Time-Efficient Logical Operations on Quantum Low-Density Parity Check Codes

We propose schemes capable of measuring an arbitrary set of commutative logical Pauli operators in time independent of the number of operators. The only condition is commutativity, a fundamental requirement for simultaneous measurements in quantum mechanics. Quantum low-density parity check (qLDPC) codes show great promise for realizing fault-tolerant quantum computing. They are particularly significant for early fault-tolerant technologies as they can encode many logical qubits using relatively few physical qubits. By achieving simultaneous measurements of logical operators, our approaches enable fully parallelized quantum computing, thus minimizing computation time. Our schemes are applicable to any qLDPC codes and maintain the low density of parity checks while measuring multiple logical operators simultaneously. These results enhance the feasibility of applying early fault-tolerant technologies to practical problems.