Parallel Logical Measurements via Quantum Code Surgery

• URL: http://arxiv.org/abs/2503.05003v1
• Date: Thu, 06 Mar 2025 22:05:52 GMT
• Title: Parallel Logical Measurements via Quantum Code Surgery
• Authors: Alexander Cowtan, Zhiyang He, Dominic J. Williamson, Theodore J. Yoder,
• Abstract summary: Quantum code surgery is a flexible and low overhead technique for performing logical measurements on quantum error-correcting codes.<n>We present a code surgery scheme, applicable to any Calderbank-Shor-Steane quantum low-density parity check (LDPC) code, that fault-tolerantly measures many logical Pauli operators in parallel.
• Score: 42.95092131256421
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum code surgery is a flexible and low overhead technique for performing logical measurements on quantum error-correcting codes, which generalises lattice surgery. In this work, we present a code surgery scheme, applicable to any Calderbank-Shor-Steane quantum low-density parity check (LDPC) code, that fault-tolerantly measures many logical Pauli operators in parallel. For a collection of logically disjoint Pauli product measurements supported on $t$ logical qubits, our scheme uses $O\big(t \omega (\log t + \log^3\omega)\big)$ ancilla qubits, where $\omega \geq d$ is the maximum weight of the single logical Pauli representatives involved in the measurements, and $d$ is the code distance. This is all done in time $O(d)$ independent of $t$. Our proposed scheme preserves both the LDPC property and the fault-distance of the original code, without requiring ancillary logical codeblocks which may be costly to prepare. This addresses a shortcoming of several recently introduced surgery schemes which can only be applied to measure a limited number of logical operators in parallel if they overlap on data qubits.

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