Related papers: Description and error analysis of quantum alghorit…
Geometric phases have stimulated researchers for its potential applications in many areas of science. One of them is fault-tolerant quantum computation. A preliminary requisite of quantum computation is the implementation of controlled…
We study solutions to the quantum trajectory evolution of $N$-mode open quantum systems possessing a time-independent Hamiltonian, linear Heisenberg-picture dynamics, and Gaussian measurement noise. In terms of the mode annihilation and…
We propose a Newton algorithm to characterize the Hamiltonian of a quantum system interacting with a given laser field. The algorithm is based on the assumption that the evolution operator of the system is perfectly known at a fixed time.…
In this work we develop several new simulation algorithms for 1D many-body quantum mechanical systems combining the Matrix Product State variational ansatz with Taylor, Pade and Arnoldi approximations to the evolution operator. By comparing…
We show that by a suitable choice of a time dependent Hamiltonian, Deutsch's algorithm can be implemented by an adiabatic quantum computer. We extend our analysis to the Deutsch-Jozsa problem and estimate the required running time for both…
The use of the quantizer-dequantizer formalism to describe the evolution of a quantum system is reconsidered. We show that it is possible to embed a manifold in the space of quantum states of a given auxiliary system by means of an…
Quantum computation offers potential exponential speedups for simulating certain physical systems, but its application to nonlinear dynamics is inherently constrained by the requirement of unitary evolution. We propose the quantum Koopman…
We analyze in detail the discrete--time quantum walk on the line by separating the quantum evolution equation into Markovian and interference terms. As a result of this separation, it is possible to show analytically that the quadratic…
In this survey the possible approaches to the description of the evolution of states of quantum many-particle systems by means of the possible modifications of the density operator which kernel known as density matrix are considered. In…
Gradient descent is a fundamental algorithm in both theory and practice for continuous optimization. Identifying its quantum counterpart would be appealing to both theoretical and practical quantum applications. A conventional approach to…
We introduce stochastic and quantum finite-state transducers as computation-theoretic models of classical stochastic and quantum finitary processes. Formal process languages, representing the distribution over a process's behaviors, are…
The method of quantum tomography, which allows us to track with high accuracy the evolution of multilevel quantum systems (qudits) in Hilbert spaces of various dimensions is presented. The developed algorithms for quantum control are based…
Differential evolution (DE) is a population based evolutionary algorithm widely used for solving multidimensional global optimization problems over continuous spaces. However, the design of its operators makes it unsuitable for many…
We consider the problem of the driven harmonic oscillator in the probability representation of quantum mechanics, where the oscillator states are described by fair nonnegative probability distributions of position measured in rotated and…
We present techniques to construct the Deutsch-Hayden representation for quantum field operators and apply them to an entangled state of identical nonrelativistic spin-1/2 fermions localized in well-separated spatial regions. Using these…
Quantum computing is a new way of data processing based on the concept of quantum mechanics. Quantum circuit design is a process of converting a quantum gate to a series of basic gates and is divided into two general categories based on the…
We address the quantum dynamics of second harmonic generation with a perturbative approach. By inspecting the Taylor expansion of the unitary evolution, we identify the subsequent application of annihilation and creation operators as…
In this paper we introduce an alternative approach to studying the evolution of a quantum harmonic oscillator subject to an arbitrary time dependent force. With the purpose of finding the evolution operator, certain unitary transformations…
We develop theoretical methods for the implementation of creation and destruction operators in separate registers of a quantum computer, allowing for a transparent and dynamical creation and destruction of particle modes in second…
Designing quantum algorithms for simulating quantum systems has seen enormous progress, yet few studies have been done to develop quantum algorithms for open quantum dynamics despite its importance in modeling the system-environment…