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Quantum Codes for Topological Quantum Computation
This book offers a structured algebraic and geometric approach to the classification and construction of quantum codes for topological quantum...
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Topological Quantum Codes
As is already known, the computer-based on quantum properties is very promising. However, for this to become a reality, it is necessary to overcome...
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Hyperbolic quantum color codes with normal subgroup structure derived from the Reidemeister–Schreier method
Given the importance of hyperbolic quantum color codes and Euclidean quantum color codes, this paper considers the study of the former codes on...
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The Interplay Between Color Codes and Toric Codes
In each of the two previous chapters, we dealt with mathematical structures and properties related to topological toric codes and topological color...
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Color Codes
As seen in previous chapters, in 1996 a new class of codes, now known as CSS codes, was proposed by Robert Calderbank, Peter Shor, and Andrew Steane....
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Building manifolds from quantum codes
We give a procedure for “reverse engineering" a closed, simply connected, Riemannian manifold with bounded local geometry from a sparse chain complex...
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Quantum Operads
The most standard description of symmetries of a mathematical structure produces a group. However, when the definition of this structure is motivated...
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Introduction
This book is intended to be an introductory material on topological quantum codes, with the necessary elements from a mathematical and engineering...
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Basics of Quantum Information Processing
In this chapter, we present a collection of basic ideas in quantum information processing. First idea to present is the quantum gate operations,...
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Quantum Error Correction
DiVincenzo criterionDiVincenzo criteria #5 from Chap. 18 states that the qubit lifetimes should be long...
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Quantum simulators, phase transitions, resonant tunneling, and variances: A many-body perspective
This 2021 report summarizes our activities at the HLRS facilities Hawk and Hazel Hen in the framework of the multiconfigurational time-dependent...
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A Generalization of Gleason’s Frame Function for Quantum Measurement
The goal is to extend Gleason’s notion of a frame function, which is essential in his fundamental theorem in quantum measurement, to a more general...
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Quantum Graphs as Quantum Relations
The “noncommutative graphs” which arise in quantum error correction are a special case of the quantum relations introduced in Weaver (Quantum...
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Applications and Quantum Supremacy
As the quantum computing landscape evolves, a number of QC applications are becoming clear..
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Representations of Graph States with Neural Networks
Quantum many-body problem (QMBP) has become a hot topic in high energy physics and condensed matter physics. With the exponential increasing of the...
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Brain and Its Universal Logical Model of Multi-Agent Biological Systems
We build a topological model, based on intuitionistic logic, for multi-agent biological systems (such as Physarum polycephalum , bacterial colonies or...
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The Mathematics of László Lovász
This is an exposition of the contributions of László Lovász to mathematics and computer science written on the occasion of the bestowal of the Abel...
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Nonlinear Dynamics of Atomic and Molecular Systems in an Electromagnetic Field: Deterministic Chaos and Strange Attractors
We present a new mathematical approach to studying deterministic chaos and strange attractors in dynamics of nonlinear processes in atomic and...
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Quantum Computing with Octonions
There are two schools of “measurement-only quantum computation”. The first (Phys. Rev. Lett. 86 (22), 5188–5191 (
2001 )) using prepared entanglement...
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Coboundary expansion, equivariant overlap, and crossing numbers of simplicial complexes
We prove the following quantitative Borsuk–Ulam-type result (an equivariant analogue of Gromov’s Topological Overlap Theorem): Let X be a free...