Measurement-Free Fault-Tolerant Quantum Error Correction in Near-Term Devices

Authors:
raw_author_name: Sascha Heußen
raw_affiliation_string: Institute for Quantum Information, RWTH Aachen University, Aachen 52056, Germany; Institute for Theoretical Nanoelectronics (PGI-2), Forschungszentrum Jülich, Jülich 52425, Germany
raw_author_name: David F. Locher
raw_affiliation_string: Institute for Quantum Information, RWTH Aachen University, Aachen 52056, Germany; Institute for Theoretical Nanoelectronics (PGI-2), Forschungszentrum Jülich, Jülich 52425, Germany
raw_author_name: Markus Müller
raw_affiliation_string: Institute for Quantum Information, RWTH Aachen University, Aachen 52056, Germany; Institute for Theoretical Nanoelectronics (PGI-2), Forschungszentrum Jülich, Jülich 52425, Germany

Abstract: Logical qubits can be protected from decoherence by performing quantum error-correction (QEC) cycles repeatedly. Algorithms for fault-tolerant QEC must be compiled to the specific hardware platform under consideration in order to practically realize a quantum memory that operates for in principle arbitrary long times. All circuit components must be assumed as noisy unless specific assumptions about the form of the noise are made. Modern QEC schemes are challenging to implement experimentally in physical architectures where in-sequence measurements and feed forward of classical information cannot be reliably executed fast enough or even at all. Here we provide a novel scheme to perform QEC cycles without the need of measuring qubits that is fully fault-tolerant with respect to all components used in the circuit. Our scheme can be used for any low-distance CSS code since its only requirement towards the underlying code is a transversal cnot gate. Similarly to Steane-type EC, we coherently copy errors to a logical auxiliary qubit but then apply a coherent feedback operation from the auxiliary system to the logical data qubit. The logical auxiliary qubit is prepared fault tolerantly without measurements, too. We benchmark logical failure rates of the scheme in comparison to a flag-qubit-based EC cycle. We map out a parameter region where our scheme is feasible and estimate physical error rates necessary to achieve the break-even point of beneficial QEC with our scheme. We outline how our scheme could be implemented in ion traps and with neutral atoms in a tweezer array. For recently demonstrated capabilities of atom shuttling and native multiatom Rydberg gates, we achieve moderate circuit depths and beneficial performance of our scheme while not breaking fault tolerance. These results thereby enable practical fault-tolerant QEC in hardware architectures that do not support midcircuit measurements.13 MoreReceived 30 August 2023Revised 20 December 2023Accepted 22 January 2024DOI:https://doi.org/10.1103/PRXQuantum.5.010333Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum circuitsQuantum error correctionQuantum protocolsQuantum Information, Science & Technology