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Relaxation of the EM algorithm via quantum annealing

Hideyuki Miyahara, Koji Tsumura
2016 2016 American Control Conference (ACC)  

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2016 pre-print arXiv:1606.01484v1 fatcat:kzdqunisr5bvfkys7uk5w6cysq
In order to deal with this difficulty, we propose a deterministic quantum annealing EM algorithm by introducing the mathematical mechanism of quantum fluctuations into the conventional EM algorithm because  ...  quantum fluctuations induce the tunnel effect and are expected to relax the difficulty of nonconvex optimization problems in the maximum likelihood estimation problems.  ...  Deterministic quantum annealing EM algorithm (DQAEM) Here, we derive DQAEM, which is the main concept of this paper, by introducing the mechanism of quantum fluctuations into EM.  ... 
doi:10.1109/acc.2016.7526110 dblp:conf/amcc/MiyaharaT16 fatcat:eiptzezncnfxplro2al4iezyla
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Hideyuki Miyahara, Koji Tsumura. "Relaxation of the EM algorithm via quantum annealing." 2016 American Control Conference (ACC) (2016) 4779-4784

Relaxation of the EM algorithm via quantum annealing for Gaussian mixture models

Hideyuki Miyahara, Koji Tsumura, Yuki Sughiyama
2016 2016 IEEE 55th Conference on Decision and Control (CDC)  

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2017 pre-print arXiv:1701.03268v1 fatcat:j4sb3qdfujarhftylvuha5h4ni
We propose a modified expectation-maximization algorithm by introducing the concept of quantum annealing, which we call the deterministic quantum annealing expectation-maximization (DQAEM) algorithm.  ...  The expectation-maximization (EM) algorithm is an established algorithm to compute maximum likelihood estimates and applied to many practical applications.  ...  To relax the problem, Ueda and Nakano proposed a deterministic simulated annealing expectation-maximization (DSAEM) algorithm 1 , and it succeeds to relax the difficulty of the multimodality in EM.  ... 
doi:10.1109/cdc.2016.7798981 dblp:conf/cdc/MiyaharaTS16 fatcat:jmx25rojvjfilayd2nv4ob66ka
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Hideyuki Miyahara, Koji Tsumura, Yuki Sughiyama. "Relaxation of the EM algorithm via quantum annealing for Gaussian mixture models." 2016 IEEE 55th Conference on Decision and Control (CDC) (2016) 4674-4679

Deterministic quantum annealing expectation-maximization algorithm

Hideyuki Miyahara, Koji Tsumura, Yuki Sughiyama
2017 Journal of Statistical Mechanics: Theory and Experiment  

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2017 pre-print arXiv:1704.05822v1 fatcat:bqe3hfedc5dhdihs6vtx7rc4ny
Motivated by QA, we propose a quantum annealing extension of EM, which we call the deterministic quantum annealing expectation-maximization (DQAEM) algorithm.  ...  On the other hand, in the field of physics, quantum annealing (QA) was proposed as a novel optimization approach.  ...  of Science.  ... 
doi:10.1088/1742-5468/aa967e fatcat:3jljtpayhbekddbyofuqhq3wa4
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Hideyuki Miyahara, Koji Tsumura, Yuki Sughiyama. "Deterministic quantum annealing expectation-maximization algorithm." Journal of Statistical Mechanics: Theory and Experiment 2017.11 (2017) 113404

Quantum annealing correction with minor embedding

Walter Vinci, Tameem Albash, Gerardo Paz-Silva, Itay Hen, Daniel A. Lidar
2015 Physical Review A. Atomic, Molecular, and Optical Physics  

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2015 pre-print
arXiv:1507.02658v1 fatcat:7zsze5uiezggjjofcwfs4ge2em
Quantum annealing provides a promising route for the development of quantum optimization devices, but the usefulness of such devices will be limited in part by the range of implementable problems as dictated  ...  We introduce and study quantum annealing correction schemes designed to improve the performance of quantum annealers in conjunction with minor embedding, thus leading to a hybrid scheme defined over an  ...  Access to the D-Wave Two was made avail-  ... 
doi:10.1103/physreva.92.042310 fatcat:z4u2bjocwjcrdis6ddfpfj7ola
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Walter Vinci, Tameem Albash, Gerardo Paz-Silva, Itay Hen, Daniel A. Lidar. "Quantum annealing correction with minor embedding." Physical Review A. Atomic, Molecular, and Optical Physics 92.4 (2015)

Engineering Reflective Metasurfaces with Ising Hamiltonian and Quantum Annealing

Charles Ross, Gabriele Gradoni, Qi Jian Lim, Zhen Peng
2021 IEEE Transactions on Antennas and Propagation  

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To rapidly explore the configuration states, we encode the Ising coefficients with quantum annealing algorithms, taking advantage of the fact that the adiabatic evolution efficiently performs energy minimization  ...  Thereby, the problem of achieving the scattering profile is recast into finding the ground-state solution of the associated Ising Hamiltonian.  ...  Simulated annealing performs the energy minimization of Ising Hamiltonian via the implementation of Metropolis-Hasting algorithm on classical machines.  ... 
doi:10.1109/tap.2021.3137424 fatcat:boneqvjfwbhtnble4a44tak3eu
Open Access
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Charles Ross, Gabriele Gradoni, Qi Jian Lim, Zhen Peng. "Engineering Reflective Metasurfaces with Ising Hamiltonian and Quantum Annealing." IEEE Transactions on Antennas and Propagation 70.4 (2021) 1-1

Reverse Quantum Annealing Approach to Portfolio Optimization Problems [article]

Davide Venturelli, Alexei Kondratyev
2018 arXiv   pre-print

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2018 pre-print
arXiv:1810.08584v1 fatcat:ql2upfcaznaz3isedxyhu4iecy
binary optimization forms programmable in the analog D-Wave Quantum Annealer 2000Q.  ...  The optimized reverse annealing protocol is found to be more than 100 times faster than the corresponding forward quantum annealing on average.  ...  trap during the reverse annealing, while the annealing pause (and to some extent the final forward annealing) allows the system to thermalize and relax in the neighborhood of the newfound  ... 
arXiv:1810.08584v2 fatcat:bwsyahwagjfmlg44y76lnphqvq
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Davide Venturelli, Alexei Kondratyev. "Reverse Quantum Annealing Approach to Portfolio Optimization Problems." arXiv (2018)

Relaxation versus adiabatic quantum steady-state preparation

Lorenzo Campos Venuti, Tameem Albash, Milad Marvian, Daniel Lidar, Paolo Zanardi
2017 Physical Review A  

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2016 pre-print
arXiv:1612.07979v1 fatcat:d76avbyvyvc7zazdwv3helwfwu
2017 accepted
arXiv:1612.07979v2 fatcat:fkv7bdmj6zdc5naqvt3yprkrxu
Adiabatic preparation of the ground states of many-body Hamiltonians in the closed system limit is at the heart of adiabatic quantum computation, but in reality systems are always open.  ...  Using known rigorous bounds for the open-system adiabatic theorem and for mixing times, we are then led to a disturbing conclusion that at first appears to doom efforts to build physical quantum annealers  ...  at realizing physical quantum annealers [42] .  ... 
doi:10.1103/physreva.95.042302 fatcat:g6yax6x42bagjibxz5xrpr3hgq
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Lorenzo Campos Venuti, Tameem Albash, Milad Marvian, Daniel Lidar, Paolo Zanardi. "Relaxation versus adiabatic quantum steady-state preparation." Physical Review A 95.4 (2017)

Quantum relaxation for quadratic programs over orthogonal matrices [article]

Andrew Zhao, Nicholas C. Rubin
2023 arXiv   pre-print

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Determining extremal states of this Hamiltonian provides an outer approximation to the original problem, analogous to classical relaxations of the problem via semidefinite programming.  ...  Finally, to project the relaxed solution into the feasible space, we employ rounding procedures which return orthogonal matrices from appropriate measurements of the quantum state.  ...  ACKNOWLEDGMENTS The authors thank Ryan Babbush, Bill Huggins, Robin Kothari, Jarrod McClean, Chaithanya Rayudu, and Jun Takahashi for helpful discussions and feedback on the manuscript.  ... 
arXiv:2301.01778v1 fatcat:37gx6aomzjeo3a3wi45dbcb6wq
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Citation

Andrew Zhao, Nicholas C. Rubin. "Quantum relaxation for quadratic programs over orthogonal matrices." arXiv (2023)

Optimizing quantum gates towards the scale of logical qubits [article]

Paul V. Klimov, Andreas Bengtsson, Chris Quintana, Alexandre Bourassa, Sabrina Hong, Andrew Dunsworth, Kevin J. Satzinger, William P. Livingston, Volodymyr Sivak, Murphy Y. Niu, Trond I. Andersen, Yaxing Zhang (+12 others)
2024 arXiv   pre-print

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2023 pre-print
arXiv:2308.02321v1 fatcat:ublfvqqs4fagdcl3y6tcd4khxy
2023 pre-print
arXiv:2308.02321v2 fatcat:tlhhk26fv5gexl4yhdfxljnhrm
Our control optimization strategy solves a generic scaling challenge in a way that can be adapted to a variety of quantum operations, algorithms, and computing architectures.  ...  A foundational assumption of quantum error correction theory is that quantum gates can be scaled to large processors without exceeding the error-threshold for fault tolerance.  ...  We thank the broader Google Quantum AI team for fabricating the processor, building and maintaining the cryogenic system, and general hardware and software infrastructure that enabled this experiment.  ... 
arXiv:2308.02321v3 fatcat:6fqksz5dgrd6zhnq5pxj6j3uda
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Paul V. Klimov, Andreas Bengtsson, Chris Quintana, Alexandre Bourassa, Sabrina Hong, Andrew Dunsworth, Kevin J. Satzinger, William P. Livingston, Volodymyr Sivak, Murphy Y. Niu, Trond I. Andersen, Yaxing Zhang, Desmond Chik, Zijun Chen, Charles Neill, Catherine Erickson, Alejandro Grajales Dau, Anthony Megrant, Pedram Roushan, Alexander N. Korotkov, Julian Kelly, Vadim Smelyanskiy, Yu Chen, Hartmut Neven. "Optimizing quantum gates towards the scale of logical qubits." arXiv (2024)

Quantum-Assisted Online Task Offloading and Resource Allocation in MEC-Enabled Satellite-Aerial-Terrestrial Integrated Networks [article]

Yu Zhang, Yanmin Gong, Lei Fan, Yu Wang, Zhu Han, Yuanxiong Guo
2023 arXiv   pre-print

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decomposition (HQCGBD) algorithms to solve the problem efficiently by leveraging quantum advantages in parallel computing.  ...  Numerical results validate the effectiveness of the proposed MEC-enabled SATIN schemes.  ...  Quantum annealing (QA) can be regarded as a relaxed AQC that does not necessarily require universality or adiabaticity [22] .  ... 
arXiv:2312.15808v1 fatcat:ern3tftuuraxtpnhld5r4oee2m
Open Access
Citation

Yu Zhang, Yanmin Gong, Lei Fan, Yu Wang, Zhu Han, Yuanxiong Guo. "Quantum-Assisted Online Task Offloading and Resource Allocation in MEC-Enabled Satellite-Aerial-Terrestrial Integrated Networks." arXiv (2023)

Accelerated Quantum Monte Carlo with Probabilistic Computers [article]

Shuvro Chowdhury, Kerem Y. Camsari, Supriyo Datta
2022 arXiv   pre-print

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The clockless analog hardware can be viewed as the classical counterpart of the quantum annealer and provides performance within a factor of <10 of the latter.  ...  Quantum Monte Carlo (QMC) techniques are widely used in a variety of scientific problems of great interest and much work has been dedicated to developing optimized algorithms that can accelerate QMC on  ...  This obstruction makes it difficult for an algorithm based on local update schemes to escape the obstruction, whereas a quantum annealer might help escape the obstruction faster.  ... 
arXiv:2210.17526v1 fatcat:vsmy2odbszb5xk4twbozdyktwa
Open Access
Citation

Shuvro Chowdhury, Kerem Y. Camsari, Supriyo Datta. "Accelerated Quantum Monte Carlo with Probabilistic Computers." arXiv (2022)

Verification of Quantum Optimizers [article]

Flavio Baccari, Christian Gogolin, Peter Wittek, Antonio Acín
2018 arXiv   pre-print

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2020 accepted
arXiv:1808.01275v2 fatcat:2h7rrdcad5bcng4zp5czek7pfi
We are able to verify the output of a D-Wave 2000Q device for the largest triangular lattice that can be embedded in the hardware and provide exact ground states for cases in which the quantum annealer  ...  This yields certified solutions for many of the problems that are being used to benchmark quantum annealing devices more efficiently and for larger system sizes.  ...  Verifying the solution of a quantum annealer  ... 
arXiv:1808.01275v1 fatcat:pyhd2c24bff2rpt3r4nwoujxmy
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Flavio Baccari, Christian Gogolin, Peter Wittek, Antonio Acín. "Verification of Quantum Optimizers." arXiv (2018)

The Hybrid Idea of (Energy Minimization) Optimization Methods Applied to Study PrionProtein Structures Focusing on the beta2-alpha2 Loop

Jiapu Zhang
2015 Biochemistry & Pharmacology Open Access  

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of the Victorian Government (Australia).  ...  Rubinov in honor of his 75th birthday and this paper was reported in the Workshop on Continuous Optimization: Theory, Methods and Applications, 16-17 April 2015, Ballarat, Australia.  ...  annealing algorithm within the supercomputer CM-5 to be able to solve fast the LJ problem with sizes as large as 100,000 atoms.  ... 
doi:10.4172/2167-0501.1000175 fatcat:ljwjsiajdrdytbi4tjam23bnxy
Citation

Jiapu Zhang. "The Hybrid Idea of (Energy Minimization) Optimization Methods Applied to Study PrionProtein Structures Focusing on the beta2-alpha2 Loop." Biochemistry & Pharmacology Open Access 04.04 (2015)

Error measurements for a quantum annealer using the one-dimensional Ising model with twisted boundaries [article]

Nicholas Chancellor, Philip J. D. Crowley, Tanja Đurić, Walter Vinci, Mohammad H. Amin, Andrew G. Green, Paul A. Warburton, Gabriel Aeppli
2022 arXiv   pre-print

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2020 pre-print
arXiv:2006.07685v1 fatcat:ii3m6sb6trhfxm6e6sps3i2xw4
2021 pre-print
arXiv:2006.07685v2 fatcat:jn4djnmv6rbzfimqbeecydmdnm
If quantum mechanics is introduced via a transverse field, the domain wall will behave as a particle in a box, and prefer to be nearer the middle of the chain rather than the ends.  ...  A simple characteristic of a real quantum annealer is therefore which of these limits obtains in practice.  ...  The authors thank the University of Southern California for allowing access to their D-Wave 2 quantum annealer as well as D-Wave Systems Inc. for access to the intermediategeneration annealer.  ... 
arXiv:2006.07685v3 fatcat:4xu22acbl5h45cc3uwtyac3tzm
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Nicholas Chancellor, Philip J. D. Crowley, Tanja Đurić, Walter Vinci, Mohammad H. Amin, Andrew G. Green, Paul A. Warburton, Gabriel Aeppli. "Error measurements for a quantum annealer using the one-dimensional Ising model with twisted boundaries." arXiv (2022)

Curve fitting on a quantum annealer for an advanced navigation method [article]

Philipp Isserstedt, Daniel Jaroszewski, Wolfgang Mergenthaler, Felix Paul, Bastian Harrach
2024 arXiv   pre-print

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We explore the applicability of quantum annealing to the approximation task of curve fitting.  ...  Given the size of the problem stays below a certain threshold, we find that quantum annealing yields comparable results to the classical solution.  ...  the Development of Scientific and Economic Excellence).  ... 
arXiv:2402.15308v1 fatcat:tn5mcrmlb5g6jkc7pazlwjdnzu
Citation

Philipp Isserstedt, Daniel Jaroszewski, Wolfgang Mergenthaler, Felix Paul, Bastian Harrach. "Curve fitting on a quantum annealer for an advanced navigation method." arXiv (2024)

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