Explicit construction of low-overhead gadgets for gates on quantum LDPC codes
Paul Webster, Samuel C. Smith, Lawrence Z. Cohen
TL;DR
This work tackles the high resource cost of fault-tolerant quantum computing by leveraging quantum LDPC codes and a static gadget design to measure arbitrary logical Pauli operators. The authors introduce a fixed gadget construction anchored by seed operators and code automorphisms, with bridging techniques to realize arbitrary logical measurements while preserving distance. They show the overhead scales as $\tilde{O}(d)$ for seed weights $O(d)$ and demonstrate the method on generalized bicycle codes, achieving substantial overhead reductions (roughly $11$–$24\times$) and sub-$100$ qubits per logical qubit for relevant distances $10\le d\le 24$. The results indicate a practical pathway to utility-scale quantum computing using QLDPC codes, with broad applicability to other code families that admit automorphisms.
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.