Explicit construction of low-overhead gadgets for gates on quantum LDPC codes

TL;DR

This paper introduces explicit, low-overhead gadgets for measuring logical Pauli operators on quantum LDPC codes, significantly reducing space overhead while maintaining low time overhead, advancing scalable quantum computing.

Contribution

It provides a simple, explicit construction for gadgets that measure logical operators on QLDPC codes, applicable to generalized bicycle codes, reducing space overhead substantially.

Findings

Reduces space overhead by at least an order of magnitude compared to surface codes.

Maintains low time overhead while improving space efficiency.

Applicable to codes with distances relevant for large-scale quantum computation.

Abstract

Quantum low-density parity check (QLDPC) codes can significantly reduce the overhead of quantum computing, provided the methods for performing logical operations do not require substantial space and time resources. A popular method for performing logical operations is by measuring logical Pauli operators. We present a simple, explicit construction for fixed gadgets that can measure arbitrary logical Pauli operators on QLDPC codes when dynamically connected to the code block. We apply this construction to a family of generalised bicycle codes with distances relevant to utility-scale quantum computation ($10\leq d \leq 24$) and show that it reduces the space overhead by at least an order of magnitude compared to corresponding surface code architectures, without increasing the time overhead.