# Demonstration of nonstoquastic Hamiltonian in coupled superconducting flux qubits

## TL;DR

This paper demonstrates a nonstoquastic Hamiltonian in coupled superconducting flux qubits by coupling via charge and flux degrees of freedom, potentially improving quantum annealing and simulation capabilities.

## Contribution

It introduces a novel coupling scheme for flux qubits that achieves a nonstoquastic Hamiltonian, expanding the possibilities for quantum annealing and simulation.

## Key findings

- Charge coupling manifests as YY interaction
- Destructive interference observed in quantum oscillations
- Hamiltonian shown to be nonstoquastic over a wide parameter range

## Abstract

Quantum annealing (QA) is a heuristic algorithm for finding low-energy configurations of a system, with applications in optimization, machine learning, and quantum simulation. Up to now, all implementations of QA have been limited to qubits coupled via a single degree of freedom. This gives rise to a stoquastic Hamiltonian that has no sign problem in quantum Monte Carlo (QMC) simulations. In this paper, we report implementation and measurements of two superconducting flux qubits coupled via two canonically conjugate degrees of freedom (charge and flux) to achieve a nonstoquastic Hamiltonian. Such coupling can enhance performance of QA processors, extend the range of quantum simulations. We perform microwave spectroscopy to extract circuit parameters and show that the charge coupling manifests itself as a YY interaction in the computational basis. We observe destructive interference in quantum coherent oscillations between the computational basis states of the two-qubit system. Finally, we show that the extracted Hamiltonian is nonstoquastic over a wide range of parameters.