November 4, 2024 | Andrew Cross, Zhiyang He (Sunny), Patrick Rall, Theodore Yoder
This paper introduces an improved logical measurement scheme for Quantum Low-Density Parity-Check (QLDPC) codes, known as gauge-fixed QLDPC surgery. The scheme leverages the expansion properties of the Tanner graph to reduce the space overhead required for fault-tolerant logical measurements. Specifically, it requires only $\Theta(w)$ ancilla qubits to measure a weight $w$ logical operator, where $w$ is the weight of the logical operator. The authors provide rigorous analysis of the code distance and fault distance of their scheme and present a modular decoding algorithm that achieves maximal fault-distance. They also introduce a bridge system to facilitate fault-tolerant joint measurements of logical operators, enabling the connection of different families of QLDPC codes into a universal computing architecture. The practicality of the scheme is demonstrated through circuit-level noise simulations, showing that it can perform all logical Clifford gates on the [[144,12,12]] bivariate bicycle code with a mono-layer ancilla system and 103 additional qubits. The modular decoder, combining BPOSD with matching, achieves comparable logical error rates to a fully BPOSD decoder but with significantly faster decoding times. The paper also discusses the implementation of 288 Pauli product measurements and the generation of the eleven-qubit Clifford group on the gross code block.This paper introduces an improved logical measurement scheme for Quantum Low-Density Parity-Check (QLDPC) codes, known as gauge-fixed QLDPC surgery. The scheme leverages the expansion properties of the Tanner graph to reduce the space overhead required for fault-tolerant logical measurements. Specifically, it requires only $\Theta(w)$ ancilla qubits to measure a weight $w$ logical operator, where $w$ is the weight of the logical operator. The authors provide rigorous analysis of the code distance and fault distance of their scheme and present a modular decoding algorithm that achieves maximal fault-distance. They also introduce a bridge system to facilitate fault-tolerant joint measurements of logical operators, enabling the connection of different families of QLDPC codes into a universal computing architecture. The practicality of the scheme is demonstrated through circuit-level noise simulations, showing that it can perform all logical Clifford gates on the [[144,12,12]] bivariate bicycle code with a mono-layer ancilla system and 103 additional qubits. The modular decoder, combining BPOSD with matching, achieves comparable logical error rates to a fully BPOSD decoder but with significantly faster decoding times. The paper also discusses the implementation of 288 Pauli product measurements and the generation of the eleven-qubit Clifford group on the gross code block.