Computing Efficiently in QLDPC Codes

Abstract

It is the prevailing belief that quantum error correcting techniques will be required to build a utility-scale quantum computer able to perform computations that are out of reach of classical computers. The QECCs that have been most extensively studied and therefore highly optimized, surface codes, are extremely resource intensive in terms of the number of physical qubits needed. A promising alternative, QLDPC codes, has been proposed more recently. These codes are much less resource intensive, requiring significantly fewer physical qubits per logical qubit than practical surface code implementations. A successful application of QLDPC codes would therefore drastically reduce the timeline to reaching quantum computers that can run algorithms with proven exponential speedups like Shor's algorithm and QPE. However to date QLDPC codes have been predominantly studied in the context of quantum memories; there has been no known method for implementing arbitrary logical Clifford operators in a QLDPC code proven efficient in terms of circuit depth. In combination with known methods for implementing T gates, an efficient implementation of the Clifford group unlocks resource-efficient universal quantum computation. In this paper, we introduce a new family of QLDPC codes that enable efficient compilation of the full Clifford group via transversal operations. Our construction executes any m-qubit Clifford operation in at most O(m) syndrome extraction rounds, significantly surpassing state-of-the-art lattice surgery methods. We run circuit-level simulations of depth-126 logical circuits to show that logical operations in our QLDPC codes attains near-memory performance. These results demonstrate that QLDPC codes are a viable means to reduce the resources required to implement all logical quantum algorithms, thereby unlocking a reduced timeline to commercially valuable quantum computing.