Parallel Logical Measurements via Quantum Code Surgery

Quantum code surgery is a flexible and low-overhead technique for performing logical measurements on quantum error-correcting codes, which generalizes lattice surgery. In this work, we present a code surgery scheme, applicable to any qubit stabilizer 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 ω ( log  t + log 3  ω ) ) ancilla qubits, where ω ≥ 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.