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arXiv:1606.05550

Stochastic Characteristics of Qubits and Qubit chains on the D-Wave 2X

John E. Dorband

Published Jun 17, 2016• 2 citations
arXivHTMLPDF

Abstract

This document presents a studies of the stochastic behavior of D-Wave qubits, qubit cells, and qubit chains. The purpose of this paper is to address the algorithmic behavior of execution rather than the physical behavior, though they are related. The measurements from an actual D-Wave adiabatic quantum computer are compare with calculated measurements from a theoretical adiabatic quantum computer running with an effective temperature of zero. In this way the paper attempts to shed light on how the D-Wave's behavior effects how well it minimizes its objective function and why the D-Wave performs as it does.

DOI
10.48550/arxiv.1606.05550

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This document presents a studies of the stochastic behavior of D-Wave qubits, qubit cells, and qubit chains. The purpose of this paper is to address the algorithmic behavior of execution rather than the physical behavior, though they are related. The measurements from an actual D-Wave adiabatic quantum computer are compare with calculated measurements from a theoretical adiabatic quantum computer running with an effective temperature of zero. In this way the paper attempts to shed light on how the D-Wave's behavior effects how well it minimizes its objective function and why the D-Wave performs as it does.
The purpose of the D-Wave adiabatic quantum computer is to find a set of qubit values that minimize its objective function. For various reasons, the set of qubit values returned by the D-Wave has errors. This paper presents a method of improving the results returned by the D-Wave. The method individually modifies the qubit values returned by the D-Wave to find a set of values which is a minimum of the objective function. That set however is not necessarily guaranteed to be a global minimum. The method is simple and easily incorporated into any algorithm that has direct access to the sets of values returned by the D-Wave. Examples are also presented that demonstrate the merit of using such a sample improvement method.
Quantum computation performs calculations by using quantum devices instead of electronic devices following classical physics and used by classical computers. Although general purpose quantum computers of practical scale may be many years away, special purpose quantum computers are being built with capabilities exceeding classical computers. One prominent case is the so-called D-Wave quantum computer, which is a computing hardware device built to implement quantum annealing for solving combinatorial optimization problems. Whether D-Wave computing hardware devices display a quantum behavior or can be described by a classical model has attracted tremendous attention, and it remains controversial to determine whether quantum or classical effects play a crucial role in exhibiting the computational input–output behaviors of the D-Wave devices. This paper consists of two parts where the first part provides a review of quantum annealing and its implementations, and the second part proposes statistical methodologies to analyze data generated from annealing experiments. Specifically, we introduce quantum annealing to solve optimization problems and describe D-Wave computing devices to implement quantum annealing. We illustrate implementations of quantum annealing using Markov chain Monte Carlo (MCMC) simulations carried out by classical computers. Computing experiments have been conducted to generate data and compare quantum annealing with classical annealing. We propose statistical methodologies to analyze computing experimental data from a D-Wave device and simulated data from the MCMC based annealing methods, and establish asymptotic theory and check finite sample performances for the proposed statistical methodologies. Our findings confirm bimodal histogram patterns displayed in input–output data from the D-Wave device and both U-shape and unimodal histogram patterns exhibited in input–output data from the MCMC based annealing methods. Further statistical explorations reveal possible sources for the U-shape patterns. On the other hand, our statistical analysis produces statistical evidence to indicate that input–output data from the D-Wave device are not consistent with the stochastic behaviors of any MCMC based annealing models under the study. We present a list of statistical research topics for the future study on quantum annealing and MCMC simulations.
On May 2011, D-Wave Systems Inc. announced "D-Wave One", as "the world's first commercially available quantum computer". No wonder this adiabatic quantum computer based on 128-qubit chip-set provoked an immediate controversy. Over the last 40 years, quantum computation has been a very promising yet challenging research area, facing major difficulties producing a large scale quantum computer. Today, after Google has purchased "D-Wave Two" containing 512 qubits, criticism has only increased. In this work, we examine the theory underlying the D-Wave, seeking to shed some light on this intriguing quantum computer. Starting from classical algorithms such as Metropolis algorithm, genetic algorithm (GA), hill climbing and simulated annealing, we continue to adiabatic computation and quantum annealing towards better understanding of the D-Wave mechanism. Finally, we outline some applications within the fields of information and image processing. In addition, we suggest a few related theoretical ideas and hypotheses.
The paper is based on a thesis with the same title. The purpose of this thesis is to analyse D-Wave devices using quantum effects. The research focuses on demonstrating the advantages and disadvantages of a company moving away from the circuit model in its computers. The subject of the research is the used adiabatic model of quantum computing based on the mechanism of quantum annealing. The research is based on publicly available, comprehensive documentation of D-Wave Systems. On the basis of scientific papers, conferences and information contained in websites, controversies, disadvantages and advantages of the solutions adopted have been described.
Abstract Recent access to commercially available quantum computing capabilities offers the potential for testing a host of new algorithms that take advantage of fundamentally different processing approaches. One such computing resource is D-Wave’s quantum annealing computer, which employs an energy minimization-based computing mechanism to find solutions to problems stated in an Ising formulation. These solutions, however, must be interpreted in terms of Monte Carlo-style probabilistic occurrences and histograms of candidate solutions that presume the underlying statistics of the qubits are “fair.” This paper quantifies the underlying fairness of individual qubits on a single D-Wave machine, showing that there is a measurable bias in the resulting solution as a function of which qubits are used in the calculation. Further, an example problem is demonstrated, whereby the same problem formulation yields distinctly different solution probabilities by changing which physical qubits are employed.
The shift of interest from general purpose quantum computers to adiabatic quantum computing or quantum annealing calls for a broadly applicable and easy to implement test to assess how quantum or adiabatic is a specific hardware. Here we propose such a test based on an exactly solvable many body system-the quantum Ising chain in transverse field-and implement it on the D-Wave machine. An ideal adiabatic quench of the quantum Ising chain should lead to an ordered broken symmetry ground state with all spins aligned in the same direction. An actual quench can be imperfect due to decoherence, noise, flaws in the implemented Hamiltonian, or simply too fast to be adiabatic. Imperfections result in topological defects: Spins change orientation, kinks punctuating ordered sections of the chain. The number of such defects quantifies the extent by which the quantum computer misses the ground state, and is, therefore, imperfect.