# Towards a heralded eigenstate preserving measurement of multi-qubit parity in circuit QED

## TL;DR

This paper proposes a high-fidelity, eigenstate-preserving multi-qubit parity measurement method in circuit QED, utilizing dynamical decoupling and heralding techniques to improve quantum error correction in superconducting qubits.

## Contribution

It introduces a novel heralded parity measurement scheme with dynamical decoupling to enhance eigenstate preservation and measurement fidelity in circuit QED systems.

## Key findings

- Dynamical decoupling reduces decoherence during photon detection.
- Sequence of displacement operations suppresses detector bias.
- Heralded detection guarantees successful parity measurement even with finite efficiency.

## Abstract

Eigenstate-preserving multi-qubit parity measurements lie at the heart of stabilizer quantum error correction, which is a promising approach to mitigate the problem of decoherence in quantum computers. In this work we explore a high-fidelity, eigenstate-preserving parity readout for superconducting qubits dispersively coupled to a microwave resonator, where the parity bit is encoded in the amplitude of a coherent state of the resonator. Detecting photons emitted by the resonator via a current biased Josephson junction yields information about the parity bit. We analyse theoretically the measurement back-action in the limit of a strongly coupled fast detector and show that in general such a parity measurement, while approximately Quantum Non-Demolition (QND) is not eigenstate-preserving. To remediate this shortcoming we propose a simple dynamical decoupling technique during photon detection, which greatly reduces decoherence within a given parity subspace. Furthermore, by applying a sequence of fast displacement operations interleaved with the dynamical decoupling pulses, the natural bias of this binary detector can be efficiently suppressed. Finally, we introduce the concept of a heralded parity measurement, where a detector click guarantees successful multi-qubit parity detection even for finite detection efficiency.