Related papers: Conservation laws and quantum error correction: to…
Realizing the full potential of quantum computation requires Quantum Error Correction (QEC). QEC reduces error rates by encoding logical information across redundant physical qubits, enabling errors to be detected and corrected. A common…
Fast decoding algorithms are decisive for real-time quantum error correction and for analyzing properties of error correction codes. Here, we develop variants of the union-find decoder that simplify its implementation and provide potential…
Reed-Muller (RM) codes exhibit good performance under maximum-likelihood (ML) decoding due to their highly-symmetric structure. In this paper, we explore the question of whether the code symmetry of RM codes can also be exploited to achieve…
We present a two-step decoder for the parity code and evaluate its performance in code-capacity and faulty-measurement settings. For noiseless measurements, we find that the decoding problem can be reduced to a series of repetition codes…
Transversal logical gates offer the opportunity for fast and low-noise logic, particularly when interspersed by a single round of parity check measurements of the underlying code. Using such circuits for the surface code requires decoding…
Fast classical processing is essential for most quantum fault-tolerance architectures. We introduce a sliding-window decoding scheme that provides fast classical processing for the surface code through parallelism. Our scheme divides the…
We introduce Decision Tree Decoders (DTDs), which rely only on the sparsity of the binary check matrix, making them broadly applicable for decoding any quantum low-density parity-check (qLDPC) code and fault-tolerant quantum circuits. DTDs…
Quantum error correction is the building block for constructing fault-tolerant quantum processors that can operate reliably even if its constituting elements are corrupted by decoherence. In this context, real-time decoding is a necessity…
We present a method, called matching synthesis, for decoding quantum codes that produces an enhanced assignment of errors from an ensemble of decoders. We apply matching synthesis to develop a decoder named Libra, and show in simulations…
All utility-scale quantum computers will require some form of Quantum Error Correction in which logical qubits are encoded in a larger number of physical qubits. One promising encoding is known as the colour code which has broad…
A fault-tolerant quantum computation requires an efficient means to detect and correct errors that accumulate in encoded quantum information. In the context of machine learning, neural networks are a promising new approach to quantum error…
Quantum computers require error correction to achieve universal quantum computing. However, current decoding of quantum error-correcting codes relies on classical computation, which is slower than quantum operations in superconducting…
A quantized message passing decoding algorithm for low-density parity-check codes is presented. The algorithm relies on the min approximation at the check nodes, and on modelling the variable node inbound messages as observations of an…
Fault-tolerant quantum computing demands decoders that are fast, accurate, and adaptable to circuit structure and realistic noise. While machine learning (ML) decoders have demonstrated impressive performance for quantum memory, their use…
With the rapid developments in quantum hardware comes a push towards the first practical applications on these devices. While fully fault-tolerant quantum computers may still be years away, one may ask if there exist intermediate forms of…
The typical model for measurement noise in quantum error correction is to randomly flip the binary measurement outcome. In experiments, measurements yield much richer information - e.g., continuous current values, discrete photon counts -…
Color codes present distinct advantages for fault-tolerant quantum computing, such as high encoding rates and the transversal implementation of Clifford gates. However, existing matching-based decoders for the color codes such as the…
An efficient decoder is essential for quantum error correction, and data-driven neural decoders have emerged as promising, flexible solutions. Here, we introduce a diffusion model framework to infer logical errors from syndrome measurements…
Low check weight is practically crucial code property for fault-tolerant quantum computing, which underlies the strong interest in quantum low-density parity-check (qLDPC) codes. Here, we explore the theory of weight-constrained stabilizer…
While low-density parity-check (LDPC) codes are near capacity-achieving when paired with iterative decoders, these decoders may not output a codeword due to the existence of pseudocodewords. Thus, pseudocodewords have been studied to give…