Quantum annealing with a network of all-to-all connected, two-photon driven Kerr nonlinear oscillators

TL;DR

This paper introduces a scalable quantum annealing approach using a network of Kerr nonlinear oscillators, encoding Ising spins in coherent states, and demonstrates its noise resilience and potential for large-scale quantum optimization in circuit QED.

Contribution

It proposes a novel quantum annealing paradigm with all-to-all connected Kerr resonators encoding Ising spins, enhancing noise resilience and scalability for quantum optimization.

Findings

Numerical simulations show resilience to photon loss.

The scheme maps complex optimization problems onto a network of resonators.

A realistic circuit QED implementation is proposed.

Abstract

Quantum annealing aims to solve combinatorial optimization problems mapped on to Ising interactions between quantum spins. A critical factor that limits the success of a quantum annealer is its sensitivity to noise, and intensive research is consequently focussed towards developing noise-resilient annealers. Here we propose a new paradigm for quantum annealing with a scalable network of all-to-all connected, two-photon driven Kerr-nonlinear resonators. Each of these resonators encode an Ising spin in a robust degenerate subspace formed by two coherent states of opposite phases. The fully-connected optimization problem is mapped onto local fields driving the resonators, which are themselves connected by local four-body interactions. We describe an adiabatic annealing protocol in this system and analyze its performance in the presence of photon loss. Numerical simulations indicate substantial resilience to this noise channel, making it a promising platform for implementing a large scale quantum Ising machine. Finally, we propose a realistic implementation of this scheme in circuit QED.