Extractors: Building a Quantum Computer with QLDPC Codes

Zhiyang (Sunny) He (MIT) https://simons.berkeley.edu/talks/zhiyang-sunny-he-mit-2025-05-28 Quantum Algorithms, Complexity, and Fault Tolerance Reunion 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 extractors, which is a new primitive that can augment any QLDPC memory into a computational block. In particular, any logical Pauli operator supported on the memory can be fault-tolerantly measured in O(d) physical syndrome extraction 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 \tilde{O}(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.