# A quantum annealer with fully programmable all-to-all coupling via Floquet engineering

## TL;DR

This paper proposes a scalable quantum annealer architecture with full connectivity and programmability using Floquet engineering, enabling more efficient solutions to complex optimization problems with current superconducting circuit technology.

## Contribution

It introduces a novel Floquet-based method to achieve full all-to-all coupling in quantum annealers with resources linear in the number of spins, suitable for superconducting circuits.

## Key findings

- Full connectivity and programmability achieved with linear resources.
- Analytical and numerical evidence supports feasibility with current technology.
- Potential extension to bosonic quantum simulators and arbitrary lattice models.

## 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 a cost of the coupling strengths between spins being smaller than they would be had the spins been directly coupled. Our proposal is well-suited to implementation with superconducting circuits, and we give analytical and numerical evidence that fully connected, fully programmable quantum annealers with $1000$ qubits could be constructed with Josephson parametric oscillators having cavity-photon lifetimes of $\sim 100$ microseconds, and other system-parameter values that are routinely achieved with current technology. 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.