Related papers: Parallel decoding of multiple logical qubits in te…
Decoders that provide an estimate of the probability of a logical failure conditioned on the error syndrome ("soft-output decoders") can reduce the overhead cost of fault-tolerant quantum memory and computation. In this work, we construct…
Fault-tolerant quantum computation relies on scaling up quantum error correcting codes in order to suppress the error rate on the encoded quantum states. Topological codes, such as the surface code or color codes are leading candidates for…
We consider realistic, multi-parameter error models and investigate the performance of the surface code for three possible fault-tolerant superconducting quantum computer architectures. We map amplitude and phase damping to a diagonal Pauli…
We classify the time complexities of three important decoding problems for quantum stabilizer codes. First, regardless of the channel model, quantum bounded distance decoding is shown to be NP-hard, like what Berlekamp, McEliece and Tilborg…
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…
We analyze the performance of quantum stabilizer codes, one of the most important classes for practical implementations, on both symmetric and asymmetric quantum channels. To this aim, we first derive the weight enumerator (WE) for the…
Hypergraph product codes introduced by Tillich and Z\'emor are a class of quantum LDPC codes with constant rate and distance scaling with the square-root of the block size. Quantum expander codes, a subclass of these codes, can be decoded…
Bell measurements (BMs) are ubiquitous in quantum information and technology. They are basic elements for quantum commmunication, computation, and error correction. In particular, when performed on logical qubits encoded in physical…
Random classical linear codes are widely believed to be hard to decode. While slightly sub-exponential time algorithms exist when the coding rate vanishes sufficiently rapidly, all known algorithms at constant rate require exponential time.…
Color codes are a class of topological quantum codes with a high error threshold and large set of transversal encoded gates, and are thus suitable for fault tolerant quantum computation in two-dimensional architectures. Recently,…
The stabilization of a quantum computer by repeated error correction can be reduced almost entirely to repeated preparation of blocks of qubits in quantum codeword states. These are multi-particle entangled states with a high degree of…
The problem of joint source-channel coding is considered for a stationary remote (noisy) Gaussian source and a Gaussian channel. The encoder and decoder are assumed to be causal and their combined operations are subject to a delay…
As parallel computing trends towards the exascale, scientific data produced by high-fidelity simulations are growing increasingly massive. For instance, a simulation on a three-dimensional spatial grid with 512 points per dimension that…
Modern platforms for potential qubit candidates, such as trapped ions or neutral atoms, allow long range connectivity between distant physical qubits through shuttling. This opens up an avenue for transversal logical CNOT gates between…
Decoding stabilizer codes such as the surface and toric codes involves evaluating free-energy differences in a disordered statistical mechanics model, in which the randomness comes from the observed pattern of error syndromes. We study the…
We address the challenge of incorporating encoded quantum memories into an exact secret key rate analysis for small and intermediate-scale quantum repeaters. To this end, we introduce the check matrix model and quantify the resilience of…
Sparse coding provides a versatile framework for efficiently capturing and representing crucial data (information) concisely, which plays an essential role in various computer science fields, including data compression, feature extraction,…
In this work we develop a general tensor network decoder for 2D codes. Specifically, we propose a decoder that approximates maximally likelihood decoding for 2D stabiliser and subsystem codes subject to Pauli noise. For a code consisting of…
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)…
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…