D-Wave Publications

Selected Papers

Observation of topological phenomena in a programmable lattice of 1,800 qubits

Andrew King et. al

The work of Berezinskii, Kosterlitz and Thouless in the 1970s revealed exotic phases of matter governed by the topological properties of low-dimensional materials such as thin films of superfluids and superconductors. A hallmark of this phenomenon is the appearance and interaction of vortices and antivortices in an angular degree of freedom—typified by the classical XY model—owing to thermal fluctuations. In the two-dimensional Ising model this angular degree of freedom is absent in the classical case, but with the addition of a transverse field it can emerge from the interplay between frustration and quantum fluctuations. Consequently, a Kosterlitz–Thouless phase transition has been predicted in the quantum system—the two-dimensional transverse-field Ising model—by theory and simulation. Here we demonstrate a large- scale quantum simulation of this phenomenon in a network of 1,800 in situ programmable superconducting niobium flux qubits whose pairwise couplings are arranged in a fully frustrated square-octagonal lattice. Essential to the critical behaviour, we observe the emergence of a complex order parameter with continuous rotational symmetry, and the onset of quasi-long-range order as the system approaches a critical temperature. We describe and use a simple approach to statistical estimation with an annealing-based quantum processor that performs Monte Carlo sampling in a chain of reverse quantum annealing protocols. Observations are consistent with classical simulations across a range of Hamiltonian parameters. We anticipate that our approach of using a quantum processor as a programmable magnetic lattice will find widespread use in the simulation and development of exotic materials.

(22 Aug 2018) Nature (Vol. 560, Issue 7719, August 22, 2018)

Read the Synopsis   See arXiv: https://arxiv.org/abs/1803.02047

Phase transitions in a programmable quantum spin glass simulator

R. Harris et. al

Understanding magnetic phases in quantum mechanical systems is one of the essential goals in condensed matter physics, and the advent of prototype quantum simulation hardware has provided new tools for experimentally probing such systems. We report on the experimental realization of a quantum simulation of interacting Ising spins on three-dimensional cubic lattices up to dimensions 8 × 8 × 8 on a D-Wave processor (D-Wave Systems, Burnaby, Canada). The ability to control and read out the state of individual spins provides direct access to several order parameters, which we used to determine the lattice’s magnetic phases as well as critical disorder and one of its universal exponents. By tuning the degree of disorder and effective transverse magnetic field, we observed phase transitions between a paramagnetic, an antiferromagnetic, and a spin-glass phase.

(13 Jul 2018) Science Vol. 361, Issue 6398, pp. 162-165
DOI: 10.1126/science.aat2025

Link to full text       

 

Quantum Variational Autoencoder

Amir Khoshaman, Walter Vinci, Brandon Denis, Evgeny Andriyash,and Mohammad H. Amin 

Variational autoencoders (VAEs) are powerful generative models with the salient ability to perform inference. Here, we introduce a quantum variational autoencoder (QVAE): a VAE whose latent generative process is implemented as a quantum Boltzmann machine (QBM). We show that our model can be trained end-to-end by maximizing a well-defined loss-function: a “quantum” lower- bound to a variational approximation of the log-likelihood. We use quantum Monte Carlo (QMC) simulations to train and evaluate the performance of QVAEs. To achieve the best performance, we first create a VAE platform with discrete latent space generated by a restricted Boltzmann machine (RBM). Our model achieves state-of-the-art performance on the MNIST dataset when compared against similar approaches that only involve discrete variables in the generative process. We consider QVAEs with a smaller number of latent units to be able to perform QMC simulations, which are computationally expensive. We show that QVAEs can be trained effectively in regimes where quantum effects are relevant despite training via the quantum bound. Our findings open the way to the use of quantum computers to train QVAEs to achieve competitive performance for generative models. Placing a QBM in the latent space of a VAE leverages the full potential of current and next-generation quantum computers as sampling devices.

(22 Feb 2018) https://arxiv.org/pdf/1802.05779.pdf 

Can quantum Monte Carlo simulate quantum annealing?

Evgeny Andriyash and Mohammad H. Amin

"Recent theoretical and experimental studies have suggested that quantum Monte Carlo (QMC) simulation can behave similarly to quantum annealing (QA)...Here, we compare incoherent tunneling and QMC escape using perturbation theory, which has much wider validity than WKB approximation. We show that the two do not scale the same way when there are multiple homotopy-inequivalent paths for tunneling. We demonstrate through examples that frustration can generate an exponential number of tunneling paths, which under certain conditions can lead to an exponential advantage for incoherent tunneling over classical QMC escape. We provide analytical and numerical evidence for such an advantage and show that it holds beyond perturbation theory."

(27 Mar 2017) Link to PDF.

Benchmarking Quantum Hardware for Training of Fully Visible Boltzmann Machines
Dmytro Korenkevych, Yanbo Xue, Zhengbing Bian, Fabian Chudak, William G. Macready, Jason Rolfe, Evgeny Andriyash

“Quantum annealing (QA) is a hardware-based heuristic optimization and sampling method applicable to discrete undirected graphical models. While similar to simulated annealing, QA relies on quantum, rather than thermal, effects to explore complex search spaces. For many classes of problems, QA is known to offer computational advantages over simulated annealing. Here we report on the ability of recent QA hardware to accelerate training of fully visible Boltzmann machines.”

(14 Nov 2016) https://arxiv.org/abs/1611.04528

Discrete Variational Autoencoders
Jason Tyler Rolfe

“Probabilistic models with discrete latent variables naturally capture datasets composed of discrete classes. However, they are difficult to train efficiently, since back propagation through discrete variables is generally not possible. We introduce a novel class of probabilistic models, comprising an undirected discrete component and a directed hierarchical continuous component, that can be trained efficiently using the variational autoencoder framework. The discrete component captures the distribution over the disconnected smooth manifolds induced by the continuous component. As a result, this class of models efficiently learns both the class of objects in an image, and their specific realization in pixels, from unsupervised data; and outperforms state-of-the-art methods on the permutation-invariant MNIST, OMNIGLOT, and Caltech-101 Silhouettes datasets.”

(7 Sep 2016) http://arxiv.org/abs/1609.02200

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) Link to PDF.

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

2019

PixelVAE++: Improved PixelVAE with Discrete Prior
Hossein Sadeghi, Evgeny Andriyash, Walter Vinci, Lorenzo Buffoni, and Mohammad H. Amin

Constructing powerful generative models for natural images is a challenging task. PixelCNN models capture details and local information in images very well but have limited receptive field. Variational autoencoders with a factorial decoder can capture global information easily, but they often fail to reconstruct details faithfully. PixelVAE combines the best features of the two models and constructs a generative model that is able to learn local and global structures. Here we introduce PixelVAE++, a VAE with three types of latent variables and a PixelCNN++ for the decoder. We introduce a novel architecture that reuses a part of the decoder as an encoder. We achieve the state of the art performance on binary data sets such as MNIST and Omniglot and achieve the state of the art performance on CIFAR-10 among latent variable models while keeping the latent variables informative.

(26 Aug 2019) https://arxiv.org/abs/1908.09948

Quantum-Assisted Genetic Algorithm
James King et al.

Genetic algorithms, which mimic evolutionary processes to solve optimization problems, can be enhanced by using powerful semi-local search algorithms as mutation operators. Here, we introduce reverse quantum annealing, a class of quantum evolutions that can be used for performing families of quasi-local or quasi-nonlocal search starting from a classical state, as novel sources of mutations. Reverse annealing enables the development of genetic algorithms that use quantum fluctuation for mutations and classical mechanisms for the crossovers—we refer to these as Quantum-Assisted Genetic Algorithms (QAGAs). We describe a QAGA and present experimental results using a D-Wave 2000Q quantum annealing processor. On a set of spin-glass inputs, standard (forward) quantum annealing finds good solutions very quickly but struggles to find global optima. In contrast, our QAGA proves effective at finding global optima for these inputs. This successful interplay of nonlocal classical and quantum fluctuations could provide a promising step toward practical applications of Noisy Intermediate-Scale Quantum (NISQ) devices for heuristic discrete optimization,

(2 July 2019) arXiv: https://arxiv.org/pdf/1907.00707.pdf 

The Mathematics of Quantum-Enabled Applications on the D-Wave Quantum Computer
Jesse J. Berwald

This article covers quantum computing from the angle of adiabatic quantum computing [7,13], which has proven to have the shortest horizon to real-world applications, partly due to a slightly easier path to development2 than alternative approaches such as gate-model quantum computers. In this article we cover background on quantum annealing computing generally, the canonical problem formulation necessary to program the D-Wave quantum processing unit (QPU), and discuss how such a problem is compiled onto the QPU. We also cover recent joint work solving a problem from topological data analysis on the DWave quantum computer. The goal of the article is to cover the above from a mathematical viewpoint, accessible to a wide range of levels, and introduce as many people as possible to a small portion of the mathematics encountered in this industry.
(June/July 2019) Notices of the American Mathematical Society Vol. 66, No. 6, pp. 832-841
Link to PDF

Demonstration of nonstoquastic Hamiltonian in coupled superconducting flux qubits

I. Ozfidan et. al

Quantum annealing (QA) is a heuristic algorithm for finding low-energy configurations of a system, with applications in optimization, machine learning, and quantum simulation. Up to now, all implementations of QA have been limited to qubits coupled via a single degree of freedom. This gives rise to a stoquastic Hamiltonian that has no sign problem in quantum Monte Carlo (QMC) simulations. In this paper, we report implementation and measurements of two superconducting flux qubits coupled via two canonically conjugate degrees of freedom (charge and flux) to achieve a nonstoquastic Hamiltonian. Such coupling can enhance performance of QA processors, extend the range of quantum simulations. We perform microwave spectroscopy to extract circuit parameters and show that the charge coupling manifests itself as a YY interaction in the computational basis. We observe destructive interference in quantum coherent oscillations between the computational basis states of the two-qubit system. Finally, we show that the extracted Hamiltonian is nonstoquastic over a wide range of parameters.

(14 Mar 2019) https://arxiv.org/abs/1903.06139

2018

Solving SAT and MaxSAT with a Quantum Annealer: Foundations, Encodings, and Preliminary Results

Zhengbing Bian, Fabian Chudak, William Macready, Aidan Roy, Roberto Sebastiani, Stefano Varotti

Quantum annealers (QAs) are specialized quantum computers that minimize objective functions over discrete variables by physically exploiting quantum effects. Current QA platforms allow for the optimization of quadratic objectives defined over binary variables (qubits), also known as Ising problems. In the last decade, QA systems as implemented by D-Wave have scaled with Moore-like growth. Current architectures provide 2048 sparsely-connected qubits, and continued exponential growth is anticipated, together with increased connectivity.
We explore the feasibility of such architectures for solving SAT and MaxSAT problems as QA systems scale. We develop techniques for effectively encoding SAT –and, with some limitations, MaxSAT– into Ising problems compatible with sparse QA architectures. We provide the theoretical foundations for this mapping, and present encoding techniques that combine offline Satisfiability and Optimization Modulo Theories with on-the-fly placement and routing. Preliminary empirical tests on a current generation 2048-qubit D-Wave system support the feasibility of the approach for certain SAT and MaxSAT problems

(6 Nov 2018) https://arxiv.org/pdf/1811.02524.pdf

Theory of open quantum dynamics with hybrid noise

Anatoly Yu Smirnov and Mohammad H Amin

We develop a theory to describe dynamics of a non-stationary open quantum system interacting with a hybrid environment, which includes high-frequency and low-frequency noise components. One part of the system–bath interaction is treated in a perturbative manner, whereas the other part is considered exactly. This approach allows us to derive a set of master equations where the relaxation rates are expressed as convolutions of the Bloch–Redfield and Marcus formulas. Our theory enables analysis of systems that have extremely small energy gaps in the presence of a realistic environment. As an illustration, we apply the theory to the 16 qubit quantum annealing problem with dangling qubits (Dickson et al 2013 Nat. Commun. 4 1903) and show qualitative agreement with experimental results.

(26 Oct 2018) New Journal of Physics, Volume 20, October 2018

Computing Wasserstein Distance for Persistence Diagrams on a Quantum Computer

Jesse J. Berwald, Joel M. Gottlieb, Elizabeth Munch 

Persistence diagrams are a useful tool from topological data analysis which can be used to provide a concise description of a filtered topological space. What makes them even more useful in practice is that they come with a notion of a metric, the Wasserstein distance (closely related to but not the same as the homonymous metric from probability theory). Further, this metric provides a notion of stability; that is, small noise in the input causes at worst small differences in the output. In this paper, we show that the Wasserstein distance for persistence diagrams can be computed through quantum annealing. We provide a formulation of the problem as a Quadratic Unconstrained Binary Optimization problem, or QUBO, and prove correctness. Finally, we test our algorithm, exploring parameter choices and problem size capabilities, using a D-Wave 2000Q quantum annealing computer.

(2 Nov 2018) https://arxiv.org/abs/1809.06433

GumBolt: Extending Gumbel trick to Boltzmann priors

Amir H. Khoshaman, Mohammad H. Amin

Boltzmann machines (BMs) are appealing candidates for powerful priors in variational autoencoders (VAEs), as they are capable of capturing nontrivial and multi-modal distributions over discrete variables. However, indifferentiability of the discrete units prohibits using the reparameterization trick, essential for low-noise back propagation. The Gumbel trick resolves this problem in a consistent way by relaxing the variables and distributions, but it is incompatible with BM priors. Here, we propose the GumBolt, a model that extends the Gumbel trick to BM priors in VAEs. GumBolt is significantly simpler than the recently proposed methods with BM prior and outperforms them by a considerable margin. It achieves state-of-the-art performance on permutation invariant MNIST and OMNIGLOT datasets in the scope of models with only discrete latent variables. Moreover, the performance can be further improved by allowing multi-sampled (importance-weighted) estimation of log-likelihood in training, which was not possible with previous models.

(18 May 2018) https://arxiv.org/abs/1805.07349

DVAE#: Discrete Variational Autoencoders with Relaxed Boltzmann Priors

Arash Vahdat, Evgeny Andriyash, William G. Macready

Boltzmann machines are powerful distributions that have been shown to be an effective prior over binary latent variables in variational autoencoders (VAEs). However, previous methods for training discrete VAEs have used the evidence lower bound and not the tighter importance-weighted bound. We propose two approaches for relaxing Boltzmann machines to continuous distributions that permit training with importance-weighted bounds. These relaxations are based on generalized overlapping transformations and the Gaussian integral trick. Experiments on the MNIST and OMNIGLOT datasets show that these relaxations outperform previous discrete VAEs with Boltzmann priors.

(18 May 2018) https://arxiv.org/abs/1805.07445

Theory of open quantum dynamics with hybrid noise

Anatoly Yu. Smirnov, Mohammad H. Amin

We develop a theory to describe dynamics of a nonstationary open quantum system interacting with a hybrid environment, which includes high-frequency and low-frequency noise components. One part of the system-bath interaction is treated in a perturbative manner, whereas the other part is considered exactly. This approach allows us to derive a set of master equations where the relaxation rates are expressed as convolutions of the Bloch-Redfield and Marcus formulas. Our theory enables analysis of systems that have extremely small energy gaps in the presence of a realistic environment. We apply the theory to an example of the 16-qubit quantum annealing problem with dangling qubits and show qualitative agreement with experimental results.

(21 Feb 2018) https://arxiv.org/abs/1802.07715

Toward Robustness against Label Noise in Training Deep Discriminative Neural Networks

Arash Vahdat

Collecting large training datasets, annotated with high-quality labels, is costly and time-consuming. This paper proposes a novel framework for training deep convolutional neural networks from noisy labeled datasets that can be obtained cheaply. The problem is formulated using an undirected graphical model that represents the relationship between noisy and clean labels, trained in a semi-supervised setting. In our formulation, the inference over latent clean labels is tractable and is regularized during training using auxiliary sources of information. The proposed model is applied to the image labeling problem and is shown to be effective in labeling unseen images as well as reducing label noise in training on CIFAR-10 and MS COCO datasets.

(23 Feb 2018) Link to paper

DVAE++: Discrete Variational Autoencoders with Overlapping Transformations

Arash Vahdat, William G. Macready, Zhengbing Bian, Amir Khoshaman

Training of discrete latent variable models remains challenging because passing gradient information through discrete units is difficult. We propose a new class of smoothing transformations based on a mixture of two overlapping distributions, and show that the proposed transformation can be used for training binary latent models with either directed or undirected priors. We derive a new variational bound to efficiently train with Boltzmann machine priors. Using this bound, we develop DVAE++, a generative model with a global discrete prior and a hierarchy of convolutional continuous variables. Experiments on several benchmarks show that overlapping transformations outperform other recent continuous relaxations of discrete latent variables including Gumbel-Softmax (Maddison et al., 2016; Jang et al., 2016), and discrete variational autoencoders (Rolfe, 2016).

(14 Feb 2018) https://arxiv.org/pdf/1802.04920.pdf

2017

From Near to Eternity: Spin-glass planting, tiling puzzles, and constraint satisfaction problems

Firas Hamze (D-Wave); Darryl C. Jacob, Andrew J. Ochoa (Texas A&M University); Wenlong Wang (KTH Royal Institute of Technology,Texas A&M University); and Helmut G. Katzgraber (Texas A&M University, 1QBit Technologies)

We present a methodology for generating Ising Hamiltonians of tunable complexity and with a priori known ground states based on a decomposition of the model graph into edge-disjoint subgraphs. The idea is illustrated with a spin-glass model defined on a cubic lattice, where subproblems, whose couplers are restricted to the two values {-1,+1}, are specified on unit cubes and are parametrized by their local degeneracy. The construction is shown to be equivalent to a type of three-dimensional constraint satisfaction problem known as the tiling puzzle. By varying the proportions of subproblem types, the Hamiltonian can span a dramatic range of typical computational complexity, from fairly easy to many orders of magnitude more difficult than prototypical bimodal and Gaussian spin glasses in three space dimensions. We corroborate this behavior via experiments with different algorithms and discuss generalizations and extensions to different types of graphs.

(Nov 15, 2017) https://arxiv.org/abs/1711.04083

Toward Robustness against Label Noise in Training Deep Discriminative Neural Networks

Arash Vahdat

Collecting large training datasets, annotated with high-quality labels, is costly and time-consuming. This paper proposes a novel framework for training deep convolutional neural networks from noisy labeled datasets that can be obtained cheaply. The problem is formulated using an undirected graphical model that represents the relationship between noisy and clean labels, trained in a semi- supervised setting. In our formulation, the inference over latent clean labels is tractable and is regularized during training using auxiliary sources of information. The proposed model is applied to the image labeling problem and is shown to be effective in labeling unseen images as well as reducing label noise in training on CIFAR-10 and MS COCO datasets.

(03 Nov 2017) https://arxiv.org/pdf/1706.00038.pdf 

Experimental demonstration of perturbative anticrossing mitigation using nonuniform driver Hamiltonians

Trevor Lanting, Andrew D. King, Bram Evert, and Emile Hoskinson

"Perturbative anticrossings have long been identified as a potential computational bottleneck for quantum annealing. This bottleneck can appear, for example, when a uniform transverse driver Hamiltonian is applied to each qubit. Previous theoretical research sought to alleviate such anticrossings by adjusting the transverse driver Hamiltonians on individual qubits according to a perturbative approximation. Here we apply this principle to a physical implementation of quantum annealing in a D-Wave 2000Q system. We use samples from the quantum annealing hardware and per-qubit anneal offsets to produce nonuniform driver Hamiltonians. On small instances with severe perturbative anticrossings, our algorithm yields an increase in minimum eigengaps, ground-state success probabilities, and escape rates from metastable valleys. We also demonstrate that the same approach can mitigate biased sampling of degenerate ground states."

Physical Review A (16 Oct 2017) https://journals.aps.org/pra/abstract/10.1103/PhysRevA.96.042322

Experimental demonstration of perturbative anticrossing mitigation using non-uniform driver Hamiltonians

Trevor Lanting, Andrew D. King, Bram Evert, Emile Hoskinson

"Perturbative anticrossings have long been identified as a potential computational bottleneck for quantum annealing. This bottleneck can appear, for example, when a uniform transverse driver Hamiltonian is applied to each qubit. Previous theoretical research sought to alleviate such anticrossings by adjusting the transverse driver Hamiltonians on individual qubits according to a perturbative approximation. Here we apply this principle to a physical implementation of quantum annealing in a D-Wave 2000Q system. We use samples from the quantum annealing hardware and per-qubit anneal offsets to produce nonuniform driver Hamiltonians. On small instances with severe perturbative anticrossings, our algorithm yields an increase in minimum eigengaps, ground state success probabilities, and escape rates from metastable valleys. We also demonstrate that the same approach can mitigate biased sampling of degenerate ground states."

(10 Aug 2017) https://arxiv.org/abs/1708.03049

Quantum eigenstate tomography with qubit tunneling spectroscopy

Anatoly Yu. Smirnov and Mohammad H. Amin

"Measurement of the energy eigenvalues (spectrum) of a multi-qubit system has recently become possible by qubit tunneling spectroscopy (QTS). In the standard QTS experiments, an incoherent probe qubit is strongly coupled to one of the qubits of the system in such a way that its incoherent tunneling rate provides information about the energy eigenvalues of the original (source) system. In this paper, we generalize QTS by coupling the probe qubit to many source qubits. We show that by properly choosing the couplings, one can perform projective measurements of the source system energy eigenstates in an arbitrary basis, thus performing quantum eigenstate tomography. As a practical example of a limited tomography, we apply our scheme to probe the eigenstates of a kink in a frustrated transverse Ising chain."

(25 Feb 2017) Link to PDF.

2016

Global warming: Temperature estimation in annealers

Jack Raymond, Sheir Yarkoni, Evgeny Andriyash

"Sampling from a Boltzmann distribution is NP-hard and so requires heuristic approaches. Quantum annealing is one promising candidate. The failure of annealing dynamics to equilibrate on practical time scales is a well understood limitation, but does not always prevent a heuristically useful distribution from being generated. In this paper we evaluate several methods for determining a useful operational temperature range for annealers.

(2 Jun 2016) Download PDF. Link to Supplementary Material.

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

 

A frequency and sensitivity tunable microresonator array for high-speed quantum processor readout

J. D. Whittaker,  L. J. Swenson, M. H. Volkmann, P. Spear, F. Altomare,  A. J. Berkley, B. Bumble, P. Bunyk, P. K. Day, B. H. Eom, R. Harris, J. P. Hilton, E. Hoskinson, M. W. Johnson, A. Kleinsasser, E. Ladizinsky, T. Lanting, T. Oh, I. Perminov, E. Tolkacheva, and J. Yao

"Superconducting microresonators have been successfully utilized as detection elements for a wide variety of applications. With multiplexing factors exceeding 1000 detectors per transmission line, they are the most scalable low-temperature detector technology demonstrated to date. For high-throughput applications, fewer detectors can be coupled to a single wire but utilize a larger per-detector bandwidth. For all existing designs, fluctuations in fabrication tolerances result in a non-uniform shift in resonance frequency and sensitivity, which ultimately limits the efficiency of bandwidth utilization. Here, we present the design, implementation, and initial characterization of a superconducting microresonator readout integrating two tunable inductances per detector. We demonstrate that these tuning elements provide independent control of both the detector frequency and sensitivity, allowing us to maximize the transmission line bandwidth utilization. Finally, we discuss the integration of these detectors in a multilayer fabrication stack for high-speed readout of the D-Wave quantum processor, highlighting the use of control and routing circuitry composed of single-flux-quantum loops to minimize the number of control wires at the lowest temperature stage."

(Jan 2016) Journal of Applied Physics 119, 014506 (2016);  https://doi.org/10.1063/1.4939161

2015

Fast clique minor generation in Chimera qubit connectivity graphs
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

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
A practical heuristic for finding graph minors

Jun Cai, Bill Macready, Aidan Roy

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

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 

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

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

Approximate diagonalization method for large-scale Hamiltonians

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

2011

Probing high-frequency noise with macroscopic resonant tunneling

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

Importance of Explicit Vectorization for CPU and GPU Software Performance

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

The Ising model: teaching an old problem new tricks

Z. Bian et al. 
Link to PDF

Investigating the Performance of an Adiabatic Quantum Optimization Processor

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

Does adiabatic quantum optimization fail for NP-complete problems?

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

Quantum annealing with manufactured spins
M.W. Johnson et al.

Nature Vol. 473, pages194–198 (2011)

Link to article

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

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

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

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
M. H. S. Amin et al.

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

2008

Minor-Embedding in Adiabatic Quantum Computation: I. The Parameter Setting Problem
V. Choi et al.
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
Effect of Local Minima on Adiabatic Quantum Optimization
M. H. S. Amin et al.
Phys. Rev. Lett. 100, 130503 (2008) arXiv:0709.0528
Thermally Assisted Adiabatic Quantum Computation
M. H. S. Amin et al.
Phys. Rev. Lett. 100, 060503 (2008) arXiv:cond-mat/0609332
Probing Noise in Flux Qubits via Macroscopic Resonant Tunneling
R. Harris et al.
Phys. Rev. Lett. 101, 117003 (2008) arXiv:0712.0838
Realizable Hamiltonians for Universal Adiabatic Quantum Computers
J. D. Biamonte et al.
Phys. Rev. A 78, 012352 (2008) aXiv:0704.1287

2007

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

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
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
Direct Josephson coupling between superconducting flux qubits
M. Grajcar et al.
Phys. Rev. B 72, (2005) 020503(R) arXiv:cond-mat/0501085

2004

Evidence for Entangled States of Two Coupled Flux Qubits
A. Izmalkov et al.
Phys. Rev. Lett. 93, 037003 (2004) arXiv:cond-mat/0312332
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
Quasiparticle Decoherence in d-Wave Superconducting Qubits
M. H. S. Amin et al.
Phys. Rev. Lett. 92, 017001 (2004) arXiv:cond-mat/0304255
Observation of macroscopic Landau-Zener tunneling in a superconducting device
A. Izmalkov et al.
Euro. Phys. Lett. 65, 844, (2004) arXiv:cond-mat/0307506
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
Superconducting quantum storage and processing
M. H. S. Amin et al.
IEEE International Solid State Circuit Conference (ISSCC), Tech. Dig., p296(2004)

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)
Nonequilibrium quasiclassical theory for Josephson structures
M. H. S. Amin, et al.
Phys. Rev. B 68, 054505 (2003) arXiv:cond-mat/0207724
Josephson-phase qubit without tunneling
M. H. S. Amin et al.
Phys. Rev. B 67, 100508 (2003) arXiv:cond-mat/0211638
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
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
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
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
Tunable coupling of superconducting qubits
A. Blais et al.
Phys. Rev. Lett. 90, 127901 (2003) arXiv:cond-mat/0207112

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
Low-frequency characterization of quantum tunneling in flux qubits
Y. S. Greenberg et al.
Phys. Rev. B 66, 214525 (2002) arXiv:cond-mat/0208076
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
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

2001

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
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
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