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Title: Probing for quantum speedup in spin-glass problems with planted solutions

Abstract

The availability of quantum annealing devices with hundreds of qubits has made the experimental demonstration of a quantum speedup for optimization problems a coveted, albeit elusive goal. Going beyond earlier studies of random Ising problems, here we introduce a method to construct a set of frustrated Ising-model optimization problems with tunable hardness. We study the performance of a D-Wave Two device (DW2) with up to 503 qubits on these problems and compare it to a suite of classical algorithms, including a highly optimized algorithm designed to compete directly with the DW2. The problems are generated around predetermined ground-state configurations, called planted solutions, which makes them particularly suitable for benchmarking purposes. The problem set exhibits properties familiar from constraint satisfaction (SAT) problems, such as a peak in the typical hardness of the problems, determined by a tunable clause density parameter. We bound the hardness regime where the DW2 device either does not or might exhibit a quantum speedup for our problem set. While we do not find evidence for a speedup for the hardest and most frustrated problems in our problem set, we cannot rule out that a speedup might exist for some of the easier, less frustrated problems. Our empiricalmore » findings pertain to the specific D-Wave processor and problem set we studied and leave open the possibility that future processors might exhibit a quantum speedup on the same problem set.« less

Authors:
; ; ; ; ;
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1565492
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 92; Journal Issue: 4; Journal ID: ISSN 1050-2947
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
Optics; Physics

Citation Formats

Hen, Itay, Job, Joshua, Albash, Tameem, Rønnow, Troels F., Troyer, Matthias, and Lidar, Daniel A. Probing for quantum speedup in spin-glass problems with planted solutions. United States: N. p., 2015. Web. doi:10.1103/physreva.92.042325.
Hen, Itay, Job, Joshua, Albash, Tameem, Rønnow, Troels F., Troyer, Matthias, & Lidar, Daniel A. Probing for quantum speedup in spin-glass problems with planted solutions. United States. doi:10.1103/physreva.92.042325.
Hen, Itay, Job, Joshua, Albash, Tameem, Rønnow, Troels F., Troyer, Matthias, and Lidar, Daniel A. Thu . "Probing for quantum speedup in spin-glass problems with planted solutions". United States. doi:10.1103/physreva.92.042325.
@article{osti_1565492,
title = {Probing for quantum speedup in spin-glass problems with planted solutions},
author = {Hen, Itay and Job, Joshua and Albash, Tameem and Rønnow, Troels F. and Troyer, Matthias and Lidar, Daniel A.},
abstractNote = {The availability of quantum annealing devices with hundreds of qubits has made the experimental demonstration of a quantum speedup for optimization problems a coveted, albeit elusive goal. Going beyond earlier studies of random Ising problems, here we introduce a method to construct a set of frustrated Ising-model optimization problems with tunable hardness. We study the performance of a D-Wave Two device (DW2) with up to 503 qubits on these problems and compare it to a suite of classical algorithms, including a highly optimized algorithm designed to compete directly with the DW2. The problems are generated around predetermined ground-state configurations, called planted solutions, which makes them particularly suitable for benchmarking purposes. The problem set exhibits properties familiar from constraint satisfaction (SAT) problems, such as a peak in the typical hardness of the problems, determined by a tunable clause density parameter. We bound the hardness regime where the DW2 device either does not or might exhibit a quantum speedup for our problem set. While we do not find evidence for a speedup for the hardest and most frustrated problems in our problem set, we cannot rule out that a speedup might exist for some of the easier, less frustrated problems. Our empirical findings pertain to the specific D-Wave processor and problem set we studied and leave open the possibility that future processors might exhibit a quantum speedup on the same problem set.},
doi = {10.1103/physreva.92.042325},
journal = {Physical Review. A},
issn = {1050-2947},
number = 4,
volume = 92,
place = {United States},
year = {2015},
month = {10}
}

Works referenced in this record:

Quantum computers
journal, March 2010


Goals and opportunities in quantum simulation
journal, April 2012

  • Cirac, J. Ignacio; Zoller, Peter
  • Nature Physics, Vol. 8, Issue 4
  • DOI: 10.1038/nphys2275

Quantum annealing with manufactured spins
journal, May 2011

  • Johnson, M. W.; Amin, M. H. S.; Gildert, S.
  • Nature, Vol. 473, Issue 7346
  • DOI: 10.1038/nature10012

Quantum annealing: The fastest route to quantum computation?
journal, February 2015


Quantum stochastic optimization
journal, December 1989


Sherrington-Kirkpatrick model in a transverse field: Absence of replica symmetry breaking due to quantum fluctuations
journal, June 1989


Global energy minimum searches using an approximate solution of the imaginary time Schroedinger equation
journal, June 1993

  • Amara, Patricia; Hsu, D.; Straub, John E.
  • The Journal of Physical Chemistry, Vol. 97, Issue 25
  • DOI: 10.1021/j100127a023

Quantum annealing: A new method for minimizing multidimensional functions
journal, March 1994


Quantum annealing in the transverse Ising model
journal, November 1998


Quantum annealing by the path-integral Monte Carlo method: The two-dimensional random Ising model
journal, September 2002


Theory of Quantum Annealing of an Ising Spin Glass
journal, March 2002


Quantum Annealing of a Disordered Magnet
journal, April 1999


A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
journal, April 2001


Defining and detecting quantum speedup
journal, June 2014


Optimization by Simulated Annealing
journal, May 1983


Colloquium : Quantum annealing and analog quantum computation
journal, September 2008


Spin glasses: Experimental facts, theoretical concepts, and open questions
journal, October 1986


Evidence for quantum annealing with more than one hundred qubits
journal, February 2014

  • Boixo, Sergio; Rønnow, Troels F.; Isakov, Sergei V.
  • Nature Physics, Vol. 10, Issue 3
  • DOI: 10.1038/nphys2900

Architectural Considerations in the Design of a Superconducting Quantum Annealing Processor
journal, August 2014

  • Bunyk, P. I.; Hoskinson, Emile M.; Johnson, Mark W.
  • IEEE Transactions on Applied Superconductivity, Vol. 24, Issue 4
  • DOI: 10.1109/TASC.2014.2318294

Minor-embedding in adiabatic quantum computation: II. Minor-universal graph design
journal, October 2010


Experimental signature of programmable quantum annealing
journal, June 2013

  • Boixo, Sergio; Albash, Tameem; Spedalieri, Federico M.
  • Nature Communications, Vol. 4, Issue 1
  • DOI: 10.1038/ncomms3067

Thermally assisted quantum annealing of a 16-qubit problem
journal, May 2013

  • Dickson, N. G.; Johnson, M. W.; Amin, M. H.
  • Nature Communications, Vol. 4, Issue 1
  • DOI: 10.1038/ncomms2920

Error-corrected quantum annealing with hundreds of qubits
journal, February 2014

  • Pudenz, Kristen L.; Albash, Tameem; Lidar, Daniel A.
  • Nature Communications, Vol. 5, Issue 1
  • DOI: 10.1038/ncomms4243

Consistency tests of classical and quantum models for a quantum annealer
journal, April 2015


Quantum annealing correction for random Ising problems
journal, April 2015


Quantum and classical dynamics in adiabatic computation
journal, October 2014


Quantum Optimization of Fully Connected Spin Glasses
journal, September 2015


Reexamining classical and quantum models for the D-Wave One processor: The role of excited states and ground state degeneracy
journal, February 2015

  • Albash, T.; Rønnow, T. F.; Troyer, M.
  • The European Physical Journal Special Topics, Vol. 224, Issue 1
  • DOI: 10.1140/epjst/e2015-02346-0

Entanglement in a Quantum Annealing Processor
journal, May 2014


Glassy Chimeras Could Be Blind to Quantum Speedup: Designing Better Benchmarks for Quantum Annealing Machines
journal, April 2014


Hiding Solutions in Random Satisfiability Problems: A Statistical Mechanics Approach
journal, April 2002


Hiding Quiet Solutions in Random Constraint Satisfaction Problems
journal, June 2009


Complexity of Stoquastic Frustration-Free Hamiltonians
journal, January 2010

  • Bravyi, Sergey; Terhal, Barbara
  • SIAM Journal on Computing, Vol. 39, Issue 4
  • DOI: 10.1137/08072689X

The scaling window of the 2-SAT transition: Scaling Window of the 2-SAT Transition
journal, April 2001

  • Bollobás, Béla; Borgs, Christian; Chayes, Jennifer T.
  • Random Structures & Algorithms, Vol. 18, Issue 3
  • DOI: 10.1002/rsa.1006

Max 2-SAT with up to 108 qubits
journal, April 2014


Determining computational complexity from characteristic ‘phase transitions’
journal, July 1999

  • Monasson, Rémi; Zecchina, Riccardo; Kirkpatrick, Scott
  • Nature, Vol. 400, Issue 6740
  • DOI: 10.1038/22055

Decoherence in adiabatic quantum computation
journal, June 2015


Quantum adiabatic Markovian master equations
journal, December 2012


Robustness of adiabatic quantum computation
journal, December 2001


Adiabatic quantum optimization with the wrong Hamiltonian
journal, December 2013


Collective Monte Carlo Updating for Spin Systems
journal, January 1989


Bucket elimination: A unifying framework for reasoning
journal, September 1999


Jeffreys' prior is asymptotically least favorable under entropy risk
journal, August 1994


Quantum versus classical annealing of Ising spin glasses
journal, March 2015