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The minimum distance of a linear code is a key concept in information theory. Therefore, the time required by its computation is very important to many problems in this area. In this paper, we introduce a family of implementations of the…
The minimum distance of a code is an important concept in information theory. Hence, computing the minimum distance of a code with a minimum computational cost is a crucial process to many problems in this area. In this paper, we present…
The distance of a classical or quantum code is a key figure of merit which reflects its capacity to detect errors. Quantum LDPC code families have considerable promise in reducing the overhead required for fault-tolerant quantum…
Quantum error correction and the use of quantum error correction codes is likely to be essential for the realisation of practical quantum computing. Because the error models of quantum devices vary widely, quantum codes which are tailored…
The techniques of distance verification known for general linear codes are re-applied to quantum stabilizer codes. Then distance verification is addressed for classical and quantum LDPC codes. New complexity bounds for distance verification…
The stabiliser formalism plays a central role in quantum computing, error correction, and fault tolerance. Conversions between and verifications of different specifications of stabiliser states and Clifford gates are important components of…
We study the hardness of the problem of finding the distance of quantum error-correcting codes. The analogous problem for classical codes is known to be NP-hard, even in approximate form. For quantum codes, various problems related to…
Although qubit coherence times and gate fidelities are continuously improving, logical encoding is essential to achieve fault tolerance in quantum computing. In most encoding schemes, correcting or tracking errors throughout the computation…
Quantum error-correcting codes (QECCs) is at the heart of fault-tolerant quantum computing. As the size of quantum platforms is expected to grow, one of the open questions is to design new optimal codes of ever-increasing size. A related…
We generalize the Brouwer-Zimmermann algorithm, which is the most efficient general algorithm for computing the minimum distance of a random linear code, to the case of generalized Hamming weights. We also adapt this algorithm to compute…
We survey the existing techniques for calculating code distances of classical codes and apply these techniques to generic quantum codes. For classical and quantum LDPC codes, we also present a new linked-cluster technique. It reduces…
We present a construction of Hermitian operators and quantum states labelled by strings from a finite field. The distance between these operators or states is then simply related (typically, proportional) to the Hamming distance between…
Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of…
We propose a series of quantum algorithms for computing a wide range of quantum entropies and distances, including the von Neumann entropy, quantum R\'{e}nyi entropy, trace distance, and fidelity. The proposed algorithms significantly…
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.…
Quantum computers hold the potential to surpass classical computers in solving complex computational problems. However, the fragility of quantum information and the error-prone nature of quantum operations make building large-scale,…
Stabilizer codes form an important class of quantum error correcting codes which have an elegant theory, efficient error detection, and many known examples. Constructing stabilizer codes of length $n$ is equivalent to constructing subspaces…
In this work we examine recently proposed distance-based classification method designed for near-term quantum processing units with limited resources. We further study possibilities to reduce the quantum resources without any efficiency…
We present several quantum algorithms for performing nearest-neighbor learning. At the core of our algorithms are fast and coherent quantum methods for computing distance metrics such as the inner product and Euclidean distance. We prove…
Symmetry is an important and unifying notion in many areas of physics. In quantum mechanics, it is possible to eliminate degrees of freedom from a system by leveraging symmetry to identify the possible physical transitions. This allows us…