Zhiyang He, Massachusetts Institute of Technology

Abstract

To build a large-scale fault-tolerant quantum computer, quantum low-density parity-check (LPDC) codes have been established as promising candidates for low-overhead memory when compared to the surface codes. Performing logical computation on QLDPC memory, however, has been a long-standing challenge in theory and in practice.

In this work, we propose a new primitive, which we call an extractor, that can augment any QLDPC memory into a computational block well-suited for Pauli-based computation. In particular, any logical Pauli operator supported on the memory can be fault-tolerantly measured in one logical cycle, consisting of O(d) physical syndrome measurement cycles, without rearranging qubit connectivity.  We further propose the extractor architecture, which is a fixed-connectivity, LDPC architecture built by connecting many extractor-augmented computational (EAC) blocks with bridge systems. When combined with any source of high fidelity |T⟩ states, our architecture can implement universal quantum circuits via parallel logical measurements, such that all single-block Clifford gates are compiled away. The size of an extractor on an n qubit code is Õ(n), where the precise overhead has immense room for practical optimizations.

Joint work with Alexander Cowtan, Dominic Williamson and Theodore Yoder: arxiv.org/abs/2503.10390.