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Quantum error correction (QEC) is an essential concept for any quantum information processing device. Typically, QEC is designed with minimal assumptions about the noise process; this generic assumption exacts a high cost in efficiency and…
Realizing the potential of quantum computing will require achieving sufficiently low logical error rates. Many applications call for error rates in the $10^{-15}$ regime, but state-of-the-art quantum platforms typically have physical error…
Fault tolerance in quantum protocols requires contributions from error-correcting codes and their suitable decoders. Quantum Low-Density Parity Check (QLDPC) codes are one of the most explored quantum codes that have good coding rate and…
Quantum error correction uses the measurement of syndromes and classical decoding algorithms to estimate the location and type of errors while protecting the encoded quantum bits. Here we consider how prior information and Bayesian updates…
Fault-tolerant quantum computation (FTQC) requires fast and accurate decoding of quantum errors, which is often formulated as a minimum-weight perfect matching (MWPM) problem. A determinant-based approach has been proposed as a novel method…
Superconducting quantum processor units (QPUs) are incapable of producing massive datasets for quantum error correction (QEC) because of hardware limitations. Thus, QEC decoders heavily depend on synthetic data from qubit error models.…
We describe a scheme for quantum error correction that employs feedback and weak measurement rather than the standard tools of projective measurement and fast controlled unitary gates. The advantage of this scheme over previous protocols…
Quantum error correction (QEC) for fault-tolerant quantum computing requires a balanced decoding solution that offers high performance, low complexity, and low latency. However, the de facto standard, belief propagation (BP) combined with…
Hypergraph product codes are a class of constant-rate quantum low-density parity-check (LDPC) codes equipped with a linear-time decoder called small-set-flip (SSF). This decoder displays sub-optimal performance in practice and requires very…
Different choices of quantum error-correcting codes can reduce the demands on the physical hardware needed to build a quantum computer. To achieve the full potential of a code, we must develop practical decoding algorithms that can correct…
Low-depth random circuit codes possess many desirable properties for quantum error correction but have so far only been analyzed in the code capacity setting where it is assumed that encoding gates and syndrome measurements are noiseless.…
We investigate a family of fault-tolerant quantum error correction schemes based on the concatenation of small error detection or error correction codes with the three-dimensional cluster state. We propose fault-tolerant state preparation…
Minimum-Weight Perfect Matching (MWPM) decoding is important to quantum error correction decoding because of its accuracy. However, many believe that it is difficult, if possible at all, to achieve the microsecond latency requirement posed…
We introduce a prototype FPGA decoder implementing the recently discovered Relay-BP algorithm and targeting memory experiments on the $[[144,12,12]]$ bivariate bicycle quantum low-density parity check code. The decoder is both fast and…
Quantum low-density parity-check (QLDPC) codes have emerged as a promising technique for quantum error correction. A variety of decoders have been proposed for QLDPC codes and many of them utilize belief propagation (BP) decoding in some…
The impact of both multiplicative and additive hardware impairments (HWIs) on multiple-input multiple-output affine frequency division multiplexing (MIMO-AFDM) systems is investigated. For small-scale MIMO-AFDM systems, a tight bit error…
Recently, low-resolution LDPC decoders have been introduced that perform mutual information maximizing signal processing. However, the optimal quantization in variable and check nodes requires expensive non-uniform operations. Instead, we…
We estimate and analyze the error rates and the resource overheads of the repetition cat qubit approach to universal and fault-tolerant quantum computation. The cat qubits stabilized by two-photon dissipation exhibit an extremely biased…
Quantum computation holds the promise of solving certain complex problems exponentially faster than classical computers. However, the high prevalent noise in current quantum devices impedes the accurate execution of even basic algorithms.…
Decoding algorithms are essential to fault-tolerant quantum-computing architectures. In this perspective we explore decoding algorithms for the surface code; a prototypical quantum low-density parity-check code that underlies many of the…