Obstacles to Continuous Quantum Error Correction via Parity Measurements

TL;DR

This paper demonstrates that common parity-measurement protocols in circuit QED hinder continuous quantum error correction by corrupting logical information, highlighting the need for native three-body interactions or alternative encoding strategies.

Contribution

It identifies a fundamental limitation in continuous quantum error correction protocols using parity measurements and suggests viable alternative architectures.

Findings

Parity measurements in circuit QED can corrupt logical information during continuous operation.

Approximation of three-body interactions by two-body couplings causes measurement backaction issues.

Native three-body interactions or erasure-based encodings can overcome these limitations.

Abstract

Time-continuous quantum error correction, necessary to protect quantum information under time-dependent Hamiltonians, relies on weak continuous syndrome measurements. Implementing these measurements requires a continuous coupling among at least two qubits and a meter, a demanding requirement. We show that, under continuous operation, common parity-measurement protocols in the circuit quantum electrodynamics platform corrupt the logical information. The failure arises from approximating the three-body interaction by a sum of two-body couplings to the meter, which prevents simultaneous suppression of measurement backaction on the logical and error subspaces. We argue that the same mechanism applies more generally beyond the circuit quantum electrodynamics setting. Taken together, our results impose a practical limitation on continuous stabilizer quantum error correction and point to the viable alternatives -- architectures that realize native three-body interactions, or erasure-based encodings in which the error subspace need not be protected.