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

Hen, Itay; Job, Joshua; Albash, Tameem; Rønnow, Troels F.; Troyer, Matthias; Lidar, Daniel A.

doi:10.1103/physreva.92.042325

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 »« less

Authors:

Hen, Itay ^[1]; Job, Joshua ^[2]; Albash, Tameem ^[1]; Rønnow, Troels F. ^[3]; Troyer, Matthias ^[3]; Lidar, Daniel A. ^[2]

Univ. of Southern California, Marina del Rey, CA (United States); Univ. of Southern California, Los Angeles, CA (United States)
Univ. of Southern California, Los Angeles, CA (United States)
Eidgenoessische Technische Hochschule, Zurich (Switzerland)

Publication Date:: Fri Oct 23 00:00:00 EDT 2015

Research Org.:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)

Sponsoring Org.:: USDOE Office of Science (SC); US Army Research Office (ARO); Lockheed Martin Corporation; Swiss National Science Foundation (SNF); European Research Council (ERC)

OSTI Identifier:: 1565492

Alternate Identifier(s):: OSTI ID: 1224652

Grant/Contract Number:: AC05-00OR22725; W911NF-12-1-0523; W911NF-11-1-0268; SIMCOFE

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review A - Atomic, Molecular, and Optical Physics

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:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 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.

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                    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.  https://doi.org/10.1103/physreva.92.042325

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                    Hen, Itay, Job, Joshua, Albash, Tameem, Rønnow, Troels F., Troyer, Matthias, and Lidar, Daniel A. Fri .  
"Probing for quantum speedup in spin-glass problems with planted solutions".  United States.  https://doi.org/10.1103/physreva.92.042325.  https://www.osti.gov/servlets/purl/1565492.

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@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 - Atomic, Molecular, and Optical Physics},

  number       = 4,

  volume       = 92,

  place        = {United States},

  year         = {Fri Oct 23 00:00:00 EDT 2015},

  month        = {Fri Oct 23 00:00:00 EDT 2015}

}

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Slutskii, Mikhail; Albash, Tameem; Barash, Lev
arXiv
DOI: 10.48550/arxiv.1904.04420

Similar Records in DOE PAGES and OSTI.GOV collections:

Quantum annealing correction with minor embedding

Journal Article Vinci, Walter ; Albash, Tameem ; Paz-Silva, Gerardo ; ... - Physical Review A - Atomic, Molecular, and Optical Physics

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 by hardware constraints. To overcome constraints imposed by restricted connectivity between qubits, a larger set of interactions can be approximated using minor embedding techniques whereby several physical qubits are used to represent a single logical qubit. However, minor embedding introduces new types of errors due to its approximate nature. Here we introduce and study quantum annealing correction schemes designed to improve the performance of quantum annealers in conjunctionmore »« less
Cited by 58
https://doi.org/10.1103/physreva.92.042310

Full Text Available
Demonstration of a Scaling Advantage for a Quantum Annealer over Simulated Annealing

Journal Article Albash, Tameem ; Lidar, Daniel A. - Physical Review. X

The observation of an unequivocal quantum speedup remains an elusive objective for quantum computing. A more modest goal is to demonstrate a scaling advantage over a class of classical algorithms for a computational problem running on quantum hardware. The D-Wave quantum annealing processors have been at the forefront of experimental attempts to address this goal, given their relatively large numbers of qubits and programmability. A complete determination of the optimal time-to-solution using these processors has not been possible to date, preventing definitive conclusions about the presence of a scaling advantage. The main technical obstacle has been the inability to verifymore »« less
Cited by 104
https://doi.org/10.1103/PhysRevX.8.031016
Reexamination of the evidence for entanglement in a quantum annealer

Journal Article Albash, Tameem ; Hen, Itay ; Spedalieri, Federico M. ; ... - Physical Review A - Atomic, Molecular, and Optical Physics

A recent experiment claimed to provide evidence of up to eight-qubit entanglement in a D-Wave quantum annealing device. However, entanglement was measured using qubit tunneling spectroscopy, a technique that provides indirect access to the state of the system at intermediate times during the anneal by performing measurements at the end of the anneal with a probe qubit. In addition, an underlying assumption was that the quantum transverse-field Ising Hamiltonian, whose ground states are already highly entangled, is an appropriate model of the device and not some other (possibly classical) model. This begs the question of whether alternative classical or semiclassicalmore »« less
Cited by 24
https://doi.org/10.1103/physreva.92.062328

Full Text Available
Reexamining classical and quantum models for the D-Wave One processor: The role of excited states and ground state degeneracy

Journal Article Albash, T. ; Rønnow, T. F. ; Troyer, M. ; ... - European Physical Journal. Special Topics

We revisit the evidence for quantum annealing in the D-Wave One device (DW1) based on the study of random Ising instances. Using the probability distributions of finding the ground states of such instances, previous work found agreement with both simulated quantum annealing (SQA) and a classical rotor model. Thus the DW1 ground state success probabilities are consistent with both models, and a different measure is needed to distinguish the data and the models. Here in this paper we consider measures that account for ground state degeneracy and the distributions of excited states, and present evidence that for these new measuresmore »« less
Cited by 67
https://doi.org/10.1140/epjst/e2015-02346-0

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Quantum optimization of maximum independent set using Rydberg atom arrays

Journal Article Ebadi, S. ; Keesling, A. ; Cain, M. ; ... - Science

Realizing quantum speedup for practically relevant, computationally hard problems is a central challenge in quantum information science. Using Rydberg atom arrays with up to 289 qubits in two spatial dimensions, we experimentally investigate quantum algorithms for solving the maximum independent set problem. We use a hardware-efficient encoding associated with Rydberg blockade, realize closed-loop optimization to test several variational algorithms, and subsequently apply them to systematically explore a class of graphs with programmable connectivity. We find that the problem hardness is controlled by the solution degeneracy and number of local minima, and we experimentally benchmark the quantum algorithm’s performance against classicalmore »« less
https://doi.org/10.1126/science.abo6587

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

Abstract

Citation Formats

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

Quantum computers journal, March 2010

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

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

Entanglement in a Quantum Annealing Processor journal, May 2014

Quantum stochastic optimization journal, December 1989

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

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

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

Quantum annealing with manufactured spins journal, May 2011

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

Robustness of adiabatic quantum computation journal, December 2001

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

Complexity of Stoquastic Frustration-Free Hamiltonians journal, January 2010

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

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

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

Quantum Annealing of a Disordered Magnet journal, April 1999

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

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

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

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

Quantum adiabatic Markovian master equations journal, December 2012

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

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

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

Collective Monte Carlo Updating for Spin Systems journal, January 1989

Quantum annealing in the transverse Ising model journal, November 1998

Defining and detecting quantum speedup journal, June 2014

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

Quantum and classical dynamics in adiabatic computation journal, October 2014

Optimization by Simulated Annealing journal, May 1983

Statistical Physics of Spin Glasses and Information Processing book, July 2001

Goals and opportunities in quantum simulation journal, April 2012

Experimental signature of programmable quantum annealing journal, June 2013

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

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

Quantum computers journal, December 2002

Complexity of stoquastic frustration-free Hamiltonians text, January 2008

Hiding Quiet Solutions in Random Constraint Satisfaction Problems text, January 2009

Minor-embedding in adiabatic quantum computation: II. Minor-universal graph design text, January 2010

Quantum Adiabatic Markovian Master Equations text, January 2012

Entanglement in a quantum annealing processor text, January 2014

Architectural considerations in the design of a superconducting quantum annealing processor text, January 2014

Consistency Tests of Classical and Quantum Models for a Quantum Annealer text, January 2014

Quantum annealing correction for random Ising problems text, January 2014

Quantum Annealing of a Disordered Magnet text, January 2001

Hiding solutions in random satisfiability problems: A statistical mechanics approach text, January 2001

Enhancing quantum annealing performance for the molecular similarity problem journal, April 2017

Boosting quantum annealer performance via sample persistence journal, May 2017

Simulated versus reduced noise quantum annealing in maximum independent set solution to wireless network scheduling journal, November 2018

How quantum is the speedup in adiabatic unstructured search? journal, April 2019

Hard combinatorial problems and minor embeddings on lattice graphs journal, May 2019

On the computational complexity of curing non-stoquastic Hamiltonians journal, April 2019

Quantum annealing versus classical machine learning applied to a simplified computational biology problem journal, February 2018

Analog errors in quantum annealing: doom and hope journal, November 2019

An approach to quantum-computational hydrologic inverse analysis journal, May 2018

Unraveling Quantum Annealers using Classical Hardness journal, October 2015

Maximum-Entropy Inference with a Programmable Annealer journal, March 2016

Quantum information processing with superconducting circuits: a review journal, September 2017

Machine learning & artificial intelligence in the quantum domain: a review of recent progress journal, June 2018

Estimating the density of states of frustrated spin systems journal, July 2019

Analog nature of quantum adiabatic unstructured search journal, November 2019

The pitfalls of planar spin-glass benchmarks: raising the bar for quantum annealers (again) journal, July 2017

A deceptive step towards quantum speedup detection journal, July 2018

Analog errors in Ising machines journal, April 2019

Searching for quantum speedup in quasistatic quantum annealers journal, November 2015

Best-case performance of quantum annealers on native spin-glass benchmarks: How chaos can affect success probabilities journal, January 2016

Direct comparison of quantum and simulated annealing on a fully connected Ising ferromagnet journal, August 2017

Nested quantum annealing correction at finite temperature: p -spin models journal, June 2019

Power of Pausing: Advancing Understanding of Thermalization in Experimental Quantum Annealers journal, April 2019

Equation Planting: A Tool for Benchmarking Ising Machines journal, July 2019

Site- and bond-percolation thresholds in K n , n -based lattices: Vulnerability of quantum annealers to random qubit and coupler failures on chimera topologies journal, April 2016

From near to eternity: Spin-glass planting, tiling puzzles, and constraint-satisfaction problems journal, April 2018

Temperature Scaling Law for Quantum Annealing Optimizers journal, September 2017

Demonstration of a Scaling Advantage for a Quantum Annealer over Simulated Annealing journal, July 2018

A hybrid quantum-classical paradigm to mitigate embedding costs in quantum annealing journal, August 2019

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

Quantum computers
journal, March 2010

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

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

Entanglement in a Quantum Annealing Processor
journal, May 2014

Quantum stochastic optimization
journal, December 1989

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

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

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

Quantum annealing with manufactured spins
journal, May 2011

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

Robustness of adiabatic quantum computation
journal, December 2001

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

Complexity of Stoquastic Frustration-Free Hamiltonians
journal, January 2010

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

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

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

Quantum Annealing of a Disordered Magnet
journal, April 1999

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

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

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

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

Quantum adiabatic Markovian master equations
journal, December 2012

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

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

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

Collective Monte Carlo Updating for Spin Systems
journal, January 1989

Quantum annealing in the transverse Ising model
journal, November 1998

Defining and detecting quantum speedup
journal, June 2014

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

Quantum and classical dynamics in adiabatic computation
journal, October 2014

Optimization by Simulated Annealing
journal, May 1983

Statistical Physics of Spin Glasses and Information Processing
book, July 2001

Goals and opportunities in quantum simulation
journal, April 2012

Experimental signature of programmable quantum annealing
journal, June 2013

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

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

Quantum computers
journal, December 2002

Complexity of stoquastic frustration-free Hamiltonians
text, January 2008

Hiding Quiet Solutions in Random Constraint Satisfaction Problems
text, January 2009

Minor-embedding in adiabatic quantum computation: II. Minor-universal graph design
text, January 2010

Quantum Adiabatic Markovian Master Equations
text, January 2012

Entanglement in a quantum annealing processor
text, January 2014

Architectural considerations in the design of a superconducting quantum annealing processor
text, January 2014

Consistency Tests of Classical and Quantum Models for a Quantum Annealer
text, January 2014

Quantum annealing correction for random Ising problems
text, January 2014

Quantum Annealing of a Disordered Magnet
text, January 2001

Hiding solutions in random satisfiability problems: A statistical mechanics approach
text, January 2001

Enhancing quantum annealing performance for the molecular similarity problem
journal, April 2017

Boosting quantum annealer performance via sample persistence
journal, May 2017

Simulated versus reduced noise quantum annealing in maximum independent set solution to wireless network scheduling
journal, November 2018

How quantum is the speedup in adiabatic unstructured search?
journal, April 2019

Hard combinatorial problems and minor embeddings on lattice graphs
journal, May 2019

On the computational complexity of curing non-stoquastic Hamiltonians
journal, April 2019

Quantum annealing versus classical machine learning applied to a simplified computational biology problem
journal, February 2018

Analog errors in quantum annealing: doom and hope
journal, November 2019

An approach to quantum-computational hydrologic inverse analysis
journal, May 2018

Unraveling Quantum Annealers using Classical Hardness
journal, October 2015

Maximum-Entropy Inference with a Programmable Annealer
journal, March 2016

Quantum information processing with superconducting circuits: a review
journal, September 2017

Machine learning & artificial intelligence in the quantum domain: a review of recent progress
journal, June 2018

Estimating the density of states of frustrated spin systems
journal, July 2019

Analog nature of quantum adiabatic unstructured search
journal, November 2019

The pitfalls of planar spin-glass benchmarks: raising the bar for quantum annealers (again)
journal, July 2017

A deceptive step towards quantum speedup detection
journal, July 2018

Analog errors in Ising machines
journal, April 2019

Searching for quantum speedup in quasistatic quantum annealers
journal, November 2015

Best-case performance of quantum annealers on native spin-glass benchmarks: How chaos can affect success probabilities
journal, January 2016

Direct comparison of quantum and simulated annealing on a fully connected Ising ferromagnet
journal, August 2017

Nested quantum annealing correction at finite temperature: $p$ -spin models
journal, June 2019

Power of Pausing: Advancing Understanding of Thermalization in Experimental Quantum Annealers
journal, April 2019

Equation Planting: A Tool for Benchmarking Ising Machines
journal, July 2019

Site- and bond-percolation thresholds in $K_{n, n}$ -based lattices: Vulnerability of quantum annealers to random qubit and coupler failures on chimera topologies
journal, April 2016

From near to eternity: Spin-glass planting, tiling puzzles, and constraint-satisfaction problems
journal, April 2018

Temperature Scaling Law for Quantum Annealing Optimizers
journal, September 2017

Demonstration of a Scaling Advantage for a Quantum Annealer over Simulated Annealing
journal, July 2018

A hybrid quantum-classical paradigm to mitigate embedding costs in quantum annealing
journal, August 2019

Deploying a quantum annealing processor to detect tree cover in aerial imagery of California
journal, February 2017

Quantum Robotics: A Primer on Current Science and Future Perspectives
journal, January 2017

Physics-Inspired Optimization for Quadratic Unconstrained Problems Using a Digital Annealer
journal, April 2019