Quantum-Assisted Greedy Algorithms

We show how to leverage quantum annealers (QAs) to better select candidates in greedy algorithms. Unlike conventional greedy algorithms that employ problem-specific heuristics for making locally optimal choices at each stage, we use QAs that sample from the ground state of a problem-dependent Hamiltonians at cryogenic temperatures and use retrieved samples to estimate the probability distribution of problem variables. More specifically, we look at each spin of the Ising model as a random variable and contract all problem variables whose corresponding uncertainties are negligible. Our empirical results on a D-Wave 2000Q quantum proces-sor demonstrate that the proposed quantum-assisted greedy algorithm (QAGA) scheme can find notably better solutions compared to the state-of-the-art techniques in the realm of quantum annealing.

[1]  John Preskill,et al.  Information-theoretic bounds on quantum advantage in machine learning , 2021, Physical review letters.

[2]  Tim Finin,et al.  Multi-qubit correction for quantum annealers , 2020, Scientific Reports.

[3]  Tim Finin,et al.  Reinforcement Quantum Annealing: A Hybrid Quantum Learning Automata , 2020, Scientific Reports.

[4]  Catherine C. McGeoch,et al.  Theory versus practice in annealing-based quantum computing , 2020, Theor. Comput. Sci..

[5]  Aidan Roy,et al.  Next-Generation Topology of D-Wave Quantum Processors , 2020, 2003.00133.

[6]  Ramin Ayanzadeh,et al.  Leveraging Artificial Intelligence to Advance Problem-Solving with Quantum Annealers , 2020 .

[7]  Tim Finin,et al.  Reinforcement Quantum Annealing: A Quantum-Assisted Learning Automata Approach , 2020, ArXiv.

[8]  Ramin Ayanzadeh,et al.  A Survey on Compressive Sensing: Classical Results and Recent Advancements , 2019, ArXiv.

[9]  Hristo Djidjev,et al.  Optimizing the Spin Reversal Transform on the D-Wave 2000Q , 2019, 2019 IEEE International Conference on Rebooting Computing (ICRC).

[10]  Masoud Mohseni,et al.  Quantum-Assisted Genetic Algorithm , 2019, ArXiv.

[11]  Timothy W. Finin,et al.  SAT-based Compressive Sensing , 2019, ArXiv.

[12]  John E. Dorband,et al.  Applying Multi-qubit Correction to Frustrated Cluster Loops on an Adiabatic Quantum Computer , 2019, ArXiv.

[13]  Shinichiro Taguchi,et al.  Improving solutions by embedding larger subproblems in a D-Wave quantum annealer , 2019, Scientific Reports.

[14]  Timothy W. Finin,et al.  Quantum Annealing Based Binary Compressive Sensing with Matrix Uncertainty , 2019, ArXiv.

[15]  John E. Dorband,et al.  Extending the D-Wave with support for Higher Precision Coefficients , 2018, ArXiv.

[16]  John E. Dorband,et al.  A Method of Finding a Lower Energy Solution to a QUBO/Ising Objective Function , 2018, ArXiv.

[17]  John Preskill,et al.  Quantum Computing in the NISQ era and beyond , 2018, Quantum.

[18]  Hans-J. Briegel,et al.  Machine learning \& artificial intelligence in the quantum domain , 2017, ArXiv.

[19]  Wojciech H. Zurek,et al.  Defects in Quantum Computers , 2017, Scientific Reports.

[20]  Rupak Biswas,et al.  A NASA perspective on quantum computing: Opportunities and challenges , 2017, Parallel Comput..

[21]  Velimir V. Vesselinov,et al.  Nonnegative/Binary matrix factorization with a D-Wave quantum annealer , 2017, PloS one.

[22]  Lucas Lamata,et al.  Basic protocols in quantum reinforcement learning with superconducting circuits , 2017, Scientific Reports.

[23]  Jacob biamonte,et al.  Quantum machine learning , 2016, Nature.

[24]  Hidetoshi Nishimori,et al.  Exponential Enhancement of the Efficiency of Quantum Annealing by Non-Stoquastic Hamiltonians , 2016, Frontiers ICT.

[25]  J. Christopher Beck,et al.  A Hybrid Quantum-Classical Approach to Solving Scheduling Problems , 2016, SOCS.

[26]  Aidan Roy,et al.  Mapping Constrained Optimization Problems to Quantum Annealing with Application to Fault Diagnosis , 2016, Front. ICT.

[27]  Steven H. Adachi,et al.  Application of Quantum Annealing to Training of Deep Neural Networks , 2015, ArXiv.

[28]  D. Venturelli,et al.  Quantum Annealing Implementation of Job-Shop Scheduling , 2015 .

[29]  Aidan Roy,et al.  Discrete optimization using quantum annealing on sparse Ising models , 2014, Front. Phys..

[30]  Daniel A. Lidar,et al.  Quantum annealing correction for random Ising problems , 2014, 1408.4382.

[31]  Zoran Levnajić,et al.  Frontiers in ICT , 2014 .

[32]  Bryan O'Gorman,et al.  A case study in programming a quantum annealer for hard operational planning problems , 2014, Quantum Information Processing.

[33]  Aidan Roy,et al.  A practical heuristic for finding graph minors , 2014, ArXiv.

[34]  Dmitri V. Averin,et al.  Decoherence induced deformation of the ground state in adiabatic quantum computation , 2012, Scientific Reports.

[35]  M. W. Johnson,et al.  Quantum annealing with manufactured spins , 2011, Nature.

[36]  Masayuki Ohzeki,et al.  Quantum annealing: An introduction and new developments , 2010, 1006.1696.

[37]  Kurunathan Ratnavelu,et al.  FRONTIERS IN PHYSICS , 2009 .

[38]  H. Nishimori,et al.  Quantum annealing in the transverse Ising model , 1998, cond-mat/9804280.

[39]  Ronald A. DeVore,et al.  Some remarks on greedy algorithms , 1996, Adv. Comput. Math..

[40]  J. D. Doll,et al.  Quantum annealing: A new method for minimizing multidimensional functions , 1994, chem-ph/9404003.