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Quantum error correction offers a promising path for performing quantum computations with low errors. Although a fully fault-tolerant execution of a quantum algorithm remains unrealized, recent experimental developments, along with…
Quantum codes excel at correcting local noise but fail to correct leakage faults that excite qubits to states outside the computational space. Aliferis and Terhal have shown that an accuracy threshold exists for leakage faults using gadgets…
Kitaev's toric code is one of the most prominent models for fault-tolerant quantum computation, currently regarded as the leading solution for connectivity constrained quantum technologies. Significant effort has been recently devoted to…
We study the effectiveness of quantum error correction against coherent noise. Coherent errors (for example, unitary noise) can interfere constructively, so that in some cases the average infidelity of a quantum circuit subjected to…
Fault-tolerant quantum computation with depolarization error often requires demanding error threshold and resource overhead. If the operations can maintain high noise bias -- dominated by dephasing error with small bit-flip error -- we can…
The goal of this paper is to review the theoretical basis for achieving a faithful quantum information transmission and processing in the presence of noise. Initially encoding and decoding, implementing gates and quantum error correction…
Quantum error correction promises a viable path to fault-tolerant computations, enabling exponential error suppression when the device's error rates remain below the protocol's threshold. This threshold, however, strongly depends on the…
Large-scale, fault-tolerant quantum computations will be enabled by quantum error-correcting codes (QECC). This work presents the first systematic technique to test the accuracy and effectiveness of different QECC decoding schemes by…
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,…
A crucial insight for practical quantum error correction is that different types of errors, such as single-qubit Pauli operators, typically occur with different probabilities. Finding an optimal quantum code under such biased noise is a…
The color code is remarkable for its ability to perform fault-tolerant logic gates. This motivates the design of practical decoders that minimise the resource cost of color-code quantum computation. Here we propose a decoder for the planar…
We propose a generative adversarial network (GAN)-based decoder for quantum topological codes and apply it to enhance a quantum teleportation protocol under depolarizing noise. By constructing and training the GAN's generator and…
The weighted-Hamming metric generalizes the Hamming metric by assigning different weights to blocks of coordinates. It is well-suited for applications such as coding over independent parallel channels, each of which has a different level of…
Scalable realisation of quantum computing is reliant on the development of fault tolerant devices. Analysis of quantum error correction protocols typically considers incoherent noise models or noise-free syndrome measurements. While this is…
We can design efficient quantum error-correcting (QEC) codes by tailoring them to our choice of quantum architecture. Useful tools for constructing such codes include Clifford deformations and appropriate gauge fixings of compass codes. In…
I make a rough estimate of the accuracy threshold for fault tolerant quantum computing with concatenated codes. First I consider only gate errors and use the depolarizing channel error model. I will follow P.Shor (quant-ph/9505011) for…
In this work we study the single-shot performance of higher dimensional hypergraph product codes decoded using belief-propagation and ordered-statistics decoding [Panteleev and Kalachev, 2021]. We find that decoding data qubit and syndrome…
Universal fault-tolerant quantum computation will require real-time decoding algorithms capable of quickly extracting logical outcomes from the stream of data generated by noisy quantum hardware. We propose modular decoding, an approach…
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…
We present a semidefinite program optimization approach to quantum error correction that yields codes and recovery procedures that are robust against significant variations in the noise channel. Our approach allows us to optimize the…