Multimode physics of the unimon circuit

TL;DR

This paper develops a detailed theoretical and numerical model for the multimode physics of the unimon superconducting circuit, revealing how high-frequency modes influence qubit properties and enabling potential multimode quantum information processing.

Contribution

It introduces an efficient method to account for multimode effects in the unimon circuit, highlighting the impact of high-frequency modes and mode coupling on qubit characteristics.

Findings

High-frequency modes cause significant renormalization of Josephson energy.

Unexcited high-lying modes affect qubit energy and anharmonicity.

Strong cross-Kerr coupling exists between low-lying modes when the junction is offset.

Abstract

We consider a superconducting half-wavelength resonator that is grounded at its both ends and contains a single Josephson junction. Previously this circuit was considered as a unimon qubit in the single-mode approximation where dc-phase-biasing the junction to $\pi$ leads to increased anharmonicity and 99.9% experimentally observed single-qubit gate fidelity. Inspired by the promising first experimental results, we develop here a theoretical and numerical model for the detailed understanding of the multimode physics of the unimon circuit. To this end, first, we consider the high-frequency modes of the unimon circuit and find that even though these modes are at their ground state, they imply a significant renormalization to the Josephson energy. We introduce an efficient method how the relevant modes can be fully taken into account and show that unexcited high-lying modes lead to corrections in the qubit energy and anharmonicity. Interestingly, provided that the junction is offset from the middle of the circuit, we find strong cross-Kerr coupling strengths between a few low-lying modes. This observation paves the way for the utilization of the multimode structure, for example, as several qubits embedded into a single unimon circuit.