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Quantum error correction allows for faulty quantum systems to behave in an effectively error free manner. One important class of techniques for quantum error correction is the class of quantum subsystem codes, which are relevant both to…
Quantum dense coding has been demonstrated experimentally in terms of quantum logic gates and circuits in quantum computation and NMR technique. Two bits of information have been transmitted through manipulating one of the maximally…
In this paper we provide a basic introduction of the core ideas and theories surrounding fault-tolerant quantum computation. These concepts underly the theoretical framework of large-scale quantum computation and communications and are the…
Quantum computation of vibrational properties of molecules is a promising platform to obtain computational advantages for computational chemistry. However, fault-tolerant quantum computations of vibrational properties remain a relatively…
Designing quantum error correcting codes that promise a high error threshold, low resource overhead and efficient decoding algorithms is crucial to achieve large-scale fault-tolerant quantum computation. The concatenated quantum Hamming…
We investigate the usage of highly efficient error correcting codes of multilevel systems to protect encoded quantum information from erasure errors and implementation to repetitively correct these errors. Our scheme makes use of quantum…
We consider the possibility of encoding m classical bits into much fewer n quantum bits so that an arbitrary bit from the original m bits can be recovered with a good probability, and we show that non-trivial quantum encodings exist that…
We consider the problem of optimally decoding a quantum error correction code -- that is to find the optimal recovery procedure given the outcomes of partial "check" measurements on the system. In general, this problem is NP-hard. However,…
Two-dimensional (2D) convolutional codes are a generalization of (1D) convolutional codes, which are very appropriate for transmission over an erasure channel. In this paper, we present a decoding algorithm for 2D convolutional codes over…
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.…
High-rate concatenated quantum codes offer a promising pathway toward fault-tolerant quantum computation, yet designing efficient decoders that fully exploit their error-correction capability remains a significant challenge. In this work,…
Quantum synchronizable codes are quantum error-correcting codes designed to correct the effects of both quantum noise and block synchronization errors. While it is known that quantum synchronizable codes can be constructed from cyclic codes…
Quantum process characterization is a fundamental task in quantum information processing, yet conventional methods, such as quantum process tomography, require prohibitive resources and lack scalability. Here, we introduce an efficient…
Variational quantum algorithms have been acknowledged as a leading strategy to realize near-term quantum advantages in meaningful tasks, including machine learning and combinatorial optimization. When applied to tasks involving classical…
Quantum codes are subspaces of the state space of a quantum system that are used to protect quantum information. Some common classes of quantum codes are stabilizer (or additive) codes, non-stabilizer (or non-additive) codes obtained from…
Quantum machine learning is an approach that aims to improve the performance of machine learning methods by leveraging the properties of quantum computers. In quantum circuit learning (QCL), a supervised learning method that can be…
Quantum cryptography -- the application of quantum computing techniques to cryptography has been extensively investigated. Two major directions of quantum cryptography are quantum key distribution (QKD) and quantum encryption, with the…
We investigate a quantum coding for quantum communication over a PD (partially degradable) degradable quantum channel. For a PD channel, the degraded environment state can be expressed from the channel output state up to a degrading map. PD…
The main ideas of quantum error correction are introduced. These are encoding, extraction of syndromes, error operators, and code construction. It is shown that general noise and relaxation of a set of 2-state quantum systems can always be…
The quantum error correction theory is as a rule formulated in a rather convoluted way, in comparison to classical algebraic theory. This work revisits the error correction in a noisy quantum channel so as to make it intelligible to…