Patch-planting spin-glass solution for benchmarking.

We introduce an algorithm to generate (not solve) spin-glass instances with planted solutions of arbitrary size and structure. First, a set of small problem patches with open boundaries is solved either exactly or with a heuristic, and then the individual patches are stitched together to create a large problem with a known planted solution. Because in these problems frustration is typically smaller than in random problems, we first assess the typical computational complexity of the individual patches using population annealing Monte Carlo, and introduce an approach that allows one to fine-tune the typical computational complexity of the patch-planted system. The scaling of the typical computational complexity of these planted instances with various numbers of patches and patch sizes is investigated and compared to random instances.

[1]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[2]  Károly F. Pál,et al.  The ground state energy of the Edwards-Anderson Ising spin glass with a hybrid genetic algorithm , 1996 .

[3]  K. Hukushima,et al.  Exchange Monte Carlo Method and Application to Spin Glass Simulations , 1995, cond-mat/9512035.

[4]  H. Katzgraber,et al.  Population annealing: Theory and application in spin glasses. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  J. Machta,et al.  Population annealing with weighted averages: a Monte Carlo method for rough free-energy landscapes. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[7]  James Edward Gubernatis,et al.  The Monte Carlo Method in the Physical Sciences: Celebrating the 50th Anniversary of the Metropolis Algorithm , 2003 .

[8]  Helmut G. Katzgraber,et al.  Universality in three-dimensional Ising spin glasses: A Monte Carlo study , 2006, cond-mat/0602212.

[9]  Helmut G. Katzgraber,et al.  Evidence against a mean-field description of short-range spin glasses revealed through thermal boundary conditions , 2014, 1408.0438.

[10]  Alex Selby Efficient subgraph-based sampling of Ising-type models with frustration , 2014, 1409.3934.

[11]  Alejandro Perdomo-Ortiz,et al.  Strengths and weaknesses of weak-strong cluster problems: A detailed overview of state-of-the-art classical heuristics versus quantum approaches , 2016, 1604.01746.

[12]  A. Alan Middleton,et al.  Persistence and memory in patchwork dynamics for glassy models , 2008 .

[13]  Andrew J. Ochoa,et al.  Best-case performance of quantum annealers on native spin-glass benchmarks: How chaos can affect success probabilities , 2015, 1505.02278.

[14]  Daniel A. Lidar,et al.  Quantum annealing correction with minor embedding , 2015, 1507.02658.

[15]  Firas Hamze,et al.  Seeking Quantum Speedup Through Spin Glasses: The Good, the Bad, and the Ugly , 2015, 1505.01545.

[16]  Andrew J. Ochoa,et al.  Efficient Cluster Algorithm for Spin Glasses in Any Space Dimension. , 2015, Physical review letters.

[17]  Daniel A. Lidar,et al.  Probing for quantum speedup in spin-glass problems with planted solutions , 2015, 1502.01663.

[18]  Óscar Promio Muñoz Quantum Annealing in the transverse Ising Model , 2018 .

[19]  Wenlong Wang,et al.  Comparing Monte Carlo methods for finding ground states of Ising spin glasses: Population annealing, simulated annealing, and parallel tempering. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  M. Troyer,et al.  Quantum versus classical annealing of Ising spin glasses , 2014, Science.

[21]  西森 秀稔 Statistical physics of spin glasses and information processing : an introduction , 2001 .

[22]  Itay Hen,et al.  Practical engineering of hard spin-glass instances , 2016, 1605.03607.

[23]  Daniel A. Lidar,et al.  Evidence for quantum annealing with more than one hundred qubits , 2013, Nature Physics.

[24]  Wang,et al.  Replica Monte Carlo simulation of spin glasses. , 1986, Physical review letters.

[25]  Mark W. Johnson,et al.  Architectural Considerations in the Design of a Superconducting Quantum Annealing Processor , 2014, IEEE Transactions on Applied Superconductivity.

[26]  Daniel A. Lidar,et al.  Experimental signature of programmable quantum annealing , 2012, Nature Communications.

[27]  J. Houdayer,et al.  A cluster Monte Carlo algorithm for 2-dimensional spin glasses , 2001 .

[28]  Vasil S. Denchev,et al.  Computational multiqubit tunnelling in programmable quantum annealers , 2015, Nature Communications.

[29]  S. Knysh,et al.  Quantum Optimization of Fully-Connected Spin Glasses , 2014, 1406.7553.

[30]  R. Car,et al.  Theory of Quantum Annealing of an Ising Spin Glass , 2002, Science.

[31]  Finding Low-Temperature States With Parallel Tempering, Simulated Annealing And Simple Monte Carlo , 2002, cond-mat/0209248.

[32]  H. Katzgraber,et al.  Exponentially Biased Ground-State Sampling of Quantum Annealing Machines with Transverse-Field Driving Hamiltonians. , 2016, Physical review letters.

[33]  Gian Giacomo Guerreschi,et al.  Adiabatic quantum optimization in the presence of discrete noise: Reducing the problem dimensionality , 2014, 1407.8183.

[34]  N. Cerf,et al.  Quantum search by local adiabatic evolution , 2001, quant-ph/0107015.

[35]  G. Rinaldi,et al.  Exact ground states of Ising spin glasses: New experimental results with a branch-and-cut algorithm , 1995 .

[36]  Daniel A. Lidar,et al.  Defining and detecting quantum speedup , 2014, Science.

[37]  E. Farhi,et al.  A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem , 2001, Science.

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

[39]  S. Edwards,et al.  Theory of spin glasses , 1975 .