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  • Open Access

Obstacles to continuous quantum error correction via parity measurements

Anton Halaski and Christiane P. Koch*

  • Freie Universität Berlin, Fachbereich Physik and Dahlem Center for Complex Quantum Systems, Arnimallee 14, D-14195 Berlin, Germany

  • *Contact author: christiane.koch@fu-berlin.de
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Phys. Rev. Applied 26, 034074 – Published 30 September, 2026

DOI: https://doi.org/10.1103/8bkm-b48b

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.

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Outline

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Phys. Rev. Applied 26, 034074– Published 30 September, 2026
  • Received 17 March 2026
  • Revised 24 July 2026
  • Accepted 8 September 2026
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