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 ...
The preparation of quantum states using short quantum circuits is one of the most promising near-term applications of small quantum computers, especially if the circuit is short enough and the fidelity of gates high enough that it can be executed without quantum error correction. Such quantum state preparation can be used in variational approaches, optimizing parameters in the circuit to minimize the energy of the constructed quantum state for a given problem Hamiltonian. For this purpose we propose a simple-to-implement class of quantum states motivated by adiabatic state preparation. We test its accuracy and determine the required circuit depth for a Hubbard model on ladders with up to 12 sites (24 spin-orbitals), and for small molecules. We find that this ansatz converges faster than previously proposed schemes based on unitary coupled clusters. While the required number of measurements is astronomically large for quantum chemistry applications to molecules, applying the variational approach to the Hubbard model (and related models) is found to be far less demanding and potentially practical on small quantum computers. We also discuss another application of quantum state preparation using short quantum circuits, to prepare trial ground states of models faster than using adiabatic state preparation.
The development of small-scale quantum devices raises the question of how to fairly assess and detect quantum speedup. Here, we show how to define and measure quantum speedup and how to avoid pitfalls that might mask or fake such a speedup. We illustrate our discussion with data from tests run on a D-Wave Two device with up to 503 qubits. By using random spin glass instances as a benchmark, we found no evidence of quantum speedup when the entire data set is considered and obtained inconclusive results when comparing subsets of instances on an instance-by-instance basis. Our results do not rule out the possibility of speedup for other classes of problems and illustrate the subtle nature of the quantum speedup question.
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