Abstract
Quantum annealing is a promising approach to heuristically solving difficult combinatorial optimization problems. However, the connectivity limitations in current devices lead to an exponential degradation of performance on general problems. We propose an architecture for a quantum annealer that achieves full connectivity and full programmability while using a number of physical resources only linear in the number of spins. We do so by application of carefully engineered periodic modulations of oscillator-based qubits, resulting in a Floquet Hamiltonian in which all the interactions are tunable. This flexibility comes at the cost of the coupling strengths between qubits being smaller than they would be compared with direct coupling, which increases the demand on coherence times with increasing problem size. We analyze a specific hardware proposal of our architecture based on Josephson parametric oscillators. Our results show how the minimum-coherence-time requirements imposed by our scheme scale, and we find that the requirements are not prohibitive for fully connected problems with up to at least 1000 spins. Our approach could also have impact beyond quantum annealing, since it readily extends to bosonic quantum simulators, and would allow the study of models with arbitrary connectivity between lattice sites.
Highlights
Quantum annealers are computational devices designed for solving combinatorial optimization problems, most typically Ising optimization problems[1,2,3]
We study the design of a quantum annealer whose purpose is to solve the Ising optimization problem, defined as finding the N-spin configuration σi 2 fÀ1; þ1g (i = 1, ..., N) that minimizes the classical spin energy E(σ): = ∑j≠iCijσiσj, where C is a symmetric real matrix
C can have OðN2Þ non-zero entries. It is desirable for a quantum annealer to be fully programmable, such that there are no restrictions on the structure of C, and that the annealer not use more than N oscillators to represent a given N-spin problem, nor use more than ∝ N other physical components
Summary
Quantum annealers are computational devices designed for solving combinatorial optimization problems, most typically Ising optimization problems[1,2,3]. One of the foremost challenges in the experimental realization of quantum annealers is the requirement that quantum annealers be able to represent densely connected Ising problems with minimal overhead in the number of qubits (and other physical components) used[4,5,6,7]. If a quantum annealer is not able to directly represent a particular problem because the problem graph has higher connectivity than the physical annealer does, one incurs a penalty in the number of qubits needed to represent the Ising problem. Bus architectures have been demonstrated for superconducting-circuit qubits in the context of circuit-model quantum computing[11,12,13], and busmediated interactions naturally provide all-to-all coupling[11,14,15], with the use of one physical coupler per qubit.
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