D-Wave White Papers


Improved coherence leads to gains in quantum annealing performance

D-Wave has fabricated a series of quantum processing units (QPUs) possessing the same design but different materials within the QPU. In order to demonstrate the sensitivity of QPU performance to materials-related noise, a common set of identical spin glass problems, similar to those studied in a July 2018 Science article, has been posed to two such QPUs. The experimental results confirm a positive correlation between reduced noise and improved performance with at least a 25x speed up in solving spin glass problems having been observed.

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Probing Mid-Band and Broad-Band Noise in Lower-Noise D-Wave 2000Q Fabrication Stacks

D-Wave has been continually developing its fabrication stack in order to reduce sources of noise. Here, we present the noise assessment results for two prototype lower-noise D-Wave 2000Q fabrication stacks, recently developed as part of the low-noise quantum annealing processor development project. Using single-qubit and multi-qubit tunneling rates measurements, we compare the flux noise in lower-noise D-Wave 2000Q fabrication stacks to the base-line D-Wave 2000Q fabrication stack and show 4.3× reduction in mid-band noise and 3× reduction in broad-band noise levels. The reduced-noise levels in the newly-developed processor result in 7.4× enhancement in tunneling rates.

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Next-Generation Topology of D-Wave Quantum Processors
Kelly Boothby, Paul Bunyk, Jack Raymond, Aidan Roy

This paper presents an overview of the topology of D-Wave’s next- generation quantum processors. It provides examples of minor embed- dings and discusses performance of embedding algorithms for the new topology compared to the existing Chimera topology. It also presents some initial performance results for simple, standard Ising model classes of problems.

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A Head-to-Head Comparison of D-Wave and Rigetti QPUs

"Gate-model quantum computers are theoretically capa- ble of exceptional performance in certain applications, al- though it is unclear how useful they will be in general. The Quantum Approximate Optimization Algorithm (QAOA) of Farhi et al. has been proposed as a possible path towards making gate-model quantum computers effective at solving problems in combinatorial optimization.

Recently, Rigetti Computing published results of QAOA run on their 19-qubit gate-model quantum computer. The inputs they considered can also be solved on D-Wave quantum annealing systems, providing an opportunity to compare the two quantum processing units (QPUs) directly. Re-producing their tests, we found the probabilities of returning an optimal solution to be 99.6% for the D-Wave 2000Q and 0.001% for the Rigetti 19Q. In addition, the D-Wave 2000Q was able to solve 102 copies of the problem in parallel. The advantages in quality and size of the D-Wave 2000Q, taken together, provide an improvement of 10 million times in terms of ground-state throughput per sample."

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Synopsis: Phase transitions in a programmable quantum spin-glass simulator


In Science, July 13, 2018, researchers from D-Wave Systems Inc. report upon using a 2048-qubit quantum processing unit to experimentally study a computationally difficult problem known within the eld of quantum magnetism as the transverse eld Ising model. The researchers programmed 3-dimensional cubic lattices containing up to 512 quantum spins into their processor and studied the magnetic properties as a function of energy scales and intentionally induced disorder. The predicted phase tran- sitions between paramagnetic and ordered antiferromagnetic phases for low concentrations of disorder, and between paramagnetic and spin-glass phases for high con- centrations of disorder, were demonstrated as a function of the quantum mechanical energy scale.

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Performance advantage in quantum Boltzmann sampling

Investigations of quantum computing were originally motivated by the possibility of efficiently simulating quantum systems. Here we approach this challenge using a D-Wave 2000Q system to estimate quantum Boltzmann statistics. We compare performance with state-of-the-art classical Monte Carlo simulations of the quantum systems, and find that, over the problems studied, the D-Wave processor realizes a performance advantage over classical methods that increases with simulated system size. 



Reverse Quantum Annealing for Local Refinement of Solutions

The success of classical heuristic search algorithms often depends on the balance between global search for good regions of the solution space (exploration) and local search that refones known good solutions (exploitation). While local refinement of known solutions is not available to the canonical forward quantum annealing algorithm, D-Wave has developed a reverse annealing feature that makes this possible by annealing backward from a specified state, then forward to a new state. This enables the use of quantum annealing for the refinement of classical states via local search, making it possible to use quantum annealing as a component in more sophisticated hybrid algorithms. Local quantum search has been analyzed theoretically to explore applications such as protein folding, and has natural application in molecular dynamics, quantum simulation, and quantum chemistry, but has not been available for experiments until now. In a preliminary example, we show that reverse annealing can be used to generate new global optima up to 150 times faster than forward quantum annealing.


Virtual Graphs for High-Performance Embedded Topologies

Many optimization and machine learning algorithms are commonly described as graph problems. For example, graphical models are often used to analyze the  flow of traffic between cities or the transmission of information between neurons in an artificial neural network.

D-Wave quantum processing units (QPUs) solve graphifical models—specifically, Ising minimization problems on a physical working graph made up of qubits and couplers. The new virtual graphs feature of the D-Wave 2000Q system provides users with improved embedding performance wrapped in a simplified interface. We describe the key enabling processor technologies, and provide a simple example with performance results enabled by this new feature in the D-Wave 2000Q system. DOWNLOAD.

Quantum Performance Evaluation: A Short Reading List

Since the first release of D-Wave annealing-based quantum computers in 2010, scores of research papers have been published describing their physical properties, capabilities, and performance. The research domain is complex and rich, which means that the work is ongoing and will continue for many years.

This white paper gives a snapshot of recent work on quantum system performance evaluation, which considers both solution quality and computation time.


Optimization with Clause Problems
C. C. McGeoch, J. King, M. Mohammadi Nevisi, S. Yarkoni, and J. Hilton

We introduce a new input class called clause problems, that can be used to study local constraint structures, which occur in inputs translated from general NP-hard problems to the D-Wave native topology. We describe a small family of clause problems that are contrived to create significant challenges for two classical competition solvers, simulated annealing (SA) and the Hamze–de Frietas–Selby solver (HFS). We identify key properties of these inputs that lead to poor performance by the classical solvers, and consider whether these properties might naturally arise in problems from real-world applications.


Computational Power Consumption and Speedup

Power consumption for computation is a serious and growing issue for the world. We rely more and more on computing in everything we do as we try to satisfy our ever-increasing thirst for mobile computing, automation, machine intelligence, cloud computing, and increasingly powerful supercomputers. Highly specialized coprocessors such as D-Wave’s quantum processing units (QPUs) show promise in significantly increasing the power effciency of computing. In a recent study, D-Wave’s 2000-qubit system was shown to be up to 100 times more energy effcient than highly specialized algorithms on state-of-the-art classical computing servers when considering pure computation time, suggesting immediate relevance to large-scale energy efficient computing. 


Quantum Annealing amid Local Ruggedness and Global Frustration
J. King, S. Yarkoni, J. Raymond, I. Oz dan, A. D. King, M. Mohammadi Nevisi, J. P. Hilton, and C. C. McGeoch

We introduce a problem class with two attributes crucial to the evaluation of quantum annealing processors: local ruggedness (i.e., tall, thin energy barriers in the energy landscape) so that quantum tunneling can be harnessed as a useful resource, and global frustration so that the problems are combinatorially challenging and representative of real-world inputs. We evaluate the new 2000-qubit D-Wave quantum processing unit (QPU) on these inputs, comparing it to software solvers that include both GPU-based solvers and a CPU-based solver which is highly tailored to the D-Wave topology. The D-Wave QPU solidly outperforms the software solvers: when we consider pure annealing time, the D-Wave QPU is three to four orders of magnitude faster than software solvers in both optimization and sampling evaluations. 


Boosting integer factoring performance via quantum annealing offsets
Evgeny Andriyash, Zhengbing Bian, Fabian Chudak, Marshall Drew-Brook, Andrew D. King, William G. Macready, Aidan Roy

D-Wave quantum computing systems now allow a user to advance or delay the annealing path of individual qubits through the anneal offsets feature. Here we demonstrate the potential of this feature by using it in an integer factoring circuit. Offsets allow the user to homogenize dynamics of various computational elements in the circuit. This gives a remarkable improvement over baseline performance, in some cases making the computation more than 1000 times faster. 


Limits on Parallel Speedup for Classical Ising Model Solvers

Why can’t we put together a million cores and make it run a million times faster? Parallel computing systems offer enormous potential for significant runtime speedups over computation by a single CPU core. However, many computational tasks cannot be effciently parallelized. We explore some practical limits to achieving parallel speedups, with reference to some classical optimization solvers that are competitors to D-Wave quantum computers.


Partitioning Optimization Problems for Hybrid Classical/Quantum Execution
Michael Booth, Steven P. Reinhardt, and Aidan Roy

In this white paper we introduce qbsolv, a tool that solves large quadratic unconstrained binary optimization (QUBO) problems by partitioning into subproblems targeted for execution on a D-Wave system. Using a classical subproblem solver rather than quantum annealing, qbsolv delivers state-of-the-art numerical results and executes almost twice as fast as the best previously known implementation. We have released qbsolv as open-source software to foster greater use and experimentation in such partitioning solvers and to establish the QUBO form as a target for higher-level optimization interfaces. The software can be acccessed on GitHub at github.com/dwavesystems/qbsolv



Programming with D-Wave: Map Coloring Problem

Quantum computing, as implemented in the D-Wave system, is described by a simple but largely unfamiliar programming model. Using a simple map coloring problem this white paper describes the entire set of transformations needed to find solutions by executing a single quantum machine instruction (QMI) within this programming model. This “direct embedding” is one of several ways to program the D-Wave quantum computer.