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.
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.
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.
With the emergence of D-wave’s quantum annealing machine, the power of quantum computing has become tangible, and the development of quantum computers is accelerating rapidly. Unfortunately, at present, the minimum value search that D-wave’s quantum annealing machine can handle is limited to quadratic functions of binary integer variables. This constraint is due to both hardware and software limitations. If this constraint was to be lifted, it would undoubtedly bring about a revolution in the world. Therefore, in this study, we obtained the basic mathematics of using quantum annealing, which enables hyper-parallel computing using qubits, to find the global minimum of any minimum value problem. Furthermore, we conducted simple simulations using classical computers to demonstrate the effectiveness of the ideas and algorithms. Furthermore, we conducted simple simulations using classical computers to demonstrate the effectiveness of the ideas and algorithms. We obtained also the mathematical method of using quantum annealing in learning neural networks and solving linear equations.
A quantum computer employing a single quantum as a qubit executes real parallel computation and has various applications. Several algorithms have been proposed for quantum computation. However, these algorithms are applicable only to a limited number of applications. Therefore, a general purpose algorithm should be studied and developed for practical use in the near future. In this paper, we focus on the adiabatic evolution algorithm for general purpose quantum computation and discuss how to use this algorithm for solving an optimization problem. We show a new algorithm incorporating an artificial neural network (ANN)-like method in order to compose another Hamiltonian. The new algorithm is helpful for reducing computation cost and is easy to implement. Successful simulation results are shown.
We establish a linear quantum query lower bound for high-accuracy convex optimization over an explicit family of n-dimensional ellipsoids. We focus on linear optimization with an explicitly given objective, where the feasible set is accessed through a membership oracle. We show that any algorithm that, for every unit linear objective, returns an exactly feasible point with additive objective error Θ(n−1/2) requires Ω(n) membership queries, where the ellipsoids are contained in the unit ball. The same lower bound can be shown to hold if the returned point is only required to be approximately feasible, within Θ(n−3/2) distance from the feasible set. This resolves an open question posed by Chakrabarti, Childs, Li, and Wu~(\textit{Quantum}, 2020) and by van Apeldoorn, Gilyén, Gribling, and de Wolf~(\textit{Quantum}, 2020). Coupled with the upper bounds in these papers, the query complexity of high-accuracy convex optimization is characterized tightly up to logarithmic factors. The proof is built around a lower bound for determinant computation that is derived via a novel polynomial method based on Fourier-rank. In the continuous matrix phase-query model, computing the determinant of a real n×n matrix requires at least n/2 matrix-vector product queries. The construction also yields an Ω(n) phase-query lower bound for estimating the minimum eigenvalue of a real symmetric n×n matrix to additive accuracy Θ(n−2). These results extend the determinant and minimum-eigenvalue lower bounds of Childs, Hung, and Li~(ICALP 2021) from finite fields to the real-valued setting. Based on the same constructions, we also prove an Ω(min{κ,n}) gradient-query lower bound for constant-accuracy optimization of 1-strongly convex and κ-smooth functions, which is optimal up to a logarithmic factor.
The goal of this paper is to introduce building blocks for adiabatic quantum algorithms. Adiabatic quantum computing uses the principle of quantum annealing, which implies that a carefully controlled energy solution is optimal and corresponds to minimizing a discrete function. The input function can be influenced by rewards and penalties to favor a solution that meets restrictions that are imposed by the problem. We show how to accomplish this influence for gates in adiabatic quantum computing, particularly the controlled-NOT gate (CNOT gate) which is fundamental to all quantum gates on two or more qubits. In addition, we adapt the Toffoli gate, the Fredkin gate, and the Hadamard gate to the Ising objective function which is a foundation for discrete optimization on D-Wave System machines. The quantum work in this paper encompasses Boolean operations, some of which are used to construct gates. We think the possible advantages of the building blocks in this paper will enhance quantum algorithms on D-Wave System computers.