Related papers: Preserving MWPM-Decodability in Fault-Equivalent R…
Quantum Error Correction (QEC) decoding faces a fundamental accuracy-efficiency tradeoff. Classical methods like Minimum Weight Perfect Matching (MWPM) exhibit variable performance across noise models and suffer from polynomial complexity,…
Quantum error correction becomes a practical possibility only if the physical error rate is below a threshold value that depends on a particular quantum code, syndrome measurement circuit, and decoding algorithm. Here we present an…
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…
Spin qubits in semiconductor structures bring the promise of large-scale 2D integration, with the possibility to incorporate the control electronics on the same chip. In order to perform error correction on this platform, the characteristic…
The XZZX code is a variant of the surface code tailored to address biased noise in realistic quantum devices. We propose a simulated annealing (SA) decoder for the XZZX code. Our SA decoder is amenable to parallelization because its MCMC…
In this article we address the computational hardness of optimally decoding a quantum stabilizer code. Much like classical linear codes, errors are detected by measuring certain check operators which yield an error syndrome, and the…
In classical computing, error-correcting codes are well established and are ubiquitous both in theory and practical applications. For quantum computing, error-correction is essential as well, but harder to realize, coming along with…
Mapping quantum error correcting codes to classical disordered statistical mechanics models and studying the phase diagram of the latter has proven a powerful tool to study the fundamental error robustness and associated critical error…
Color codes are a leading class of topological quantum error-correcting codes with modest error thresholds and structural compatibility with two-dimensional architectures, which make them well-suited for fault-tolerant quantum computing…
Quantum technologies have the potential to solve certain computationally hard problems with polynomial or super-polynomial speedups when compared to classical methods. Unfortunately, the unstable nature of quantum information makes it prone…
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…
Large-scale quantum computers have the potential to hold computational capabilities beyond conventional computers for certain problems. However, the physical qubits within a quantum computer are prone to noise and decoherence, which must be…
Efficient high-performance decoding of topological stabilizer codes has the potential to crucially improve the balance between logical failure rates and the number and individual error rates of the constituent qubits. High-threshold…
The problem of recovering from qubit erasures has recently gained attention as erasures occur in many physical systems such as photonic systems, trapped ions, superconducting qubits and circuit quantum electrodynamics. While several…
Error syndromes for heavy hexagonal code and other topological codes such as surface code have typically been decoded by using Minimum Weight Perfect Matching (MWPM) based methods. Recent advances have shown that topological codes can be…
The scalability and interpretability of message-passing (MP) decoding, such as (quaternary) Belief Propagation, remain open challenges in quantum error correction. Even for surface codes, arguably the first testbed for decoding methods,…
In many physical systems it is expected that environmental decoherence will exhibit an asymmetry between dephasing and relaxation that may result in qubits experiencing discrete phase errors more frequently than discrete bit errors. In the…
We introduce the spanning tree matching (STM) decoder for surface codes, which guarantees the error correction capability up to the code's designed distance by first employing an instance of the minimum spanning tree on a subset of ancilla…
We present and analyze protocols for fault-tolerant quantum computing using color codes. We present circuit-level schemes for extracting the error syndrome of these codes fault-tolerantly. We further present an integer-program-based…
Fast and accurate quantum error correction (QEC) decoding is crucial for scalable fault-tolerant quantum computation. Most-Likely-Error (MLE) decoding, while being near-optimal, is intractable on general quantum Low-Density Parity-Check…