Yoked surface codes

Craig Gidney, Michael Newman (), Peter Brooks and Cody Jones
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Craig Gidney: Google Quantum AI
Michael Newman: Google Quantum AI
Peter Brooks: Google
Cody Jones: Google Quantum AI

Nature Communications, 2025, vol. 16, issue 1, 1-12

Abstract: Abstract One of the biggest obstacles to building a large scale quantum computer is the high qubit cost of protecting quantum information. For two-dimensional architectures, the surface code has long been the leading candidate quantum memory, but can require upwards of a thousand physical qubits per logical qubit to reach algorithmically-relevant logical error rates. In this work, we introduce a hierarchical memory formed from surface codes concatenated into high-density parity check codes. These yoked surface codes are arrayed in a rectangular grid, with parity checks (yokes) measured along each row, and optionally along each column, using lattice surgery. Our construction assumes no additional connectivity beyond a nearest-neighbor square qubit grid operating at a physical error rate of 10−3. At algorithmically-relevant logical error rates, yoked surface codes use as few as one-third the number of physical qubits per logical qubit as standard surface codes, enabling moderate-overhead fault-tolerant quantum memories in two dimensions.

Date: 2025
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DOI: 10.1038/s41467-025-59714-1

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