Evidence for quantum annealing with more than one hundred qubits

Abstract

Quantum technology is maturing to the point where quantum devices, such as quantum communication systems, quantum random number generators and quantum simulators, may be built with capabilities exceeding classical computers. A quantum annealer, in particular, solves hard optimisation problems by evolving a known initial configuration at non-zero temperature towards the ground state of a Hamiltonian encoding a given problem. Here, we present results from experiments on a 108 qubit D-Wave One device based on superconducting flux qubits. The strong correlations between the device and a simulated quantum annealer, in contrast with weak correlations between the device and classical annealing or classical spin dynamics, demonstrate that the device performs quantum annealing. We find additional evidence for quantum annealing in the form of small-gap avoided level crossings characterizing the hard problems. To assess the computational power of the device we compare it to optimised classical algorithms.Annealing a material by slow cooling is an ancient technique to improve the properties of glasses, metals and steel that has been used for more than seven millennia [1]. Mimicking this process in computer simulations is the idea behind simulated annealing as an optimisation method [2], which views the cost function of an optimisation problem as the energy of a physical system. Its configurations are sampled in a Monte Carlo simulation using the Metropolis algorithm [3], escaping from local minima by thermal fluctuations to find lower energy configurations. The goal is to find the global energy minimum (or at least a close approximation) by slowly lowering the temperature and thus obtain the solution to the optimisation problem.The phenomenon of quantum tunneling suggests that it can be more efficient to explore the state space quantum mechanically in a quantum annealer [4][5][6]. In simulated quantum annealing [7,8], one makes use of this effect by adding quantum fluctuations, which are slowly reduced while keeping the temperature constant and positive -ultimately ending up in a low energy configuration of the optimisation problem. Simulated quantum annealing, using a quantum Monte Carlo algorithm, has been observed to be more efficient than thermal annealing for certain spin glass models [8], although the opposite has been observed for k-satisfiability problems [9]. Further speedup may be expected in physical quantum annealing, either as an experimental technique for annealing a quantum spin glass [10], or -and this is what we will focus on here -as a computational technique in a programmable quantum device.In this work we report on computer simulations and experimental tests on a D-Wave One device [11] in order to address central open questions about quantum annealers: is the device actually a quantum annealer, i.e., do the quantum effects observed on 8 [11,12] and 16 qubits [13] persist when scaling problems up to more than 100 qubits, or do short coherence times turn the device into a classical, thermal annealer? Which ...

Quantum Boltzmann Machine

“…Up to now many experiments have confirmed the existence of quantum phenomena in such processors [15,[35][36][37][38], which includes entanglement [39]. A quantum annealing processor implements the time-dependent Hamiltonian…”

Quadratic unconstrained binary optimization problem preprocessing: Theory and empirical analysis

“…In addition, a new type of quantum computer based on quantum annealing with an integrated physical network structure of qubits known as a Chimera graph has also been demonstrated to very quickly find good solutions to QUBO [4]. The Chimera structure is a connected network of qubits with groups of densely connected nodes sparsely connected to other groups of densely connected nodes, having a structure similar to that of social network visualizations or to a collection of densely connected cities sparsely linked to other cities via fiber optic backbones (see Figure 1).…”

Towards quantum simulating QCD

“…While theoretical constructions for quantum computers based on ultracold trapped ions exist already for some time [11], it is difficult to predict when powerful quantum computers may become available. The D-wave devices based on a network of superconducting flux qubits have been used to operate the quantum adiabatic algorithm [12] on random instances of an Ising spin glass [13]. A comparison with simulated classical and quantum annealing algorithms led to the conclusion that the D-wave machines indeed perform quantum rather than classical annealing, but are not yet competitive with classical computers.…”