Related papers: Randomized compiling in fault-tolerant quantum com…
With fault-tolerant quantum computing (FTQC) on the horizon, it is critical to understand sources of logical error in plausible hardware implementations of quantum error-correcting codes (QECC). In this work, we consider logical error rates…
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.…
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…
Efficient and high-performance quantum error correction is essential for achieving fault-tolerant quantum computing. Low-depth random circuits offer a promising approach to identifying effective and practical encoding strategies. In this…
Decoherence of quantum states is a major hurdle towards scalable and reliable quantum computing. Lower decoherence (i.e., higher fidelity) can alleviate the error correction overhead and obviate the need for energy-intensive noise reduction…
Topological quantum error correction codes are currently among the most promising candidates for efficiently dealing with the decoherence effects inherently present in quantum devices. Numerically, their theoretical error threshold can be…
Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than…
Reducing errors is essential for reliable quantum computation. Quantum error mitigation (QEM) and quantum error correction (QEC) are two leading approaches for this task, each with challenges: QEM suffers from high sampling costs and cannot…
Fast, reliable logical operations are essential for realizing useful quantum computers. By redundantly encoding logical qubits into many physical qubits and using syndrome measurements to detect and correct errors, one can achieve low…
The promise of quantum computing is closer to reality today than ever before, thanks to rapid progress in the development of quantum hardware. Even as qubit lifetimes and gate fidelities continue to improve, realizing robust, fault-tolerant…
Color code is a promising topological code for fault-tolerant quantum computing. Insufficient research on the color code has delayed its practical application. In this work, we address several key issues to facilitate practical…
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…
Fault tolerant quantum computing methods which work with efficient quantum error correcting codes are discussed. Several new techniques are introduced to restrict accumulation of errors before or during the recovery. Classes of eligible…
We investigate a scheme of fault-tolerant quantum computation based on the cluster model. Logical qubits are encoded by a suitable code such as the Steane's 7-qubit code. Cluster states of logical qubits are prepared by post-selection…
Quantum error mitigation (QEM) is a promising technique of protecting hybrid quantum-classical computation from decoherence, but it suffers from sampling overhead which erodes the computational speed. In this treatise, we provide a…
Encoding information redundantly using quantum error-correcting (QEC) codes allows one to overcome the inherent sensitivity to noise in quantum computers to ultimately achieve large-scale quantum computation. The Steane QEC method involves…
In measurement-based quantum computing an algorithm is performed by measurements on highly-entangled resource states. To date, several implementations were demonstrated, all of them assuming perfect noise-free environments. Here we consider…
Quantum error correction codes (QECCs) play a central role in both quantum communications and quantum computation. Practical quantum error correction codes, such as stabilizer codes, are generally structured to suit a specific use, and…
Quantum error correction protects fragile quantum information by encoding it into a larger quantum system. These extra degrees of freedom enable the detection and correction of errors, but also increase the operational complexity of the…
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…