Related papers: Complexity in One- and Two-Qubit Systems
We analyze the asymptotic dynamics of quantum systems resulting from large numbers of iterations of random unitary operations. Although, in general, these quantum operations cannot be diagonalized it is shown that their resulting asymptotic…
One of the axioms of quantum field theory is the property of unitarity of the evolution operator. However, if one considers the quantum electrodynamics in the external field in the leading order of perturbation theory, one will find that…
This work discusses a variational approach to determining the time evolution operator. We directly see a glimpse of how a generalization of the quantum geometric tensor for unitary operators plays a central role in parameter evolution. We…
Quantum complexity is a measure of the minimal number of elementary operations required to approximately prepare a given state or unitary channel. Recently, this concept has found applications beyond quantum computing -- in studying the…
We present an outline of a technique to associate certain methods from time optimal quantum control with various transforms on SU(3). Unitary operators are taken from certain time dependent Hamiltonians and transformation laws are derived.…
Recently it has been shown that the complexity of SU($n$) operator is determined by the geodesic length in a bi-invariant Finsler geometry, which is constrained by some symmetries of quantum field theory. It is based on three axioms and one…
In quantum mechanics, time is introduced as a non-measurable quantity, as there is no possibility to build a hermitian operator canonically conjugated to the Hamiltonian. We cannot have, therefore, the time operator, which means that the…
In this article, we formulate the study of the unitary time evolution of systems consisting of an infinite number of uncoupled time-dependent harmonic oscillators in mathematically rigorous terms. We base this analysis on the theory of a…
Analyzing the computational complexity of evolutionary algorithms for binary search spaces has significantly increased their theoretical understanding. With this paper, we start the computational complexity analysis of genetic programming.…
It has been argued that it is incompatible to maintain unitary time-evolution for time-dependent non-Hermitian Hamiltonians when the metric operator is explicitly time-dependent. We demonstrate here that the time-dependent Dyson equation…
We study the time evolution of quantum systems with a time-dependent non-Hermitian Hamiltonian given by a linear combination of SU(1,1) and SU(2) generators.With a time-dependent metric, the pseudo-Hermitian invariant operator is…
The evolution of a mixed quantum-classical system is expressed in the mapping formalism where discrete quantum states are mapped onto oscillator states, resulting in a phase space description of the quantum degrees of freedom. By defining…
We present a quantitative analysis of the reversibility properties of classically chaotic quantum motion. We analyze the connection between reversibility and the rate at which a quantum state acquires a more and more complicated structure…
In this paper, we study time-optimal control problems related to system of two coupled qubits where the time scales involved in performing unitary transformations on each qubit are significantly different. In particular, we address the case…
Unitary operation is an essential step for quantum information processing. We first propose an iterative procedure for decomposing a general unitary operation without resorting to controlled-NOT gate and single-qubit rotation library. Based…
The time-evolution operator for an explicitly time-dependent Hamiltonian is expressed as the product of a sequence of unitary operators. These are obtained by successive time-dependent unitary transformations of the Hilbert space followed…
For quantum theories with a classical limit (which includes the large N limits of typical field theories), we derive a hierarchy of evolution equations for equal time correlators which systematically incorporate corrections to the limiting…
In order to resolve the measurement problem of Quantum Mechanics, non-unitary time evolution has been derived from the unitarity of standard quantum formalism. New wave functions of free and non-free quantum systems follow from Schroedinger…
We consider the natural generalization of the Schr\"{o}dinger equation to Markovian open system dynamics: the so-called the Lindblad equation. We give a quantum algorithm for simulating the evolution of an $n$-qubit system for time $t$…
The quaternionic description of semiconductor single-electron devices is given in the single-electron regime. The conversion scheme of complex value Hamiltonian into a quaternion is formulated for the case of single-electron semiconductor…