Related papers: Topological Quantum Computation with Gapped Bounda…
The so-called "threshold" theorem says that, once the error rate per qubit per gate is below a certain value, indefinitely long quantum computation becomes feasible, even if all of the qubits involved are subject to relaxation processes,…
In this paper, we study some topological characteristics of the n-normed spaces. We observe convergence sequences, closed sets, and bounded sets in the n-normed spaces using norms of quotient spaces that will be constructed. These norms…
In this paper we propose a Hamiltonian approach to gapped topological phases on an open surface with boundary. Our setting is an extension of the Levin-Wen model to a 2d graph on the open surface, whose boundary is part of the graph. We…
It is expected that quantum computers would enable solving various problems that are beyond the capabilities of the most powerful current supercomputers, which are based on classical technologies. In the last three decades, advances in…
Parallel fixed-parameter tractability studies how parameterized problems can be solved in parallel. A surprisingly large number of parameterized problems admit a high level of parallelization, but this does not mean that we can also…
Topological quantum sensing leverages unique topological features to suppress noise and improve the precision of parameter estimation, emerging as a promising tool in both fundamental research and practical application. In this Letter, we…
We address the problem of topology of quadrature domains, namely we give upper bounds on the connectivity of the domain in terms of the number of nodes and their multiplicities in the quadrature identity.
The rise of quantum information science has opened up a new venue for applications of the geometric phase (GP), as well as triggered new insights into its physical, mathematical, and conceptual nature. Here, we review this development by…
In this paper I discuss the formation of topological defects in quantum field theory and the relation between fractals and coherent states. The study of defect formation is particularly useful in the understanding of the same mathematical…
We give a survey of algorithms for computing topological invariants of semi-algebraic sets with special emphasis on the more recent developments in designing algorithms for computing the Betti numbers of semi-algebraic sets. Aside from…
Quantum computing provides a powerful framework for tackling computational problems that are classically intractable. The goal of this paper is to explore the use of quantum computers for solving relevant problems in systems and control…
The existence of bound states in quantum mechanics with no classical counterpart has been a subject of interest for a long time. Cross-wires and cavities connected to infinite leads are typical examples in which open geometries with bulges…
The present paper aims at developing a theory of computation of crystalline defects at finite temperature. In a one-dimensional setting we introduce Gibbs distributions corresponding to such defects and rigorously establish their asymptotic…
This paper explores the interactions between knot theory and quantum computing. On one side, knot theory has been used to create models of quantum computing, and on the other, it is a source of computational problems. Knot theory is often…
Topological semimetals and metals have emerged as a new frontier in the field of quantum materials. Novel macroscopic quantum phenomena they exhibit are not only of fundamental interest, but may hold some potential for technological…
We prove the existence of infinitely many solutions to an elliptic problem by borrowing the techniques from algebraic topology. The solution(s) thus obtained will also be proved to be bounded.
For the first time in history, we are seeing a branching point in computing paradigms with the emergence of quantum processing units (QPUs). Extracting the full potential of computation and realizing quantum algorithms with a…
Quantum computing is concerned with computer technology based on the principles of quantum mechanics, with operations performed at the quantum level. Quantum computational models make it possible to analyze the resources required for…
New inequalities for symplectic tomograms of quantum states and their connection with entropic uncertainty relations are discussed within the framework of the probability representation of quantum mechanics.
Tasked with the challenge to build better and better computers, quantum computing and classical computing face the same conundrum: the success of classical computing systems. Small quantum computing systems have been demonstrated, and…