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Physical Review A

Expander quantum low density parity check codes against long-range correlated errors in memory

Yash Deepak Kashtikar, Pranay Mathur, Sudharsan Senthil, Avhishek Chatterjee

Published May 12, 2026• 0 citations
Publisher
DOI
10.1103/q4pw-zwcv

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High-performance quantum low-density parity-check codes promise substantial reductions in the overhead of fault-tolerant quantum computation, but most constructions require long-range connectivity or qubit shuttling, both of which are difficult to realise in superconducting architectures. Here we introduce a family of quantum low-density parity-check codes that, for the first time, combines planar open-boundary layouts, finite-size advantages over surface codes, and syndrome extraction using only nearest-neighbour gates on a planar grid of qubits with either square or hexagonal connectivity. The resulting circuits achieve optimal constant-depth stabiliser measurement, independent of code size, and naturally remove leakage from the system by exchanging the roles of check and data qubits at each syndrome extraction round. We find finite-size instances such as a [[323,14,15]] code, whose code-efficiency ratio is nearly an order of magnitude larger than that of rotated surface-code patches. At around 40 circuit qubits per logical qubit, the best directional tile-code layouts reduce the per-logical per-round logical error rate by a factor of 100 relative to rotated surface-code memories. These results show that the advantages of quantum low-density parity-check codes can survive compilation into strictly planar nearest-neighbour circuits, bringing low-overhead fault-tolerant memories closer to near-term hardware.
With the development of quantum error correction techniques, many counterparts of classical error correction coding techniques have been found in quantum area. As the quantum counterpart of a good error correction code in classical communications, quantum low density parity check code becomes a promising coding technique in quantum error correction area. In this paper, a construction method of quantum low density parity check code (quantum LDPC) based on Projective Geometry is proposed, and the quantum code QLDPC [21,6] is selected as an example to illustrate the whole construction procedures. By numerical simulation, the error correction performance of QLDPC [21,6] is discussed over the bit-flipping channel. It is shown that this method is available and has some advantages.
Low-density parity-check convolutional codes offer the same good error-correcting performance as low-density parity-check block codes while having the ability to encode and decode arbitrary lengths of data. This makes these codes well suited to certain applications, such as forward error control on packet switching networks. In this paper we propose a decoder architecture for low-density parity-check convolutional codes with very large memories. These codes have very good error correcting properties and as such may be applicable in wireless sensor networks and space communication systems. We discuss a realization of this architecture for a (2048,3,6) code implemented on a field-programmable gate-array.