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Quantum computation is a subject of much theoretical promise, but has not been realized in large scale, despite the discovery of fault-tolerant procedures to overcome decoherence. Part of the reason is that the theoretically modest…
In this paper, we consider a simplified error-correcting problem: for a fixed encoding process, to find a cascade connected quantum channel such that the worst fidelity between the input and the output becomes maximum. With the use of the…
Quantum information needs to be protected by quantum error-correcting codes due to imperfect physical devices and operations. One would like to have an efficient and high-performance decoding procedure for the class of quantum stabilizer…
We construct a new error-suppression scheme that makes use of the adjoint of reversible quantum algorithms. For decoherence induced errors such as depolarization, it is presented that provided the depolarization error probability is less…
Quantum error correction (QEC) is a way to protect quantum information against noise. It consists of encoding input information into entangled quantum states known as the code space. Furthermore, to classify if the encoded information is…
The advent of promising quantum error correction (QEC) codes with efficient resource utilization and high-performance fault-tolerant quantum memories signifies a critical step towards realizing practical quantum computation. While surface…
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…
Belief-propagation (BP) decoders play a vital role in modern coding theory, but they are not suitable to decode quantum error-correcting codes because of a unique quantum feature called error degeneracy. Inspired by an exact mapping between…
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 (QEC) is required for large-scale computation, but incurs a significant resource overhead. Recent advances have shown that by jointly decoding logical qubits in algorithms composed of transversal gates, the number…
When a logical qubit is protected using a quantum error-correcting code, the net effect of coding, decoherence (a physical channel acting on qubits in the codeword) and recovery can be represented exactly by an effective channel acting…
In experimental control of quantum systems, the precision is often hindered by imperfect applied electronics that distort control pulses delivered to target quantum devices. To mitigate such error, the deconvolution method is commonly used…
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.…
Quantum error mitigation (QEM) is typically viewed as a suite of practical techniques for today's noisy intermediate-scale quantum devices, with limited relevance once fault-tolerant quantum computers become available. In this work, we…
Quantum error correction is crucial for universal fault-tolerant quantum computing. Highly accurate and low-time-complexity decoding algorithms play an indispensable role in ensuring quantum error correction works effectively. Among…
Surface codes exploit topological protection to increase error resilience in quantum computing devices and can in principle be implemented in existing hardware. They are one of the most promising candidates for active error correction, not…
Quantum Error Correction will be necessary for preserving coherent states against noise and other unwanted interactions in quantum computation and communication. We develop a general theory of quantum error correction based on encoding…
We give an introduction to the theory of quantum error correction using stabilizer codes that is geared towards the working computer scientists and mathematicians with an interest in exploring this area. To this end, we begin with an…
The importance of quantum error correction in paving the way to build a practical quantum computer is no longer in doubt. This dissertation makes a threefold contribution to the mathematical theory of quantum error-correcting codes.…
A quantum error correcting protocol can be substantially improved by taking into account features of the physical noise process. We present an efficient decoder for the surface code which can account for general noise features, including…