Parallel Logical Measurements via Quantum Code Surgery

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 qubit stabiliser 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 $O(t\omega (\log t+{\log }^3\omega ))$ ancilla qubits, where $\omega \ge d$ 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.

Improved readability and added several toy examples

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Cited by in corpus (1)

• Accelerating Fault-Tolerant Quantum Computation with Good qLDPC Codes