Directional Codes: a new family of quantum LDPC codes on hexagonal- and square-grid connectivity hardware
Gy\"orgy P. Geh\'er, David Byfield, Archibald Ruban

TL;DR
This paper introduces 'Directional Codes', a new family of quantum LDPC codes optimized for 2D grid hardware, outperforming existing codes like RPC and BB in error correction efficiency without requiring complex connectivity.
Contribution
The paper presents a novel family of quantum LDPC codes compatible with standard superconducting qubit hardware, eliminating the need for long-range connections and demonstrating superior performance.
Findings
Directional codes outperform rotated planar codes in logical error rates.
They achieve similar error correction with 18.75-45% fewer physical qubits.
Performance is validated through circuit-level noise simulations.
Abstract
Utility-scale quantum computing requires quantum error correction (QEC) to protect quantum information against noise. Currently, superconducting hardware is a promising candidate for achieving fault tolerance due to its fast gate times and feasible scalability. However, it is often restricted to two-dimensional nearest-neighbour connectivity, which is thought to be incapable of accommodating high-rate quantum low-density parity-check (qLDPC) codes that promise to greatly reduce the number of physical qubits needed to encode logical qubits. In this paper we construct a new family of qLDPC codes, which we call ``Directional Codes'', that outperforms the rotated planar code (RPC) while naturally meeting the connectivity requirements of the widely adopted square-grid, and some even the sparser hexagonal-grid. The key idea is to utilise the iSWAP gate -- a natural native gate for…
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum-Dot Cellular Automata · Quantum Information and Cryptography
