedup. We utilize our method to experimentally study the D-Wave Two chip on different temperature-chaotic problems and find, surprisingly, that its performance scales unfavorably as compared to several analogous classical algorithms. We detect, quantify and discuss several purely classical effects that possibly mask the quantum behavior of the chip.
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216
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Lechner W, Hauke P, Zoller P. A quantum annealing architecture with all-to-all connectivity from local interactions. SCIENCE ADVANCES 2015; 1:e1500838. [PMID: 26601316 PMCID: PMC4646830 DOI: 10.1126/sciadv.1500838] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2015] [Accepted: 08/15/2015] [Indexed: 05/02/2023]
Abstract
Quantum annealers are physical devices that aim at solving NP-complete optimization problems by exploiting quantum mechanics. The basic principle of quantum annealing is to encode the optimization problem in Ising interactions between quantum bits (qubits). A fundamental challenge in building a fully programmable quantum annealer is the competing requirements of full controllable all-to-all connectivity and the quasi-locality of the interactions between physical qubits. We present a scalable architecture with full connectivity, which can be implemented with local interactions only. The input of the optimization problem is encoded in local fields acting on an extended set of physical qubits. The output is-in the spirit of topological quantum memories-redundantly encoded in the physical qubits, resulting in an intrinsic fault tolerance. Our model can be understood as a lattice gauge theory, where long-range interactions are mediated by gauge constraints. The architecture can be realized on various platforms with local controllability, including superconducting qubits, NV-centers, quantum dots, and atomic systems.
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Affiliation(s)
- Wolfgang Lechner
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, 6020 Innsbruck, Austria
- Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria
- Corresponding author. E-mail:
| | - Philipp Hauke
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, 6020 Innsbruck, Austria
- Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria
| | - Peter Zoller
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, 6020 Innsbruck, Austria
- Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria
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217
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Ruben M. Molecular materials - towards quantum properties. BEILSTEIN JOURNAL OF NANOTECHNOLOGY 2015; 6:1485-1486. [PMID: 26199852 PMCID: PMC4505185 DOI: 10.3762/bjnano.6.153] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2015] [Accepted: 06/28/2015] [Indexed: 09/02/2023]
Affiliation(s)
- Mario Ruben
- Institute of Nanotechnology, Karlsruhe Institute of Technology, D-76344 Eggenstein-Leopoldshafen, Germany
- Institut de Physique et Chimie des Matériaux, Université de Strasbourg, 23 Rue du Loess, F-67200 Strasbourg, France
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218
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Nazareth DP, Spaans JD. First application of quantum annealing to IMRT beamlet intensity optimization. Phys Med Biol 2015; 60:4137-48. [DOI: 10.1088/0031-9155/60/10/4137] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
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219
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Liu CW, Polkovnikov A, Sandvik AW. Quantum versus classical annealing: insights from scaling theory and results for spin glasses on 3-regular graphs. PHYSICAL REVIEW LETTERS 2015; 114:147203. [PMID: 25910158 DOI: 10.1103/physrevlett.114.147203] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/25/2014] [Indexed: 06/04/2023]
Abstract
We discuss an Ising spin glass where each S=1/2 spin is coupled antiferromagnetically to three other spins (3-regular graphs). Inducing quantum fluctuations by a time-dependent transverse field, we use out-of-equilibrium quantum Monte Carlo simulations to study dynamic scaling at the quantum glass transition. Comparing the dynamic exponent and other critical exponents with those of the classical (temperature-driven) transition, we conclude that quantum annealing is less efficient than classical simulated annealing in bringing the system into the glass phase. Quantum computing based on the quantum annealing paradigm is therefore inferior to classical simulated annealing for this class of problems. We also comment on previous simulations where a parameter is changed with the simulation time, which is very different from the true Hamiltonian dynamics simulated here.
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Affiliation(s)
- Cheng-Wei Liu
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
| | - Anatoli Polkovnikov
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
| | - Anders W Sandvik
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
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220
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Heim B, Ronnow TF, Isakov SV, Troyer M. Quantum versus classical annealing of Ising spin glasses. Science 2015; 348:215-7. [DOI: 10.1126/science.aaa4170] [Citation(s) in RCA: 130] [Impact Index Per Article: 14.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2014] [Accepted: 02/26/2015] [Indexed: 11/02/2022]
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221
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An adiabatic quantum algorithm and its application to DNA motif model discovery. Inf Sci (N Y) 2015. [DOI: 10.1016/j.ins.2014.10.057] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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222
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Rare Earth-Doped Crystals for Quantum Information Processing. HANDBOOK ON THE PHYSICS AND CHEMISTRY OF RARE EARTHS 2015. [DOI: 10.1016/b978-0-444-63260-9.00267-4] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/03/2022]
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223
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Nishimori H, Tsuda J, Knysh S. Comparative study of the performance of quantum annealing and simulated annealing. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:012104. [PMID: 25679567 DOI: 10.1103/physreve.91.012104] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2014] [Indexed: 06/04/2023]
Abstract
Relations of simulated annealing and quantum annealing are studied by a mapping from the transition matrix of classical Markovian dynamics of the Ising model to a quantum Hamiltonian and vice versa. It is shown that these two operators, the transition matrix and the Hamiltonian, share the eigenvalue spectrum. Thus, if simulated annealing with slow temperature change does not encounter a difficulty caused by an exponentially long relaxation time at a first-order phase transition, the same is true for the corresponding process of quantum annealing in the adiabatic limit. One of the important differences between the classical-to-quantum mapping and the converse quantum-to-classical mapping is that the Markovian dynamics of a short-range Ising model is mapped to a short-range quantum system, but the converse mapping from a short-range quantum system to a classical one results in long-range interactions. This leads to a difference in efficiencies that simulated annealing can be efficiently simulated by quantum annealing but the converse is not necessarily true. We conclude that quantum annealing is easier to implement and is more flexible than simulated annealing. We also point out that the present mapping can be extended to accommodate explicit time dependence of temperature, which is used to justify the quantum-mechanical analysis of simulated annealing by Somma, Batista, and Ortiz. Additionally, an alternative method to solve the nonequilibrium dynamics of the one-dimensional Ising model is provided through the classical-to-quantum mapping.
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Affiliation(s)
- Hidetoshi Nishimori
- Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan
| | - Junichi Tsuda
- Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan
| | - Sergey Knysh
- QuAIL, NASA Ames Research Center, Moffett Field, California 94035, USA and SGT Inc., 7701 Greenbelt Road, Suite 400, Greenbelt, Maryland 20770, USA
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224
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Babbush R, Love PJ, Aspuru-Guzik A. Adiabatic quantum simulation of quantum chemistry. Sci Rep 2014; 4:6603. [PMID: 25308187 PMCID: PMC4194464 DOI: 10.1038/srep06603] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2014] [Accepted: 09/22/2014] [Indexed: 11/09/2022] Open
Abstract
We show how to apply the quantum adiabatic algorithm directly to the quantum computation of molecular properties. We describe a procedure to map electronic structure Hamiltonians to 2-body qubit Hamiltonians with a small set of physically realizable couplings. By combining the Bravyi-Kitaev construction to map fermions to qubits with perturbative gadgets to reduce the Hamiltonian to 2-body, we obtain precision requirements on the coupling strengths and a number of ancilla qubits that scale polynomially in the problem size. Hence our mapping is efficient. The required set of controllable interactions includes only two types of interaction beyond the Ising interactions required to apply the quantum adiabatic algorithm to combinatorial optimization problems. Our mapping may also be of interest to chemists directly as it defines a dictionary from electronic structure to spin Hamiltonians with physical interactions.
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Affiliation(s)
- Ryan Babbush
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138 USA
| | - Peter J. Love
- Department of Physics, Haverford College, Haverford, PA 19041, USA
| | - Alán Aspuru-Guzik
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138 USA
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225
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Horsman C, Stepney S, Wagner RC, Kendon V. When does a physical system compute? Proc Math Phys Eng Sci 2014; 470:20140182. [PMID: 25197245 PMCID: PMC4123767 DOI: 10.1098/rspa.2014.0182] [Citation(s) in RCA: 83] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2014] [Accepted: 06/11/2014] [Indexed: 11/16/2022] Open
Abstract
Computing is a high-level process of a physical system. Recent interest in non-standard computing systems, including quantum and biological computers, has brought this physical basis of computing to the forefront. There has been, however, no consensus on how to tell if a given physical system is acting as a computer or not; leading to confusion over novel computational devices, and even claims that every physical event is a computation. In this paper, we introduce a formal framework that can be used to determine whether a physical system is performing a computation. We demonstrate how the abstract computational level interacts with the physical device level, in comparison with the use of mathematical models in experimental science. This powerful formulation allows a precise description of experiments, technology, computation and simulation, giving our central conclusion: physical computing is the use of a physical system to predict the outcome of an abstract evolution. We give conditions for computing, illustrated using a range of non-standard computing scenarios. The framework also covers broader computing contexts, where there is no obvious human computer user. We introduce the notion of a ‘computational entity’, and its critical role in defining when computing is taking place in physical systems.
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Affiliation(s)
- Clare Horsman
- Department of Computer Science , University of Oxford , Oxford OX1 3QD, UK
| | - Susan Stepney
- Department of Computer Science, and York Centre for Complex Systems Analysis , University of York , York YO10 5GH, UK
| | - Rob C Wagner
- School of Physics and Astronomy, University of Leeds , Leeds LS2 9JT, UK
| | - Viv Kendon
- School of Physics and Astronomy, University of Leeds , Leeds LS2 9JT, UK
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226
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Vinci W, Markström K, Boixo S, Roy A, Spedalieri FM, Warburton PA, Severini S. Hearing the shape of the Ising model with a programmable superconducting-flux annealer. Sci Rep 2014; 4:5703. [PMID: 25029660 PMCID: PMC4103701 DOI: 10.1038/srep05703] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2014] [Accepted: 06/26/2014] [Indexed: 11/09/2022] Open
Abstract
Two objects can be distinguished if they have different measurable properties. Thus, distinguishability depends on the Physics of the objects. In considering graphs, we revisit the Ising model as a framework to define physically meaningful spectral invariants. In this context, we introduce a family of refinements of the classical spectrum and consider the quantum partition function. We demonstrate that the energy spectrum of the quantum Ising Hamiltonian is a stronger invariant than the classical one without refinements. For the purpose of implementing the related physical systems, we perform experiments on a programmable annealer with superconducting flux technology. Departing from the paradigm of adiabatic computation, we take advantage of a noisy evolution of the device to generate statistics of low energy states. The graphs considered in the experiments have the same classical partition functions, but different quantum spectra. The data obtained from the annealer distinguish non-isomorphic graphs via information contained in the classical refinements of the functions but not via the differences in the quantum spectra.
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Affiliation(s)
- Walter Vinci
- London Centre for Nanotechnology, University College London, WC1E 6BT London, UK
| | - Klas Markström
- Department of Mathematics and Mathematical Statistics, Umeå University, S-901 87 Umeå, Sweden
| | - Sergio Boixo
- 1] Information Sciences Institute and Ming-Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, CA 90089, USA [2] Google, Venice Beach, CA 90292, U.S.A
| | - Aidan Roy
- D-Wave Systems Inc., 100-4401 Still Creek Drive, Burnaby, BC V5C 6G9, Canada
| | - Federico M Spedalieri
- Information Sciences Institute and Ming-Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, CA 90089, USA
| | - Paul A Warburton
- London Centre for Nanotechnology, University College London, WC1E 6BT London, UK
| | - Simone Severini
- Department of Computer Science, and Department of Physics & Astronomy, University College London, WC1E 6BT London, UK
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227
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Otsubo Y, Inoue JI, Nagata K, Okada M. Code-division multiple-access multiuser demodulator by using quantum fluctuations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:012126. [PMID: 25122270 DOI: 10.1103/physreve.90.012126] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/08/2014] [Indexed: 06/03/2023]
Abstract
We examine the average-case performance of a code-division multiple-access (CDMA) multiuser demodulator in which quantum fluctuations are utilized to demodulate the original message within the context of Bayesian inference. The quantum fluctuations are built into the system as a transverse field in the infinite-range Ising spin glass model. We evaluate the performance measurements by using statistical mechanics. We confirm that the CDMA multiuser modulator using quantum fluctuations achieve roughly the same performance as the conventional CDMA multiuser modulator through thermal fluctuations on average. We also find that the relationship between the quality of the original information retrieval and the amplitude of the transverse field is somehow a "universal feature" in typical probabilistic information processing, viz., in image restoration, error-correcting codes, and CDMA multiuser demodulation.
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Affiliation(s)
- Yosuke Otsubo
- Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa, Chiba 277-5861, Japan
| | - Jun-Ichi Inoue
- Graduate School of Information Science and Technology, Hokkaido University, Sapporo 060-0814, Japan
| | - Kenji Nagata
- Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa, Chiba 277-5861, Japan
| | - Masato Okada
- Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa, Chiba 277-5861, Japan and Brain Science Institute, RIKEN, Wako, Saitama 351-0198, Japan
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228
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Rønnow TF, Wang Z, Job J, Boixo S, Isakov SV, Wecker D, Martinis JM, Lidar DA, Troyer M. Quantum computing. Defining and detecting quantum speedup. Science 2014; 345:420-4. [PMID: 25061205 DOI: 10.1126/science.1252319] [Citation(s) in RCA: 88] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
The development of small-scale quantum devices raises the question of how to fairly assess and detect quantum speedup. Here, we show how to define and measure quantum speedup and how to avoid pitfalls that might mask or fake such a speedup. We illustrate our discussion with data from tests run on a D-Wave Two device with up to 503 qubits. By using random spin glass instances as a benchmark, we found no evidence of quantum speedup when the entire data set is considered and obtained inconclusive results when comparing subsets of instances on an instance-by-instance basis. Our results do not rule out the possibility of speedup for other classes of problems and illustrate the subtle nature of the quantum speedup question.
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Affiliation(s)
- Troels F Rønnow
- Theoretische Physik, ETH (Eidgenössische Technische Hochschule) Zurich, 8093 Zurich, Switzerland
| | - Zhihui Wang
- Department of Chemistry, University of Southern California, Los Angeles, CA 90089, USA. Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, CA 90089, USA
| | - Joshua Job
- Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, CA 90089, USA. Department of Physics, University of Southern California, Los Angeles, CA 90089, USA
| | - Sergio Boixo
- Google, 150 Main Street, Venice Beach, CA 90291, USA. Information Sciences Institute, University of Southern California, Los Angeles, CA 90089, USA
| | | | - David Wecker
- Quantum Architectures and Computation Group, Microsoft Research, Redmond, WA 98052, USA
| | - John M Martinis
- Department of Physics, University of California Santa Barbara, CA 93106-9530, USA
| | - Daniel A Lidar
- Department of Chemistry, University of Southern California, Los Angeles, CA 90089, USA. Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, CA 90089, USA. Department of Physics, University of Southern California, Los Angeles, CA 90089, USA. Information Sciences Institute, University of Southern California, Los Angeles, CA 90089, USA. Department of Electrical Engineering, University of Southern California, Los Angeles, CA 90089, USA
| | - Matthias Troyer
- Theoretische Physik, ETH (Eidgenössische Technische Hochschule) Zurich, 8093 Zurich, Switzerland.
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229
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Clark KB. Basis for a neuronal version of Grover's quantum algorithm. Front Mol Neurosci 2014; 7:29. [PMID: 24860419 PMCID: PMC4029008 DOI: 10.3389/fnmol.2014.00029] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2014] [Accepted: 03/31/2014] [Indexed: 11/25/2022] Open
Abstract
Grover's quantum (search) algorithm exploits principles of quantum information theory and computation to surpass the strong Church–Turing limit governing classical computers. The algorithm initializes a search field into superposed N (eigen)states to later execute nonclassical “subroutines” involving unitary phase shifts of measured states and to produce root-rate or quadratic gain in the algorithmic time (O(N1/2)) needed to find some “target” solution m. Akin to this fast technological search algorithm, single eukaryotic cells, such as differentiated neurons, perform natural quadratic speed-up in the search for appropriate store-operated Ca2+ response regulation of, among other processes, protein and lipid biosynthesis, cell energetics, stress responses, cell fate and death, synaptic plasticity, and immunoprotection. Such speed-up in cellular decision making results from spatiotemporal dynamics of networked intracellular Ca2+-induced Ca2+ release and the search (or signaling) velocity of Ca2+ wave propagation. As chemical processes, such as the duration of Ca2+ mobilization, become rate-limiting over interstore distances, Ca2+ waves quadratically decrease interstore-travel time from slow saltatory to fast continuous gradients proportional to the square-root of the classical Ca2+ diffusion coefficient, D1/2, matching the computing efficiency of Grover's quantum algorithm. In this Hypothesis and Theory article, I elaborate on these traits using a fire-diffuse-fire model of store-operated cytosolic Ca2+ signaling valid for glutamatergic neurons. Salient model features corresponding to Grover's quantum algorithm are parameterized to meet requirements for the Oracle Hadamard transform and Grover's iteration. A neuronal version of Grover's quantum algorithm figures to benefit signal coincidence detection and integration, bidirectional synaptic plasticity, and other vital cell functions by rapidly selecting, ordering, and/or counting optional response regulation choices.
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Affiliation(s)
- Kevin B Clark
- Research and Development Service, Veterans Affairs Greater Los Angeles Healthcare System Los Angeles, CA, USA ; Complex Biological Systems Alliance North Andover, MA, USA
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230
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Kurcz A, Bermudez A, García-Ripoll JJ. Hybrid quantum magnetism in circuit QED: from spin-photon waves to many-body spectroscopy. PHYSICAL REVIEW LETTERS 2014; 112:180405. [PMID: 24856680 DOI: 10.1103/physrevlett.112.180405] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/26/2013] [Indexed: 06/03/2023]
Abstract
We introduce a model of quantum magnetism induced by the nonperturbative exchange of microwave photons between distant superconducting qubits. By interconnecting qubits and cavities, we obtain a spin-boson lattice model that exhibits a quantum phase transition where both qubits and cavities spontaneously polarize. We present a many-body ansatz that captures this phenomenon all the way, from a the perturbative dispersive regime where photons can be traced out, to the nonperturbative ultrastrong coupling regime where photons must be treated on the same footing as qubits. Our ansatz also reproduces the low-energy excitations, which are described by hybridized spin-photon quasiparticles, and can be probed spectroscopically from transmission experiments in circuit QED, as shown by simulating a possible experiment by matrix-product-state methods.
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Affiliation(s)
- Andreas Kurcz
- Instituto de Física Fundamental, IFF-CSIC, Calle Serrano 113 b, Madrid E-28006, Spain
| | - Alejandro Bermudez
- Instituto de Física Fundamental, IFF-CSIC, Calle Serrano 113 b, Madrid E-28006, Spain
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231
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Babbush R, Perdomo-Ortiz A, O'Gorman B, Macready W, Aspuru-Guzik A. Construction of Energy Functions for Lattice Heteropolymer Models: Efficient Encodings for Constraint Satisfaction Programming and Quantum Annealing. ADVANCES IN CHEMICAL PHYSICS 2014. [DOI: 10.1002/9781118755815.ch05] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/05/2023]
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232
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Kais S. Introduction to Quantum Information and Computation for Chemistry. ADVANCES IN CHEMICAL PHYSICS 2014. [DOI: 10.1002/9781118742631.ch01] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
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233
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Back to The Future: A Roadmap for Quantum Simulation From Vintage Quantum Chemistry. ADVANCES IN CHEMICAL PHYSICS 2014. [DOI: 10.1002/9781118742631.ch02] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register]
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234
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Using thermal boundary conditions to engineer the quantum state of a bulk magnet. Proc Natl Acad Sci U S A 2014; 111:3689-94. [PMID: 24567389 DOI: 10.1073/pnas.1316070111] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The degree of contact between a system and the external environment can alter dramatically its proclivity to quantum mechanical modes of relaxation. We show that controlling the thermal coupling of cubic-centimeter-sized crystals of the Ising magnet LiHo(x)Y(1-x)F4 to a heat bath can be used to tune the system between a glassy state dominated by thermal excitations over energy barriers and a state with the hallmarks of a quantum spin liquid. Application of a magnetic field transverse to the Ising axis introduces both random magnetic fields and quantum fluctuations, which can retard and speed the annealing process, respectively, thereby providing a mechanism for continuous tuning between the destination states. The nonlinear response of the system explicitly demonstrates quantum interference between internal and external relaxation pathways.
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235
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Quantum phases in circuit QED with a superconducting qubit array. Sci Rep 2014; 4:4083. [PMID: 24522250 PMCID: PMC3923215 DOI: 10.1038/srep04083] [Citation(s) in RCA: 41] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2013] [Accepted: 01/27/2014] [Indexed: 11/21/2022] Open
Abstract
Circuit QED on a chip has become a powerful platform for simulating complex many-body physics. In this report, we realize a Dicke-Ising model with an antiferromagnetic nearest-neighbor spin-spin interaction in circuit QED with a superconducting qubit array. We show that this system exhibits a competition between the collective spin-photon interaction and the antiferromagnetic nearest-neighbor spin-spin interaction, and then predict four quantum phases, including: a paramagnetic normal phase, an antiferromagnetic normal phase, a paramagnetic superradiant phase, and an antiferromagnetic superradiant phase. The antiferromagnetic normal phase and the antiferromagnetic superradiant phase are new phases in many-body quantum optics. In the antiferromagnetic superradiant phase, both the antiferromagnetic and superradiant orders can coexist, and thus the system possesses symmetry. Moreover, we find an unconventional photon signature in this phase. In future experiments, these predicted quantum phases could be distinguished by detecting both the mean-photon number and the magnetization.
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236
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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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237
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Cai Z, Barthel T. Algebraic versus Exponential Decoherence in Dissipative Many-Particle Systems. PHYSICAL REVIEW LETTERS 2013; 111:150403. [PMID: 24160582 DOI: 10.1103/physrevlett.111.150403] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2013] [Indexed: 06/02/2023]
Abstract
The interplay between dissipation and internal interactions in quantum many-body systems gives rise to a wealth of novel phenomena. Here we investigate spin-1/2 chains with uniform local couplings to a Markovian environment using the time-dependent density matrix renormalization group. For the open XXZ model, we discover that the decoherence time diverges in the thermodynamic limit. The coherence decay is then algebraic instead of exponential. This is due to a vanishing gap in the spectrum of the corresponding Liouville superoperator and can be explained on the basis of a perturbative treatment. In contrast, decoherence in the open transverse-field Ising model is found to be always exponential. In this case, the internal interactions can both facilitate and impede the environment-induced decoherence.
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Affiliation(s)
- Zi Cai
- Department of Physics and Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, 80333 Munich, Germany
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238
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Bian Z, Chudak F, Macready WG, Clark L, Gaitan F. Experimental determination of Ramsey numbers. PHYSICAL REVIEW LETTERS 2013; 111:130505. [PMID: 24116761 DOI: 10.1103/physrevlett.111.130505] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2012] [Revised: 07/31/2013] [Indexed: 06/02/2023]
Abstract
Ramsey theory is a highly active research area in mathematics that studies the emergence of order in large disordered structures. Ramsey numbers mark the threshold at which order first appears and are extremely difficult to calculate due to their explosive rate of growth. Recently, an algorithm that can be implemented using adiabatic quantum evolution has been proposed that calculates the two-color Ramsey numbers R(m,n). Here we present results of an experimental implementation of this algorithm and show that it correctly determines the Ramsey numbers R(3,3) and R(m,2) for 4≤m≤8. The R(8,2) computation used 84 qubits of which 28 were computational qubits. This computation is the largest experimental implementation of a scientifically meaningful adiabatic evolution algorithm that has been done to date.
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Affiliation(s)
- Zhengbing Bian
- D-Wave Systems, Inc., 100-4401 Still Creek Drive, Burnaby, British Columbia V5C 6G9, Canada
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239
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Open access integrated therapeutic and diagnostic platforms for personalized cardiovascular medicine. J Pers Med 2013; 3:203-37. [PMID: 25562653 PMCID: PMC4251391 DOI: 10.3390/jpm3030203] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2013] [Revised: 08/04/2013] [Accepted: 08/10/2013] [Indexed: 12/14/2022] Open
Abstract
It is undeniable that the increasing costs in healthcare are a concern. Although technological advancements have been made in healthcare systems, the return on investment made by governments and payers has been poor. The current model of care is unsustainable and is due for an upgrade. In developed nations, a law of diminishing returns has been noted in population health standards, whilst in the developing world, westernized chronic illnesses, such as diabetes and cardiovascular disease have become emerging problems. The reasons for these trends are complex, multifactorial and not easily reversed. Personalized medicine has the potential to have a significant impact on these issues, but for it to be truly successful, interdisciplinary mass collaboration is required. We propose here a vision for open-access advanced analytics for personalized cardiac diagnostics using imaging, electrocardiography and genomics.
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240
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Experimental signature of programmable quantum annealing. Nat Commun 2013; 4:2067. [DOI: 10.1038/ncomms3067] [Citation(s) in RCA: 184] [Impact Index Per Article: 16.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2012] [Accepted: 05/27/2013] [Indexed: 11/08/2022] Open
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241
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242
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Thermally assisted quantum annealing of a 16-qubit problem. Nat Commun 2013; 4:1903. [DOI: 10.1038/ncomms2920] [Citation(s) in RCA: 160] [Impact Index Per Article: 14.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2013] [Accepted: 04/23/2013] [Indexed: 11/09/2022] Open
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243
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Viehmann O, von Delft J, Marquardt F. Observing the nonequilibrium dynamics of the quantum transverse-field Ising chain in circuit QED. PHYSICAL REVIEW LETTERS 2013; 110:030601. [PMID: 23373908 DOI: 10.1103/physrevlett.110.030601] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2012] [Indexed: 06/01/2023]
Abstract
We show how a quantum Ising spin chain in a time-dependent transverse magnetic field can be simulated and experimentally probed in the framework of circuit QED with current technology. The proposed setup provides a new platform for observing the nonequilibrium dynamics of interacting many-body systems. We calculate its spectrum to offer a guideline for its initial experimental characterization. We demonstrate that quench dynamics and the propagation of localized excitations can be observed with the proposed setup and discuss further possible applications and modifications of this circuit QED quantum simulator.
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Affiliation(s)
- Oliver Viehmann
- Physics Department, Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität, München, Germany
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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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Abstract
Quantum coherence is one of the primary non-classical features of quantum systems. While protocols such as the Leggett-Garg inequality (LGI) and quantum tomography can be used to test for the existence of quantum coherence and dynamics in a given system, unambiguously detecting inherent "quantumness" still faces serious obstacles in terms of experimental feasibility and efficiency, particularly in complex systems. Here we introduce two "quantum witnesses" to efficiently verify quantum coherence and dynamics in the time domain, without the expense and burden of non-invasive measurements or full tomographic processes. Using several physical examples, including quantum transport in solid-state nanostructures and in biological organisms, we show that these quantum witnesses are robust and have a much finer resolution in their detection window than the LGI has. These robust quantum indicators may assist in reducing the experimental overhead in unambiguously verifying quantum coherence in complex systems.
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Perdomo-Ortiz A, Dickson N, Drew-Brook M, Rose G, Aspuru-Guzik A. Finding low-energy conformations of lattice protein models by quantum annealing. Sci Rep 2012; 2:571. [PMID: 22891157 PMCID: PMC3417777 DOI: 10.1038/srep00571] [Citation(s) in RCA: 95] [Impact Index Per Article: 7.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2012] [Accepted: 07/16/2012] [Indexed: 12/02/2022] Open
Abstract
Lattice protein folding models are a cornerstone of computational biophysics. Although these models are a coarse grained representation, they provide useful insight into the energy landscape of natural proteins. Finding low-energy threedimensional structures is an intractable problem even in the simplest model, the Hydrophobic-Polar (HP) model. Description of protein-like properties are more accurately described by generalized models, such as the one proposed by Miyazawa and Jernigan (MJ), which explicitly take into account the unique interactions among all 20 amino acids. There is theoretical and experimental evidence of the advantage of solving classical optimization problems using quantum annealing over its classical analogue (simulated annealing). In this report, we present a benchmark implementation of quantum annealing for lattice protein folding problems (six different experiments up to 81 superconducting quantum bits). This first implementation of a biophysical problem paves the way towards studying optimization problems in biophysics and statistical mechanics using quantum devices.
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Affiliation(s)
- Alejandro Perdomo-Ortiz
- Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, MA 02138, USA
| | - Neil Dickson
- D-Wave Systems, Inc., 100-4401 Still Creek Drive, Burnaby, British Columbia V5C 6G9, Canada
| | - Marshall Drew-Brook
- D-Wave Systems, Inc., 100-4401 Still Creek Drive, Burnaby, British Columbia V5C 6G9, Canada
| | - Geordie Rose
- D-Wave Systems, Inc., 100-4401 Still Creek Drive, Burnaby, British Columbia V5C 6G9, Canada
| | - Alán Aspuru-Guzik
- Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, MA 02138, USA
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Garnerone S, Zanardi P, Lidar DA. Adiabatic quantum algorithm for search engine ranking. PHYSICAL REVIEW LETTERS 2012; 108:230506. [PMID: 23003933 DOI: 10.1103/physrevlett.108.230506] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2011] [Indexed: 06/01/2023]
Abstract
We propose an adiabatic quantum algorithm for generating a quantum pure state encoding of the PageRank vector, the most widely used tool in ranking the relative importance of internet pages. We present extensive numerical simulations which provide evidence that this algorithm can prepare the quantum PageRank state in a time which, on average, scales polylogarithmically in the number of web pages. We argue that the main topological feature of the underlying web graph allowing for such a scaling is the out-degree distribution. The top-ranked log(n) entries of the quantum PageRank state can then be estimated with a polynomial quantum speed-up. Moreover, the quantum PageRank state can be used in "q-sampling" protocols for testing properties of distributions, which require exponentially fewer measurements than all classical schemes designed for the same task. This can be used to decide whether to run a classical update of the PageRank.
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Affiliation(s)
- Silvano Garnerone
- Institute for Quantum Computing, University of Waterloo, Waterloo, ON N2L 3G1, Canada
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