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Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 17 of 17 for “"Quantum Codes"”.
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Quantum codes on Hurwitz surfaces
Ever since the birth of the first quantum error correcting code, many error correcting techniques and formalism has been constructed so far. Among those, generating a quantum code on a locally planar geometry have lead to some interesting classes of codes. Main idea of this thesis stems from …
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Quantum Codes, Transversal Gates, and Representation Theory
… void by constructing a family of distance d = 3 codes that all implement 2I transversally [39, 42]. To do this, we introduce twisted unitary t-groups, a generalization of unitary t-groups under a twisting by an irreducible representation. We then apply representation theoretic methods to the …
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Calculation of thermodynamic and kinetic properties using semi- empirical quantum codes
Although semi-empirical quantum codes have existed for several years now, the computational chemistry has, by and large, remained the subject of major interest for organic chemists and quantum chemists. In this thesis numerous exercises are designed in order to explore various areas of chemical …
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Investigating Topological Quantum Matter: Machine Learning Topological Phases, Topological Quantum Codes, Interplay of Disorder and Topology via Transport Phenomena and Phase Transitions
Future quantum technologies must meet three inter-locking demands: (i) faithful yet compact representations of strongly–entangled quantum matter, (ii) scalable error-mitigation protocols that tame spatially correlated noise, and (iii) near-term algorithms that coax useful optimisation and learning …
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Quantum operations and codes beyond the Stabilizer-Clifford framework
The discovery of quantum error-correcting codes (QECCs) and the theory of fault-tolerant quantum computation (FTQC) have greatly improved the long-term prospects for quantum communication and computation technology. Stabilizer codes, a quantum analogue of classical additive codes, are the most …
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Optimal Quaternary Hermitian Linear Complementary Dual Codes for Entanglement-Assisted Quantum Error Correction
… suboptimal and optimal parameters from classical codes and import them into entanglement-assisted quantum codes. The thesis begins by introducing classical error correction, followed by a detailed introduction to quantum computing. Topics that are discussed in the introduction include qubits, …
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Fault-tolerant quantum computer architectures using hierarchies of quantum error-correcting codes
Quantum computers have been shown to efficiently solve a class of problems for which no efficient solution is otherwise known. Physical systems can implement quantum computation, but devising realistic schemes is an extremely challenging problem largely due to the effect of noise. A quantum …
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Algorithmic approaches to graph states under the action of local Clifford groups
Graph states are quantum states (quantum codes) in qn-dimensional space ... (q being a power of some prime number) which can be described by graphs with edges labeled from the field of order q, Fq. Graph states are determined as a common eigenvector of independent elements of the n-fold Pauli …
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Quantum Algebraic Geometry Codes
Quantum error correction is an essential aspect of quantum information theory, providing protection for quantum states against noise and decoherence. This thesis investigates the construction of quantum error correction codes derived from classical algebraic geometry (AG) codes. We present two …
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Features and Applications of Random Unitaries
… plays essential roles in the study of many-body quantum systems, and have many applications in the field of quantum information. In this thesis we will explore some features and applications of this model. We will first study the scrambling property of random circuits (i.e., sequential …
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Good families of quantum low-density parity-check codes and a geometric framework for the amplitude-damping channel
Classical low-density parity-check (LDPC) codes were first introduced by Robert Gallager in the 1960's and have reemerged as one of the most influential coding schemes. We present new families of quantum low-density parity-check error-correcting codes derived from regular tessellations of Platonic …
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Fault-Tolerant Quantum Measurement of Error Syndromes and Logical Operators
<p>Fault-tolerant quantum computation requires the measurements of error syndromes and logical operators in a way that minimizes undesired correlated errors on the quantum data. This thesis explores possible forms for performing these measurements. Our first result aims at minimizing the number of …
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Device- and application-adapted quantum error correction
Precise control of coherent quantum systems could enable new generations of sensing, communication and computing technologies. Such systems, however, are typically noisy and difficult to stabilize. One promising technique to this end is called quantum error correction, which encodes quantum states …
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Quantum Computing from Graphs
… useful as a descriptive tool for additive quantum codes, they otherwise offer little guidance for concrete constructions or coding algorithm analysis. We introduce a representation of stabilizer codes as graphs with certain structures. Specifically, the graphs take a semi-bipartite form …
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Practical fault-tolerant quantum computation
… superposition, interference, and entanglement of quantum states to compute faster than a classical computer on select tasks. Manipulating quantum systems requires great care, however, as they are quite sensitive to many sources of noise. Surpassing the limits of hardware fabrication and control, …
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Constructing CSS-T Codes from Extended Quasi-Cyclic Codes
We analyze a construction of quasi-cyclic codes in an extension field based on the polynomials which generate the corresponding codes in the base fields. We establish a set of code operations on which trace relationships between extended quasi-cyclic codes are the same as the operations taken on …