It is widely accepted that quantum error correction is essential for realizing large-scale fault-tolerant quantum computing. Recent experiments have demonstrated error correction codes operating below threshold, primarily using local planar codes such as the surface code and color code. In parallel, theoretical advances in quantum low-density parity-check (LDPC) codes promise significantly lower overheads, albeit at the cost of requiring non-local parity checks. While these results are encouraging, implementing such codes remains challenging for near-term experiments, creating obstacles to holistic benchmarking of hardware architectures capable of supporting long-range couplers. In this work, we present a simple construction recipe for small quantum LDPC codes based on recent developments in the field. Our codes are approximately twice as efficient as comparable surface codes, yet require only weight-four parity checks, which simplifies experimental realization compared to other quantum LDPC codes. We provide concrete proposals for implementations with superconducting qubits in flip-chip architectures and with semiconductor spin qubits using shuttling-based approaches.It is widely accepted that quantum error correction is essential for realizing large-scale fault-tolerant quantum computing. Recent experiments have demonstrated error correction codes operating below threshold, primarily using local planar codes such as the surface code and color code. In parallel, theoretical advances in quantum low-density parity-check (LDPC) codes promise significantly lower overheads, albeit at the cost of requiring non-local parity checks. While these results are encouraging, implementing such codes remains challenging for near-term experiments, creating obstacles to holistic benchmarking of hardware architectures capable of supporting long-range couplers. In this work, we present a simple construction recipe for small quantum LDPC codes based on recent developments in the field. Our codes are approximately twice as efficient as comparable surface codes, yet require only weight-four parity checks, which simplifies experimental realization compared to other quantum LDPC codes. We provide concrete proposals for implementations with superconducting qubits in flip-chip architectures and with semiconductor spin qubits using shuttling-based approaches.

arXiv:2507.09690Jul 13, 20251 citation

Demonstrating a four-qubit network for the surface code with superconducting qubits

Srikanth J. Srinivasan, Easwar Magesan, Jerry M. Chow +7 more

Bulletin of the American Physical SocietyMar 3, 20140 citations

Hyperbolic and semi-hyperbolic surface codes for quantum storage

Breuckmann, NP, Christophe Vuillot, Earl T. Campbell +2 more

We show how a hyperbolic surface code could be used for overhead-efficient quantum storage. We give numerical evidence for a noise threshold of $1.3 \\% $ for the $\\{4,5\\}$ -hyperbolic surface code in a phenomenological noise model (as compared with $2.9 \\% $ for the toric code). In this code family, parity checks are of weight 4 and 5, while each qubit participates in four different parity checks. We introduce a family of semi-hyperbolic codes that interpolate between the toric code and the $\\{4,5\\}$ -hyperbolic surface code in terms of encoding rate and threshold. We show how these hyperbolic codes outperform the toric code in terms of qubit overhead for a target logical error probability. We show how Dehn twists and lattice code surgery can be used to read and write individual qubits to this quantum storage medium.We show how a hyperbolic surface code could be used for overhead-efficient quantum storage. We give numerical evidence for a noise threshold of $1.3 \\% $ for the $\\{4,5\\}$-hyperbolic surface code in a phenomenological noise model (as compared with $2.9 \\% $ for the toric code). In this code family, parity checks are of weight 4 and 5, while each qubit participates in four different parity checks. We introduce a family of semi-hyperbolic codes that interpolate between the toric code and the $\\{4,5\\}$-hyperbolic surface code in terms of encoding rate and threshold. We show how these hyperbolic codes outperform the toric code in terms of qubit overhead for a target logical error probability. We show how Dehn twists and lattice code surgery can be used to read and write individual qubits to this quantum storage medium.

Sep 1, 201729 citations

Parity detection of multiple superconducting qubits

Caleb Howington, Alex Opremcak, Ivan Pechenezhskiy +4 more

Bulletin of the American Physical SocietyMar 16, 20170 citations

Hyperbolic and semi-hyperbolic surface codes for quantum storage

Nikolas P. Breuckmann, Christophe Vuillot, Earl T. Campbell +2 more

Abstract We show how a hyperbolic surface code could be used for overhead-efficient quantum storage. We give numerical evidence for a noise threshold of 1.3 % for the { 4 , 5 } -hyperbolic surface code in a phenomenological noise model (as compared with 2.9 % for the toric code). In this code family, parity checks are of weight 4 and 5, while each qubit participates in four different parity checks. We introduce a family of semi-hyperbolic codes that interpolate between the toric code and the { 4 , 5 } -hyperbolic surface code in terms of encoding rate and threshold. We show how these hyperbolic codes outperform the toric code in terms of qubit overhead for a target logical error probability. We show how Dehn twists and lattice code surgery can be used to read and write individual qubits to this quantum storage medium.Abstract We show how a hyperbolic surface code could be used for overhead-efficient quantum storage. We give numerical evidence for a noise threshold of 1.3 % for the { 4 , 5 } -hyperbolic surface code in a phenomenological noise model (as compared with 2.9 % for the toric code). In this code family, parity checks are of weight 4 and 5, while each qubit participates in four different parity checks. We introduce a family of semi-hyperbolic codes that interpolate between the toric code and the { 4 , 5 } -hyperbolic surface code in terms of encoding rate and threshold. We show how these hyperbolic codes outperform the toric code in terms of qubit overhead for a target logical error probability. We show how Dehn twists and lattice code surgery can be used to read and write individual qubits to this quantum storage medium.

arXiv:1703.00590Quantum Science and TechnologyAug 2, 201787 citations

We show how a hyperbolic surface code could be used for overhead-efficient quantum storage. We give numerical evidence for a noise threshold of $1.3 \\% $ for the

\\{4,5\\}

-hyperbolic surface code in a phenomenological noise model (as compared with $2.9 \\% $ for the toric code). In this code family, parity checks are of weight 4 and 5, while each qubit participates in four different parity checks. We introduce a family of semi-hyperbolic codes that interpolate between the toric code and the

\\{4,5\\}

-hyperbolic surface code in terms of encoding rate and threshold. We show how these hyperbolic codes outperform the toric code in terms of qubit overhead for a target logical error probability. We show how Dehn twists and lattice code surgery can be used to read and write individual qubits to this quantum storage medium.