This was part of Quantum Error Correction

LDPC surgery for logical measurements and gates on quantum codes

Ted Yoder, IBM

Wednesday, November 13, 2024



Slides
Abstract: In the last few years, quantum LDPC codes have developed to become serious contenders for the fault-tolerant architecture needed to build a large-scale quantum computer. Perhaps the frontier of qLDPC code research concerns performing logical measurements and gates fault-tolerantly with minimal additional overhead. Here, we present several extensions and generalizations of the LDPC surgery methods of Hastings [arXiv:2102.10030] and Cohen et al. [10.1126/sciadv.abn1717, 2022]. Our main result is the measurement of logical Pauli operators using a number of additional qubits scaling quasi-linearly, or in some cases linearly, with the weight of the operator to be measured. This includes joint Pauli measurements between separate, and potentially different, LDPC codeblocks. Our constructions allow a standard computational model, Pauli-based computation, to be performed at the logical level on qubits encoded into LDPC codes. Although our techniques are applicable to arbitrary LDPC codes, we also provide detailed constructions and some circuit-noise simulations for the 144 qubit “gross” code.