Quantum annealing with all-to-all connected nonlinear oscillators

Abstract

Quantum annealing aims at solving combinatorial optimization problems mapped to Ising interactions between quantum spins. Here, with the objective of developing a noise-resilient annealer, we propose a paradigm for quantum annealing with a scalable network of two-photon-driven Kerr-nonlinear resonators. Each resonator encodes an Ising spin in a robust degenerate subspace formed by two coherent states of opposite phases. A fully connected optimization problem is mapped to local fields driving the resonators, which are connected with only local four-body interactions. We describe an adiabatic annealing protocol in this system and analyse its performance in the presence of photon loss. Numerical simulations indicate substantial resilience to this noise channel, leading to a high success probability for quantum annealing. Finally, we propose a realistic circuit QED implementation of this promising platform for implementing a large-scale quantum Ising machine.

Robust quantum optimizer with full connectivity

“…Our results open up new perspectives for quantum optimization. After the present work was made public, a related but independent work was reported ( 50 ). …”

Effect of Higher-Order Nonlinearities on Amplification and Squeezing in Josephson Parametric Amplifiers

“…Similar analysis for a Josephson junction based traveling-wave parametric amplifier could help the current experimental and theoretical effort [65][66][67][68][69]. Finally, while higher-order corrections hinder the performance of the JPA for squeezing and amplification, it can become a feature for other applications of the JPA such as robust cat state preparation and stabilization [70] which can be used for quantum computation [71] and quantum annealing [72]. For this work to be self-contained, we present the standard solution to the equation of motions of the DPA discussed in Sec.…”

Coherent Ising machines—optical neural networks operating at the quantum limit

“…24,25 Fully connected superconducting Ising machines have been also proposed recently. 26,27 CLASSICAL VS. QUANTUM NEURAL NETWORKS Nonlinear devices that have a characteristic input-output relation shown in Fig. 2a represent a typical gain function of neurons in classical neural networks (CNN).…”