Technology Information

2016

IDC: Quantum Computing in the Real World

IDC recently published a Technology Spotlight on quantum computing. Download the report here. 

2015

D-Wave 2X Technology Overview

2013

Programming with D-Wave: Map Coloring Problem

This white paper uses a simple map coloring example to explain one method of programming a D-Wave system.

Programming with D-Wave white paper

D-Wave Overview

A brief introduction to D-Wave and quantum computing.

D-Wave Overview

D-Wave Publications

Selected Papers

Degeneracy, degree, and heavy tails in quantum annealing

Andrew D. King, Emile Hoskinson, Trevor Lanting, Evgeny Andriyash, Mohammad H. Amin

"Both simulated quantum annealing and physical quantum annealing have shown the emergence of "heavy tails" in their performance as optimizers: The total time needed to solve a set of random input instances is dominated by a small number of very hard instances…On similar inputs designed to suppress local degeneracy, performance of a quantum annealing processor on hard instances improves by orders of magnitude at the 512-qubit scale, while classical performance remains relatively unchanged."

 (23 Dec 2015) http://arxiv.org/abs/1512.07325

Constructing SAT Filters with a Quantum Annealer

Adam Douglass, Andrew D. King, Jack Raymond

"Presented here is a case study of SAT filter construction with a focus on constraint satisfaction problems based on MAX-CUT clauses (Not-all-equal 3-SAT, 2-in-4-SAT, etc.) and frustrated cycles in the Ising model... Solutions are sampled using a D-Wave quantum annealer, and results are measured against classical approaches."

( 27 Oct 2015) http://link.springer.com/chapter/10.1007%2F978-3-319-24318-4_9

Benchmarking a quantum annealing processor with the time-to-target metric

James King, Sheir Yarkoni, Mayssam M. Nevisi, Jeremy P. Hilton, and Catherine C. McGeoch

In this paper we introduce the Time to Target (TTT) metric and compare the performance of the D-Wave 2X on a host of native hardware problems against highly optimized and tuned solvers. 

(20 Aug, 2015)  Link to PDF

Entanglement in a quantum annealing processor

T. Lanting et. al

In this paper we present experimental evidence that, during a critical portion of QA, qubits in the D-Wave processor become entangled and entanglement persists even as these systems reach equilibrium with a thermal environment. Our results provide an encouraging sign that quantum annealing is a viable technology for large-scale quantum computing.

Physical Review X (29 May 2014) https://journals.aps.org/prx/abstract/10.1103/PhysRevX.4.021041

Thermally assisted quantum annealing of a 16-qubit problem

N G Dickson et al. 

"Efforts to develop useful quantum computers have been blocked primarily by environmental noiseHere we examine the environment’s effect on quantum annealing using 16 qubits of a superconducting quantum processor. For a problem instance with an isolated small-gap anticrossing between the lowest two energy levels, we experimentally demonstrate that, even with annealing times eight orders of magnitude longer than the predicted single-qubit decoherence time, the probabilities of performing a successful computation are similar to those expected for a fully coherent system. Moreover, for the problem studied, we show that quantum annealing can take advantage of a thermal environment to achieve a speedup factor of up to 1,000 over a closed system."

Nature Communications, 1903 (May 21 2013) http://www.nature.com/ncomms/journal/v4/n5/full/ncomms2920.html

Quantum annealing with manufactured spins

M. W. Johnson et al. 

Many interesting but practically intractable problems can be reduced to that of finding the ground state of a system of interacting spins; however, finding such a ground state remains computationally difficult..Here we use quantum annealing to find the ground state of an artificial Ising spin system comprising an array of eight superconducting flux quantum bits with programmable spin–spin couplings. We observe a clear signature of quantum annealing, distinguishable from classical thermal annealing through the temperature dependence of the time at which the system dynamics freezes.

Nature 473, 194-198 (12 May 2011) http://www.nature.com/nature/journal/v473/n7346/full/nature10012.html

2016

Mapping constrained optimization problems to quantum annealing with application to fault diagnosis

Zhengbing Bian, Fabian Chudak, Robert Israel, Brad Lackey, William G. Macready, Aidan Roy

Current quantum annealing (QA) hardware suffers from practical limitations such as finite temperature, sparse connectivity, small qubit numbers, and control error. We propose new algorithms for mapping boolean constraint satisfaction problems (CSPs) onto QA hardware mitigating these limitations. In particular we develop a new embedding algorithm for mapping a CSP onto a hardware Ising model with a fixed sparse set of interactions, and propose two new decomposition algorithms for solving problems too large to map directly into hardware.

(10 Mar 2016) http://arxiv.org/abs/1603.03111

Quantum Boltzmann Machine

Mohammad H. Amin, Evgeny Andriyash, Jason Rolfe, Bohdan Kulchytskyy, Roger Melko

Inspired by the success of Boltzmann Machines based on classical Boltzmann distribution, we propose a new machine learning approach based on quantum Boltzmann distribution of a transverse-field Ising Hamiltonian. Due to the non-commutative nature of quantum mechanics, the training process of the Quantum Boltzmann Machine (QBM) can become nontrivial. We circumvent the problem by introducing bounds on the quantum probabilities. This allows us to train the QBM efficiently by sampling. We show examples of QBM training with and without the bound, using exact diagonalization, and compare the results with classical Boltzmann training. We also discuss the possibility of using quantum annealing processors like D-Wave for QBM training and application.

(8 Jan 2016) http://arxiv.org/abs/1601.02036

 

2015

Degeneracy, degree, and heavy tails in quantum annealing

Andrew D. King, Emile Hoskinson, Trevor Lanting, Evgeny Andriyash, Mohammad H. Amin

"Both simulated quantum annealing and physical quantum annealing have shown the emergence of "heavy tails" in their performance as optimizers: The total time needed to solve a set of random input instances is dominated by a small number of very hard instances…On similar inputs designed to suppress local degeneracy, performance of a quantum annealing processor on hard instances improves by orders of magnitude at the 512-qubit scale, while classical performance remains relatively unchanged."

 (23 Dec 2015) http://arxiv.org/abs/1512.07325

Fast clique minor generation in Chimera qubit connectivity graphs
Constructing SAT Filters with a Quantum Annealer

Adam Douglass, Andrew D. King, Jack Raymond

"Presented here is a case study of SAT filter construction with a focus on constraint satisfaction problems based on MAX-CUT clauses (Not-all-equal 3-SAT, 2-in-4-SAT, etc.) and frustrated cycles in the Ising model... Solutions are sampled using a D-Wave quantum annealer, and results are measured against classical approaches."

( 27 Oct 2015) http://link.springer.com/chapter/10.1007%2F978-3-319-24318-4_9

Performance of a quantum annealer on range-limited constraint satisfaction problems

A.D.King, T.Lanting, and R.Harris

(3 Sep 2015) http://arxiv.org/pdf/1502.02098.pdf

Benchmarking a quantum annealing processor with the time-to-target metric

James King, Sheir Yarkoni, Mayssam M. Nevisi, Jeremy P. Hilton, and Catherine C. McGeoch

In this paper we introduce the Time to Target (TTT) metric and compare the performance of the D-Wave 2X on a host of native hardware problems against highly optimized and tuned solvers. 

(20 Aug, 2015)  Link to PDF

Searching for quantum speedup in quasistatic quantum annealers

Mohammad H. Amin

(13 Mar 2015) http://arxiv.org/pdf/1503.04216.pdf

Computational Role of Collective Tunneling in a Quantum Annealer

Sergio Boixo et al.

(19 Feb 2015) http://arxiv.org/pdf/1411.4036.pdf 

2014

Discrete optimization using quantum annealing on sparse Ising models

Zhengbing Bian, Fabian Chudak, Robert Israel, Brad Lackey, William G. Macready and Aidan Roy

Frontiers in Physics,  (18 Sep 2014) http://journal.frontiersin.org/Journal/10.3389/fphy.2014.00056/abstract

A practical heuristic for finding graph minors

Jun Cai, Bill Macready, Aidan Roy

(12 Jun 2014) http://arxiv.org/pdf/1406.2741.pdf

Entanglement in a quantum annealing processor

T. Lanting et. al

In this paper we present experimental evidence that, during a critical portion of QA, qubits in the D-Wave processor become entangled and entanglement persists even as these systems reach equilibrium with a thermal environment. Our results provide an encouraging sign that quantum annealing is a viable technology for large-scale quantum computing.

Physical Review X (29 May 2014) https://journals.aps.org/prx/abstract/10.1103/PhysRevX.4.021041

Architectural considerations in the design of a superconducting quantum annealing processor

P. Bunyk et al.
Pre-print (21 Jan 2014) http://arxiv.org/pdf/1401.5504v1

2013

Evidence for temperature dependent spin-diffusion as a mechanism of intrinsic flux noise in SQUIDs

T. Lanting et al.

(23 Dec 2013) http://arxiv.org/pdf/1306.1512.pdf 

Thermally assisted quantum annealing of a 16-qubit problem

N G Dickson et al. 

"Efforts to develop useful quantum computers have been blocked primarily by environmental noiseHere we examine the environment’s effect on quantum annealing using 16 qubits of a superconducting quantum processor. For a problem instance with an isolated small-gap anticrossing between the lowest two energy levels, we experimentally demonstrate that, even with annealing times eight orders of magnitude longer than the predicted single-qubit decoherence time, the probabilities of performing a successful computation are similar to those expected for a fully coherent system. Moreover, for the problem studied, we show that quantum annealing can take advantage of a thermal environment to achieve a speedup factor of up to 1,000 over a closed system."

Nature Communications, 1903 (May 21 2013) http://www.nature.com/ncomms/journal/v4/n5/full/ncomms2920.html

Adiabatic quantum optimization with qudits

M.H. Amin et al. 
Quant. Inf. Proc. 12, 1819-1829 (April 2013) doi:10.1007/s11128-012-0480-x/QuantInfProc12/

Tunneling spectroscopy using a probe qubit

A. J. Berkley et al. 
Phys. Rev. B 87, 020502(R) (2013) doi:10.1103/PhysRevB.87.020502

2012

Approximate diagonalization method for large-scale Hamiltonians

M. H. Amin et al.
Phys. Rev. A 86, 052314 (2012) doi:10.1103/PhysRevA.86.052314

Algorithmic approach to adiabatic quantum optimization

N. G. Dickson et al. 
Phys. Rev. A 85, 032303 (2012) doi:10.1103/PhysRevA.85.032303arXiv:1108.33031

2011

Probing high-frequency noise with macroscopic resonant tunneling

T. Lanting et al. 
Physical Review B PhysRevB.83.180502 arXiv:1103.1931

Quantum annealing with manufactured spins

M. W. Johnson et al. 

Many interesting but practically intractable problems can be reduced to that of finding the ground state of a system of interacting spins; however, finding such a ground state remains computationally difficult..Here we use quantum annealing to find the ground state of an artificial Ising spin system comprising an array of eight superconducting flux quantum bits with programmable spin–spin couplings. We observe a clear signature of quantum annealing, distinguishable from classical thermal annealing through the temperature dependence of the time at which the system dynamics freezes.

Nature 473, 194-198 (12 May 2011) http://www.nature.com/nature/journal/v473/n7346/full/nature10012.html

The Ising model: teaching an old problem new tricks

Z. Bian et al. 
Link to PDF

Does adiabatic quantum optimization fail for NP-complete problems?

N. G. Dickson et al.
Phys. Rev. Lett. 106, Issue 5, 050502 arXiv:1010.0669

Importance of Explicit Vectorization for CPU and GPU Software Performance

N. Dickson et al. 
Journal of Computational Physics arXiv:1004.0024

Investigating the Performance of an Adiabatic Quantum Optimization Processor

K. Karimi et al. 
Quantum Information Processing arXiv:1006.4147

2010

A scalable control system for a superconducting adiabatic quantum optimization processor

M. W. Johnson et al.
Supercond. Sci. Technol. 23, 065004 arXiv:0907.3757

Experimental Demonstration of a Robust and Scalable Flux Qubit

R. Harris et al.
Physical Review B 81, 134510 (2010) arXiv:0909.4321

High-Performance Physics Simulations Using Multi-Core CPUs and GPGPUs in a Volunteer Computing Context

K. Karimi et al.
International Journal of High Performance Computing Applications, doi: 10.1177/1094342010372928arXiv:1004.0023

Robust Parameter Selection for Parallel Tempering

F. Hamze et al
International Journal of Modern Physics C, Volume 21, issue 5 (2010) arXiv:1004.2840

Experimental Investigation of an Eight Qubit Unit Cell in a Superconducting Optimization Processor

R. Harris et al.
Phys. Rev. B 82, 024511 (2010) arXiv:1004.1628

Cotunneling in pairs of coupled flux qubits

T. Lanting et al.
Phys. Rev. B 82, 060512(R) (2010) arXiv:1006.0028

A scalable readout system for a superconducting adiabatic quantum optimization system

A. J. Berkley et al.
Supercond. Sci. Technol. 23, 105014 (2010) arXiv:0905.0891

2009

Geometrical dependence of the low-frequency noise in superconducting flux qubits
Phys. Rev. B 79, 060509 (2009) arXiv:0812.0378
Landau-Zener transitions in a superconducting flux qubit
J. Johansson et al.
Phys. Rev. B 80, 012507 (2009) arXiv:0807.0797
A Compound Josephson Junction Coupler for Flux Qubits With Minimal Crosstalk
R. Harris et al.
Phys. Rev. B 80, 052506 (2009) arXiv:0904.3784
Decoherence in adiabatic quantum computation
M. H. S. Amin et al.
Phys. Rev. A 79, 022107 (2009) arXiv:0708.0384
Non-Markovian incoherent quantum dynamics of a two-state system

M. H. S. Amin et al.
Phys. Rev. B 80, 214302 (2009) arXiv:0907.4797

Consistency of the Adiabatic Theorem

Phys. Rev. Lett. 102, 220401 (2009) arXiv:0810.4335

Landau-Zener transitions in the presence of spin environment

A. T. S. Wan et al.
Int. J. Quant. Inf. 7, 725 (2009) arXiv:cond-mat/0703085

First Order Quantum Phase Transition in Adiabatic Quantum Computation

M. H. S. Amin et al.
Phys. Rev. A 80, 062326 (2009) arXiv:0904.1387

The Role of Single Qubit Decoherence Time in Adiabatic Quantum Computation

Phys. Rev. A 80, 022303 (2009) arXiv:0803.1196

2008

Realizable Hamiltonians for Universal Adiabatic Quantum Computers
J. D. Biamonte et al.
Phys. Rev. A 78, 012352 (2008) aXiv:0704.1287
Probing Noise in Flux Qubits via Macroscopic Resonant Tunneling
R. Harris et al.
Phys. Rev. Lett. 101, 117003 (2008) arXiv:0712.0838
Thermally Assisted Adiabatic Quantum Computation
M. H. S. Amin et al.
Phys. Rev. Lett. 100, 060503 (2008) arXiv:cond-mat/0609332
Effect of Local Minima on Adiabatic Quantum Optimization
M. H. S. Amin et al.
Phys. Rev. Lett. 100, 130503 (2008) arXiv:0709.0528
Minor-Embedding in Adiabatic Quantum Computation: I. The Parameter Setting Problem
Quantum Information Processing 7, pp193-209 (2008) arXiv:0804.4884
Macroscopic Resonant Tunneling in the Presence of Low Frequency Noise
M. H. S. Amin et al.
Phys. Rev. Lett. 100, 197001 (2008) arXiv:0712.0845
On the construction of model Hamiltonians for adiabatic quantum computing and its application to finding low energy conformations of lattice protein models
A. Perdomo et al.
Physical Review A 78, 012320 (2008) arXiv:0801.3625

2007

A Characterization of global entanglement
P. J. Love et al.
Quant. Info. Proc. 6, 187 (2007) arXiv:quant-ph/0602143
Sign- and Magnitude-Tunable Coupler for Superconducting Flux Qubits
R. Harris et al.
Phys. Rev. Lett. 98, 177001 (2007) arXiv:cond-mat/0608253

2006

Rabi oscillations in systems with small anharmonicity
M. H. S. Amin et al.
Low Temp. Phys. 32, 198 (2006) arXiv:cond-mat/0407080
Four-Qubit Device with Mixed Couplings
M. Grajcar et al.
Phys. Rev. Lett. 96, 047006 (2006) arXiv:cond-mat/0509557
Adiabatic quantum computation with flux qubits, first experimental results
S. H. W. van der Ploeg et al.
IEEE Trans. App. Supercond. 17, 113 (2006) arXiv:cond-mat/0702580

2005

Simulated Quantum Computation of Molecular Energies
A. Aspuru-Guzik et al.
Science 309 p. 1704, (2005) arXiv:quant-ph/0604193
Direct Josephson coupling between superconducting flux qubits
M. Grajcar et al.
Phys. Rev. B 72, (2005) 020503(R) arXiv:cond-mat/0501085
Hamiltonian for coupled flux qubits
A. M. van den Brink et al.
Phys. Rev. B, 71, 064503 (2005) arXiv:cond-mat/0310425
Quantum nondemolition charge measurement of a Josephson qubit
M. H. S. Amin et al.
Phys. Rev. B 71, 140505 (2005) arXiv:cond-mat/0412286
Silent phase qubit based on d -wave Josephson junctions
M. H. S. Amin et al.
Phys. Rev. B 71, 064516 (2005) arXiv:cond-mat/0310224
Flux qubit in charge-phase regime
M.H.S. Amin et al.
Phys. Rev. B 71, 024504 (2005) arXiv:cond-mat/0311220
Mediated tunable coupling of flux qubits
A. M. van den Brink et al.
New J. Phys. 7 230 (2005) arXiv:cond-mat/0501148

2004

Superconducting quantum storage and processing
M. H. S. Amin et al.
IEEE International Solid State Circuit Conference (ISSCC), Tech. Dig., p296(2004)
Wigner distribution function formalism for superconductors and collisionless dynamics of the superconducting order parameter
M. H. S. Amin et al.
Low Temp. Phys. 30, 661 (2004) arXiv:cond-mat/0404401
Observation of macroscopic Landau-Zener tunneling in a superconducting device
A. Izmalkov et al.
Euro. Phys. Lett. 65, 844, (2004) arXiv:cond-mat/0307506
Quasiparticle Decoherence in d-Wave Superconducting Qubits
M. H. S. Amin et al.
Phys. Rev. Lett. 92, 017001 (2004) arXiv:cond-mat/0304255
Low-frequency measurement of the tunneling amplitude in a flux qubit
M. Grajcar et al.
Phys. Rev. B 69, 060501 (2004) arXiv:cond-mat/0303657
Evidence for Entangled States of Two Coupled Flux Qubits
A. Izmalkov et al.
Phys. Rev. Lett. 93, 037003 (2004) arXiv:cond-mat/0312332

2003

Anomalous current-phase relation as basis for HTS qubit
S. A. Charlebois et al.
Proceedings of the European Conference on Applied Superconductivity (EUCAS 2003)
Dynamical Effects of an Unconventional Current-Phase Relation in YBCO dc SQUIDs
T. Lindstrom et al.
Phys. Rev. Lett. 90, 117002 (2003) arXiv:cond-mat/0303144
Josephson-phase qubit without tunneling
M. H. S. Amin et al.
Phys. Rev. B 67, 100508 (2003) arXiv:cond-mat/0211638
Nonequilibrium quasiclassical theory for Josephson structures
M. H. S. Amin, et al.
Phys. Rev. B 68, 054505 (2003) arXiv:cond-mat/0207724
Tunable coupling of superconducting qubits
A. Blais et al.
Phys. Rev. Lett. 90, 127901 (2003) arXiv:cond-mat/0207112
Theory of weak continuous measurements in a strongly driven quantum bit
A. Y. Smirnov, et al.
Phys. Rev. B 68, 134514 (2003) arXiv:cond-mat/0306004
Continuous Monitoring of Rabi Oscillations in a Josephson Flux Qubit
E. Il'ichev et al.
Phys. Rev. Lett. 91, 097906 (2003) arXiv:cond-mat/0303433
Quasiclassical Calculations of spontaneous current in restricted geometries
M. H. S. Amin et al.
"Towards the Controllable Quantum States" edited by H. Takayanagi and J. Nitta, World Scientific Publishing Co. (2003), arXiv:cond-mat/0207617

2002

Multi-Terminal Superconducting Phase Qubit
M. H. S. Amin et al.
Physica C 368, 310 (2002) arXiv:cond-mat/0109382
High Temperature PI/2-SQUID
M. H. S. Amin et al.
IEEE Tran. Appl. Supercond. 12, 1877 (2002) arXiv:cond-mat/0107370
Time reversal breaking states and spontaneous current pattern in Josephson junctions of d-wave superconductors
M. H. S. Amin et al.
"New Trends in Superconductivity", edited by J.F. Annett and S. Kruchinin, Kluwer, Academic Publishers (2002).
Quasiclassical theory of spontaneous currents at surfaces and interfaces of d-Wave superconductors
M. H. S. Amin et al.
Physica B 318, 162 (2002) arXiv:cond-mat/0105486
DC-SQUID based on the mesoscopic multi-terminal Josephson junction
M. H. S. Amin et al.
Physica C 372-376P1, 184 (2002); Special issue: Proceeding of the 5th European Conference on Applied Superconductivity, Copenhagen, Denmark, (Sep. 2001) arXiv:cond-mat/0109384
d+is versus d+id time reversal symmetry breaking states in finite size systems
M. H. S. Amin et al.
Phys. Rev. B 66, 174515 (2002) arXiv:cond-mat/0205495
Low-frequency characterization of quantum tunneling in flux qubits
Y. S. Greenberg et al.
Phys. Rev. B 66, 214525 (2002) arXiv:cond-mat/0208076

2001

Mechanisms of spontaneous current generation in an inhomogeneous d-wave superconductor
M. H. S. Amin et al.
Phys. Rev. B 63, 212502 (2001) arXiv:cond-mat/0011416
Degenerate Ground State in a Mesoscopic YBa2Cu3O7-x Grain Boundary Josephson Junction
E. Il'ichev et al.
Phys. Rev. Lett. 86, 5369 (2001) arXiv:cond-mat/0102404
Mesoscopic multi-terminal Josephson structures. I. effects of nonlocal weak coupling
M. H. S. Amin et al.
Low Temp Phys. 27, 616 (2001) arXiv:cond-mat/0109333

Third Party Publications

Selected Papers

What is the Computational Value of Finite Range Tunneling?

Vasil S. Denchev, Sergio Boixo, Sergei V. Isakov, Nan Ding, Ryan Babbush, Vadim Smelyanskiy, John Martinis, Hartmut Neven (Google scientists)

"Quantum annealing (QA) has been proposed as a quantum enhanced optimization heuristic exploiting tunneling. Here, we demonstrate how finite range tunneling can provide considerable computational advantage. For a crafted problem designed to have tall and narrow energy barriers separating local minima, the D-Wave 2X quantum annealer achieves significant runtime advantages relative to Simulated Annealing (SA). For instances with 945 variables this results in a time-to-99%-success-probability that is ∼108 times faster than SA running on a single processor core. "

(30 Dec 2015) http://arxiv.org/abs/1512.02206

Multiple Query Optimization on the D-Wave 2X Adiabatic Quantum Computer

Immanuel Trummer and Christoph Koch, (E ́cole Polytechnique Federale de Lausanne scientists) 

"In this paper, we tackle the problem of multiple query optimization (MQO)...While the problem sizes that can be treated are currently limited, we already find a class of problem instances where the quantum annealer is three orders of magnitude faster than other approaches."

(23 Oct 2015) http://arxiv.org/pdf/1510.06437v1.pdf

 

Application of quantum annealing to training of deep neural networks

Steven H. Adachi, Maxwell P. Henderson (Lockheed Martin scientists)

"We investigated an alternative approach [to Deep Learning] that estimates model expectations of Restricted Boltzmann Machines using samples from a D-Wave quantum annealing machine...In our tests we found that the quantum sampling-based training approach achieves comparable or better accuracy with significantly fewer iterations of generative training than conventional CD-based training."

(Oct 2015) Mathpubs: http://www.mathpubs.com/detail/1510.06356v1/Application-of-Quantum-Annea...

Solving the Optimal Trading Trajectory Problem Using a Quantum Annealer

Gili Rosenberg, Poya Haghnegahdar, Phil Goddard, Peter Carr, Kesheng Wu, Marcos López de Prado

“We solve a multi-period portfolio optimization problem using D-Wave Systems' quantum annealer. We derive a formulation of the problem, discuss several possible integer encoding schemes, and present numerical examples that show high success rates.”

(22 Aug 2015) http://arxiv.org/abs/1508.06182

Benchmarking Adiabatic Quantum Optimization for Complex Network Analysis

Ojas Parekh, Jeremy Wendt, Luke Shulenburger, Andrew Landahl, Jonathan Moussa, John Aidun (Sandia National Laboratories scientists)

"We lay the foundation for a benchmarking methodology for assessing current and future quantum computers. We pose and begin addressing fundamental questions about how to fairly compare computational devices at vastly different stages of technological maturity. We critically evaluate and offer our own contributions to current quantum benchmarking efforts, in particular those involving adiabatic quantum computation and the Adiabatic Quantum Optimizers produced by D-Wave Systems, Inc. "

(Apr 2015) Link to PDF

Computational Role of Multiqubit Tunneling in a Quantum Annealer

Sergio Boixo, Vadim N. Smelyanskiy, Alireza Shabani, Sergei V. Isakov, Mark Dykman, Vasil S. Denchev, Mohammad Amin, Anatoly Smirnov, Masoud Mohseni, Hartmut Neven (Scientists from Google, NASA Ames, and D-Wave)

Quantum tunneling, a phenomenon in which a quantum state traverses energy barriers above the energy of the state itself, has been hypothesized as an advantageous physical resource for optimization. This paper demonstrates that multiqubit tunneling plays a computational role in the D-Wave processor.

(Feb 20 2015) Nature Communications http://www.nature.com/ncomms/2016/160107/ncomms10327/full/ncomms10327.html

First application of quantum annealing to IMRT beamlet intensity optimization

Daryl P Nazareth and Jason D Spaans (Roswell Park Cancer Institute)

"Optimization methods are critical to radiation therapy. A new technology, quantum annealing (QA), employs novel hardware and software techniques to address various discrete optimization problems in many fields. We report on the first application of quantum annealing to the process of beamlet intensity optimization for IMRT...This initial experiment suggests that more research into QA-based heuristics may offer significant speedup over conventional clinical optimization methods, as quantum annealing hardware scales to larger sizes."

(1 May 2015) Institute of Physics and Engineering in Medicine http://iopscience.iop.org/article/10.1088/0031-9155/60/10/4137/pdf

2016

Spanning Tree Calculations on D-Wave 2 Machines

M.A. Novotny, L. Hobl, J.S. Hall, and K. Michielsen (Department of Physics and Astronomy, and Center for Computational Sciences, Mississippi State University and Institute for Advanced Simulation, Ju ̈lich Supercomputing Centre)

"Calculations on D-Wave machines are presented, both for the 500-qubit and the 1000-qubit machines. Results are presented for spanning trees on the available K4,4 Chimera graphs of both machines. Comparing trees of approximately the same size, the frequency of finding the ground state for the 1000-qubit machine is significantly improved over the 500- qubit older generation machine."

(Feb 2016) Journal of Physics Conference Series http://iopscience.iop.org/article/10.1088/1742-6596/681/1/012005/meta

2015

What is the Computational Value of Finite Range Tunneling?

Vasil S. Denchev, Sergio Boixo, Sergei V. Isakov, Nan Ding, Ryan Babbush, Vadim Smelyanskiy, John Martinis, Hartmut Neven (Google scientists)

"Quantum annealing (QA) has been proposed as a quantum enhanced optimization heuristic exploiting tunneling. Here, we demonstrate how finite range tunneling can provide considerable computational advantage. For a crafted problem designed to have tall and narrow energy barriers separating local minima, the D-Wave 2X quantum annealer achieves significant runtime advantages relative to Simulated Annealing (SA). For instances with 945 variables this results in a time-to-99%-success-probability that is ∼108 times faster than SA running on a single processor core. "

(30 Dec 2015) http://arxiv.org/abs/1512.02206

Multiple Query Optimization on the D-Wave 2X Adiabatic Quantum Computer

Immanuel Trummer and Christoph Koch, (E ́cole Polytechnique Federale de Lausanne scientists) 

"In this paper, we tackle the problem of multiple query optimization (MQO)...While the problem sizes that can be treated are currently limited, we already find a class of problem instances where the quantum annealer is three orders of magnitude faster than other approaches."

(23 Oct 2015) http://arxiv.org/pdf/1510.06437v1.pdf

 

Application of quantum annealing to training of deep neural networks

Steven H. Adachi, Maxwell P. Henderson (Lockheed Martin scientists)

"We investigated an alternative approach [to Deep Learning] that estimates model expectations of Restricted Boltzmann Machines using samples from a D-Wave quantum annealing machine...In our tests we found that the quantum sampling-based training approach achieves comparable or better accuracy with significantly fewer iterations of generative training than conventional CD-based training."

(Oct 2015) Mathpubs: http://www.mathpubs.com/detail/1510.06356v1/Application-of-Quantum-Annea...

Solving the Optimal Trading Trajectory Problem Using a Quantum Annealer

Gili Rosenberg, Poya Haghnegahdar, Phil Goddard, Peter Carr, Kesheng Wu, Marcos López de Prado

“We solve a multi-period portfolio optimization problem using D-Wave Systems' quantum annealer. We derive a formulation of the problem, discuss several possible integer encoding schemes, and present numerical examples that show high success rates.”

(22 Aug 2015) http://arxiv.org/abs/1508.06182

Guest Column: Adiabatic Quantum Computing Challenges

ACM SIGACT News archive, Volume 46 Issue 1, March 2015, Pages 40-61 http://dl.acm.org/citation.cfm?id=2744459&dl=ACM&coll=DL&CFID=666501900&CFTOKEN=29005022

"The paper presents a brief introduction to quantum computing with focus on the adiabatic model which is illustrated with the commercial D-Wave computer. We also include new theory and experimental work done on the D-Wave computer. Finally we discuss a hybrid method of combining classical and quantum computing and a few open problems."

 

 

Benchmarking Adiabatic Quantum Optimization for Complex Network Analysis

Ojas Parekh, Jeremy Wendt, Luke Shulenburger, Andrew Landahl, Jonathan Moussa, John Aidun (Sandia National Laboratories scientists)

"We lay the foundation for a benchmarking methodology for assessing current and future quantum computers. We pose and begin addressing fundamental questions about how to fairly compare computational devices at vastly different stages of technological maturity. We critically evaluate and offer our own contributions to current quantum benchmarking efforts, in particular those involving adiabatic quantum computation and the Adiabatic Quantum Optimizers produced by D-Wave Systems, Inc. "

(Apr 2015) Link to PDF

Computational Role of Multiqubit Tunneling in a Quantum Annealer

Sergio Boixo, Vadim N. Smelyanskiy, Alireza Shabani, Sergei V. Isakov, Mark Dykman, Vasil S. Denchev, Mohammad Amin, Anatoly Smirnov, Masoud Mohseni, Hartmut Neven (Scientists from Google, NASA Ames, and D-Wave)

Quantum tunneling, a phenomenon in which a quantum state traverses energy barriers above the energy of the state itself, has been hypothesized as an advantageous physical resource for optimization. This paper demonstrates that multiqubit tunneling plays a computational role in the D-Wave processor.

(Feb 20 2015) Nature Communications http://www.nature.com/ncomms/2016/160107/ncomms10327/full/ncomms10327.html

2014

First application of quantum annealing to IMRT beamlet intensity optimization

Daryl P Nazareth and Jason D Spaans (Roswell Park Cancer Institute)

"Optimization methods are critical to radiation therapy. A new technology, quantum annealing (QA), employs novel hardware and software techniques to address various discrete optimization problems in many fields. We report on the first application of quantum annealing to the process of beamlet intensity optimization for IMRT...This initial experiment suggests that more research into QA-based heuristics may offer significant speedup over conventional clinical optimization methods, as quantum annealing hardware scales to larger sizes."

(1 May 2015) Institute of Physics and Engineering in Medicine http://iopscience.iop.org/article/10.1088/0031-9155/60/10/4137/pdf

Reexamining classical and quantum models for the D-Wave One processor

Tameem Albash, Troels F. Rønnow, Matthias Troyer, Daniel A. Lidar

(12 Sep 2014) http://arxiv.org/abs/1409.3827

Quantum annealing correction for random Ising problems

Kristen L. Pudenz, Tameem Albash, Daniel A. Lidar

(19 Aug 2014) http://arxiv.org/abs/1408.4382

A Quantum Annealing Approach for Fault Detection and Diagnosis of Graph-Based Systems

Alejandro Perdomo-Ortiz, Joseph Fluegemann, Sriram Narasimhan, Rupak Biswas, Vadim N. Smelyanskiy
(30 Jun 2014) http://arxiv.org/abs/1406.7601

Quantum Optimization of Fully-Connected Spin Glasses

Davide Venturelli, Salvatore Mandrà, Sergey Knysh, Bryan O'Gorman, Rupak Biswas, Vadim Smelyanskiy
(29 Jun 2014) http://arxiv.org/abs/1406.7553

Distinguishing Classical and Quantum Models for the D-Wave Device

Walter Vinci, Tameem Albash, Anurag Mishra, Paul A. Warburton, Daniel A. Lidar

(17 Mar 2014) http://arxiv.org/abs/1403.4228

Glassy Chimeras could be blind to quantum speedup: Designing better benchmarks for quantum annealing machines

Helmut G. Katzgraber, Firas Hamze, Ruben S. Andrist

(12 Jan 2014) http://arxiv.org/pdf/1401.1546.pdf
 

2013

Experimental determination of Ramsey numbers

Z. Bian et al.
Phys. Rev. Lett. vol. 111, 130505 (2013) arXiv:1201.1842

Error corrected quantum annealing with hundreds of qubits

K.L. Pudenz et al.
(31 Jul 2013) arXiv:1307.8190

Hearing the shape of Ising models: on the distinguishability power of Physics

W. Vinci et al.
(3 Jul 2013) arXiv:1307.1114

Experimental signature of programmable quantum annealing

S Boxio et al. 
Nature Communications, 2067 (28 June 2013) doi:10.1038/ncomms3067

MAX 2-SAT with up to 108 qubits

S. Santra
(12 Jul 2013) arXiv:1307.3931

Quantum annealing with more than one hundred qubits

S. Boxio et al.
(16 Apr 2013) arXiv:1304.4595

How Fast Can Quantum Annealers Count?

I. Hen
(21 Jan 2013) arXiv:1301.4956

Experimental Evaluation of an Adiabatic Quantum System for Combinatorial Optimization

C. C. McGeoch et al. 
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2012

Construction of Energy Functions for Lattice Heteropolymer Models: A Case Study in Constraint Satisfaction Programming and Adiabatic Quantum Optimization

R. Babbush et al.
(4 Nov 2012) arXiv:1211.3422

Solving the Graph Isomorphism Problem with a Quantum Annealer

I. Hen et al.
(6 Jul 2012) arXiv:1207.1712

Robust Classification with Adiabatic Quantum Optimization

V.S. Denchev et al. 
(5 May 2012) arXiv:1205.1148

Finding low-energy conformations of lattice protein models by quantum annealing

A. Perdomo-Ortiz et al.
(24 Apr 2012) arXiv:1204.5485

A Near-Term Quantum Computing Approach for Hard Computational Problems in Space Exploration

V.N. Smelyanskiy et al.
(12 Apr 2012) arXiv:1204.2821

Quantum Speedup by Quantum Annealing

D. Nagaj et al.
Phys. Rev. Lett. 109, 050501 (2012) arXiv:1202.6257

2009

Training a Large Scale Classifier with the Quantum Adiabatic Algorithm

H. Neven, et al.
(4 Dec 2009) arXiv:0912.0779

2008

Training a Binary Classifier with the Quantum Adiabatic Algorithm

H. Neven et al.
(4 Nov 2008) arXiv:0811.0416

Image recognition with an adiabatic quantum computer I. Mapping to quadratic unconstrained binary optimization

H. Neven et al.
(28 Apr 2008) arXiv:0804.4457