Related papers: Local decoder for the toric code via signal exchan…
Topological subsystem codes proposed recently by Bombin are quantum error correcting codes defined on a two-dimensional grid of qubits that permit reliable quantum information storage with a constant error threshold. These codes require…
We study a quantum analogue of locally decodable error-correcting codes. A q-query locally decodable quantum code encodes n classical bits in an m-qubit state, in such a way that each of the encoded bits can be recovered with high…
Topological quantum codes, such as toric and surface codes, are excellent candidates for hardware implementation due to their robustness against errors and their local interactions between qubits. However, decoding these codes efficiently…
Kitaev's quantum double models in 2D provide some of the most commonly studied examples of topological quantum order. In particular, the ground space is thought to yield a quantum error-correcting code. We offer an explicit proof that this…
We give a broad generalisation of the mapping, originally due to Dennis, Kitaev, Landahl and Preskill, from quantum error correcting codes to statistical mechanical models. We show how the mapping can be extended to arbitrary stabiliser or…
Decoding algorithms based on approximate tensor network contraction have proven tremendously successful in decoding 2D local quantum codes such as surface/toric codes and color codes, effectively achieving optimal decoding accuracy. In this…
This paper presents novel techniques for improving the error correction performance and reducing the complexity of coarsely quantized 5G-LDPC decoders. The proposed decoder design supports arbitrary message-passing schedules on a…
Qudit toric codes are a natural higher-dimensional generalization of the well-studied qubit toric code. However standard methods for error correction of the qubit toric code are not applicable to them. Novel decoders are needed. In this…
Information obtained from noise characterization of a quantum device can be used in classical decoding algorithms to improve the performance of quantum error-correcting codes. Focusing on the surface code under local (i.e. single-qubit)…
In this paper, we consider quantized decoding of LDPC codes on the binary symmetric channel. The binary message passing algorithms, while allowing extremely fast hardware implementation, are not very attractive from the perspective of…
A common approach to studying the performance of quantum error correcting codes is to assume independent and identically distributed single-qubit errors. However, the available experimental data shows that realistic errors in modern…
We provide a detailed study of the general structure of two-dimensional topological stabilizer quantum error correcting codes, including subsystem codes. Under the sole assumption of translational invariance, we show that all such codes can…
One hurdle to performing reliable quantum computations is overcoming noise. One possibility is to reduce the number of particles needing to be protected from noise and instead use systems with more states, so called qudit quantum computers.…
Quantum error correction (QEC) enables reliable computation on noisy hardware by encoding logical information across many physical qubits and periodically measuring parities to detect errors. A decoder is the classical algorithm that uses…
It was pointed out in [JSW+25] that widely-studied optimization problems such as D-regular max-k-XORSAT can be reduced to decoding of LDPC codes, using quantum algorithms related to Regev's reduction. LDPC codes have very good decoders,…
Execution of quantum algorithms on large-scale quantum computers will require extremely low logical error rates, which necessitates the development of scalable decoding architectures. Local decoders are promising candidates for this task,…
We propose a scalable decoding framework for correcting correlated hook errors in stabilizer measurement circuits. Traditional circuit-level decoding attempts to estimate the precise location of faults by constructing an extended Tanner…
We propose an error correction procedure based on a cellular automaton, the sweep rule, which is applicable to a broad range of codes beyond topological quantum codes. For simplicity, however, we focus on the three-dimensional (3D) toric…
We consider the problem of a generic stabilizer Hamiltonian under local, incoherent Pauli errors. Using two different approaches -- (i) Haah's polynomial formalism arXiv:1204.1063 and (ii) the homological perspective on CSS codes -- we…
We analyze surface codes, the topological quantum error-correcting codes introduced by Kitaev. In these codes, qubits are arranged in a two-dimensional array on a surface of nontrivial topology, and encoded quantum operations are associated…