Building a bigger Hilbert space for superconducting devices, one Bloch state at a time

TL;DR

This paper explores a novel approach to superconducting qubits by treating phase and charge as noncompact variables, leading to a Bloch band structure that could enable more robust quantum information encoding.

Contribution

It introduces a framework that lifts the traditional compact variable assumption, analyzing Bloch band structures in superconducting circuits for improved qubit design.

Findings

Identification of a Bloch band structure in superconducting circuits.

Proposal of superpositions of quasicharge states for qubit encoding.

Potential for inherently robust qubit states based on lowest Bloch band eigenstates.

Abstract

Superconducting circuits for quantum information processing are often described theoretically in terms of a discrete charge, or equivalently, a compact phase/flux, at each node in the circuit. Here we revisit the consequences of lifting this assumption for transmon and Cooper-pair-box circuits, which are constituted from a Josephson junction and a capacitor, treating both the superconducting phase and charge as noncompact variables. The periodic Josephson potential gives rise to a Bloch band structure, characterised by the Bloch quasicharge. We analyse the possibility of creating superpositions of different quasicharge states by transiently shunting inductive elements across the circuit, and suggest a choice of eigenstates in the lowest Bloch band of the spectrum that may support an inherently robust qubit encoding.