Related papers: Topological Quantum Computation with Gapped Bounda…
Topology forms a cornerstone in modern condensed matter and statistical physics, offering a new framework to classify the phases and phase transitions beyond the traditional Landau paradigm. However, it is widely believed that topological…
I will give an overview of what I see as some of the most important future directions in the theory of fault-tolerant quantum computation. In particular, I will give a brief summary of the major problems that need to be solved in fault…
We propose a scheme for translating metrological precision bounds into lower bounds on query complexity of quantum search algorithms. Within the scheme the link between quadratic performance enhancement in idealized quantum metrological and…
We draw two incomplete, biased maps of challenges in computational complexity lower bounds.
We examine a few problems of enumerative geometry and present their solutions in the framework of deformed (quantum) cohomology rings.
The subject of topological defects has become a very attractive field of study given its apparent relevance to as diverse systems as the early universe and condensed matter. As usually envisaged the topology of the manifold M of the minima…
In the framework of the Closed-Time-Path formalism, we show how topological defects may arise in Quantum Field Theory as result of a localized (inhomogeneous) condensation of particles. We demonstrate our approach on two examples; kinks in…
The theory of quantum computation can be constructed from the abstract study of anyonic systems. In mathematical terms, these are unitary topological modular functors. They underlie the Jones polynomial and arise in Witten-Chern-Simons…
We revisit the problem of boundary excitations at a topological boundary or junction defects between topological boundaries in non-chiral bosonic topological orders in 2+1 dimensions. Based on physical considerations, we derive a formula…
We study how topological crystalline defects--dislocations--reshape the real-space quantum geometric tensor and act as tunable sources of quantum geometry. We show that dislocations strongly enhance the quantum metric, establishing a direct…
Some boundedness properties of function spaces (considered as topological groups) are studied.
Topological quantum computing has recently proven itself to be a powerful computational model when constructing viable architectures for large scale computation. The topological model is constructed from the foundation of a error correction…
To arrive at some viable product design, product development processes frequently use numerical simulations and mathematical programming techniques. Topology optimization, in particular, is one of the most promising techniques for…
We present some informal remarks on aspects of relativistic quantum computing.
Quantum error correction (QEC) is crucial for realizing scalable quantum technologies, and topological quantum error correction (TQEC) has emerged as the most experimentally advanced paradigm of QEC. Existing homological and topological…
Inspired by recent breakthroughs with topological quantum materials, which pave the way to novel, high-efficiency, low-energy magnetoelectric devices and fault-tolerant quantum information processing, inter alia, topological quantum walks…
I assess the potential of quantum computation. Broad and important applications must be found to justify construction of a quantum computer; I review some of the known quantum algorithms and consider the prospects for finding new ones.…
The discovery of an algorithm for factoring which runs in polynomial time on a quantum computer has given rise to a concerted effort to understand the principles, advantages, and limitations of quantum computing. At the same time, many…
We review the field of Optical Quantum Computation, considering the various implementations that have been proposed and the experimental progress that has been made toward realizing them. We examine both linear and nonlinear approaches and…
Many particle physics models of matter admit solutions corresponding to stable or long-lived topological defects. In the context of standard cosmology it is then unavoidable that such defects will form during phase transitions in the very…