Related papers: Supersymmetry and Quantum Computation
A superintegrable system is, roughly speaking, a system that allows more integrals of motion than degrees of freedom. This review is devoted to finite dimensional classical and quantum superintegrable systems with scalar potentials and…
In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress. We now have strong theoretical evidence that quantum computers, if built, might be used as a dramatically…
Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert…
Higher dimensional supersymmetric quantum mechanics is studied. General properties of the two dimensional case are presented. For three spatial dimesions or higher, a spin structure is shown to arise naturally from the nonrelativistic…
In this dissertation, we study the intersection of quantum computing and supervised machine learning algorithms, which means that we investigate quantum algorithms for supervised machine learning that operate on classical data. This area of…
Supersymmetry applied to quantum mechanics has given new insights in various topics of theoretical physics like analytically solvable potentials, WKB approximation or KdV solitons. Duality plays a central role in many supersymmetric…
Lattice studies of spontaneous supersymmetry breaking suffer from a sign problem that in principle can be evaded through novel methods enabled by quantum computing. Focusing on lower-dimensional lattice systems with more modest resource…
Scalable modern-time fault-tolerant quantum computation and quantum communication in a network employ a large number of physical qubits. For example, IBM is reported to have made a 127-qubit quantum computer. Unlike classical computation,…
Simulations of supersymmetric field theories with spontaneously broken supersymmetry require in addition to the ultraviolet regularisation also an infrared one, due to the emergence of the massless Goldstino. The intricate interplay between…
Construction of explicit quantum circuits follows the notion of the "standard circuit model" introduced in the solid and profound analysis of elementary gates providing quantum computation. Nevertheless the model is not always optimal (e.g.…
We illustrate the application of Quantum Computing techniques to the investigation of the thermodynamical properties of a simple system, made up of three quantum spins with frustrated pair interactions and affected by a hard sign problem…
Fundamental questions in chemistry and physics may never be answered due to the exponential complexity of the underlying quantum phenomena. A desire to overcome this challenge has sparked a new industry of quantum technologies with the…
It is indicated that principal models of computation are indeed significantly related. The quantum field computation model contains the quantum computation model of Feynman. (The term "quantum field computer" was used by Freedman.) Quantum…
Symmetries in a Hamiltonian play an important role in quantum physics because they correspond directly with conserved quantities of the related system. In this paper, we propose quantum algorithms capable of testing whether a Hamiltonian…
Supersymmetric quantum mechanics is constructed in a new non-Hermitian representation. Firstly, the map between the partner operators $H^{(\pm)}$ is chosen antilinear. Secondly, both these components of a super-Hamiltonian ${\cal H}$ are…
We introduce super quantum Airy structures, which provide a supersymmetric generalization of quantum Airy structures. We prove that to a given super quantum Airy structure one can assign a unique set of free energies, which satisfy a…
Quantum Computing is a new and exciting field at the intersection of mathematics, computer science and physics. It concerns a utilization of quantum mechanics to improve the efficiency of computation. Here we present a gentle introduction…
Quantum computers hold great promise, but it remains a challenge to find efficient quantum circuits that solve interesting computational problems. We show that finding optimal quantum circuits is essentially equivalent to finding the…
Insofar as quantum computation is faster than classical, it appears to be irreversible. In all quantum algorithms found so far the speed-up depends on the extra-dynamical irreversible projection representing quantum measurement. Quantum…
I propose a method for measuring the Witten index using a lattice simulation. The index is useful to discuss spontaneous breaking of supersymmetry. As a test of the method, I also report some numerical results for the supersymmetric quantum…