Degeneracy-preserving quantum non-demolition measurement of parity-type observables for cat-qubits

TL;DR

This paper presents a method for continuous, quantum non-demolition measurement of photon-number parity in microwave cavities, crucial for error correction in cat-qubits, using a nonlinear Josephson circuit to preserve observable degeneracy.

Contribution

It introduces a novel scheme leveraging a high-impedance Josephson circuit to measure parity without disturbing the encoded quantum information.

Findings

Successful continuous QND measurement of photon-number parity.

Preservation of degeneracy enhances error correction robustness.

Implementation with high-impedance Josephson circuits demonstrated.

Abstract

A central requirement for any quantum error correction scheme is the ability to perform quantum non-demolition measurements of an error syndrome, corresponding to a special symmetry property of the encoding scheme. It is in particular important that such a measurement does not introduce extra error mechanisms, not included in the error model of the correction scheme. In this letter, we ensure such a robustness by designing an interaction with a measurement device that preserves the degeneracy of the measured observable. More precisely, we propose a scheme to perform continuous and quantum non-demolition measurement of photon-number parity in a microwave cavity. This corresponds to the error syndrome in a class of error correcting codes called the cat-codes, which have recently proven to be efficient and versatile for quantum information processing. In our design, we exploit the strongly nonlinear Hamiltonian of a high-impedance Josephson circuit, coupling a high-Q cavity storage cavity mode to a low-Q readout one. By driving the readout resonator at its resonance, the phase of the reflected/transmitted signal carries directly exploitable information on parity-type observables for encoded cat-qubits of the high-Q mode.