Related papers: The Arbitrary Trajectory Quantization Method
The power method (or iteration) is a well-known classical technique that can be used to find the dominant eigenpair of a matrix. Here, we present a variational quantum circuit method for the power iteration, which can be used to find the…
An analysis of classical mechanics in a complex extension of phase space shows that a particle in such a space can behave in a way redolant of quantum mechanics; additional degrees of freedom permit 'tunnelling' without recourse to…
A general method of quantum-to-classical reduction of quantum dynamics is described. The key aspect of our method is the similarity transformation of the Liouvillian, which provides a new perspective. In conventional studies of quantum…
Simulations that couple different classical molecular models in an adaptive way by changing the number of degrees of freedom on the fly, are available within reasonably consistent theoretical frameworks. The same does not occur when it…
Quantization of energy balance equations, which describe a separatrix -- like motion is presented. The method is based on an exact canonical transformation of the energy--time pair to the action-angle canonical pair, $ (E,t)\to (I,\theta)…
Modular pairs of some second order q-difference equations are considered. These equations may be interpreted as a quantum mechanics of a sort of hyperelliptic pendulum. It is shown the quantization of a spectrum may be provided by the…
Quantum kernel methods (QKMs) have emerged as a prominent framework for supervised quantum machine learning. Unlike variational quantum algorithms, which rely on gradient-based optimisation and may suffer from issues such as barren…
The quantum cosmological version of a nonsingular Universe presented by Mukhanov and Brandenberger in the early nineties has been developed and the Hamilton Jacobi equation has been found under semiclassical (WKB) approximation. It has been…
We investigate the possibility that the quantum theory of gravity could be constructed discretely using algebraic methods. The algebraic tools are similar to ones used in constructing topological quantum field theories.The algebraic tools…
Nonlinear electrical response permits a unique window into effects of band structure geometry. It can be calculated either starting from a Boltzmann approach for small frequencies, or using Kubo's formula for resonances at finite frequency.…
{}From Feynman's path integral, we derive quasi-classical quantization rules in supersymmetric quantum mechanics (SUSY-QM). First, we derive a SUSY counterpart of Gutzwiller's formula, from which we obtain the quantization rule of Comtet,…
The quantization of the PageRank algorithm is a promising tool for a future quantum internet. Here we present a modification of the quantum PageRank introducing arbitrary phase rotations (APR) in the underlying Szegedy's quantum walk. We…
This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy…
Energy level statistics of quantized chaotic systems have been evaluated in the semiclassical limit via their periodic orbits using the Gutzwiller and related trace formulae. Here we evaluate a spectral statistic of chaotic 4-regular…
Imaginary Time Evolution (QITE) approximates this evolution on quantum hardware but suffers from high circuit depth and numerous measurements. In this work we introduce Adaptive-time Compressed QITE (ACQ), a novel algorithm that reduces…
We show that quantum theory (QT) is a substructure of classical probabilistic physics. The central quantity of the classical theory is Hamilton's function, which determines canonical equations, a corresponding flow, and a Liouville equation…
We examine theoretic architectures and an abstract model for a restricted class of quantum computation, called here instantaneous quantum computation because it allows for essentially no temporal structure within the quantum dynamics. Using…
Recently it has been shown that the evolution of open quantum systems may be ``unraveled'' into individual ``trajectories,'' providing powerful numerical and conceptual tools. In this letter we use quantum trajectories to study mesoscopic…
We investigate electron transport through clean open quantum dots (quantum billiards). We present a semiclassical theory that allows to accurately reproduce quantum transport calculations. Quantitative agreement is reached for individual…
New insight into the correspondence between Quantum Chaos and Random Matrix Theory is gained by developing a semiclassical theory for the autocorrelation function of spectral determinants. We study in particular the unitary operators which…