Related papers: Comment on the Quantum Brachistochrone Problem
We give a quantum algorithm for solving instances of the satisfiability problem, based on adiabatic evolution. The evolution of the quantum state is governed by a time-dependent Hamiltonian that interpolates between an initial Hamiltonian,…
Starting with the quantum brachistochrone problem of the infinitesimal form, we solve the minimal time and corresponding time-dependent Hamiltonian to drive a pure quantum state with limited resources along arbitrary pre-assigned…
We describe a semidefinite relaxation method which finds lower bounds to the ground state energy of a quantum Hamiltonian subject to Hermitian linear constraints along with approximations of ground state expectation values. We show that…
Standard quantum theory represents a composite system at a given time by a joint state, but it does not prescribe a joint state for a composite of systems at different times. If a more even-handed treatment of space and time is possible,…
Several novel approaches have been proposed to resolve the problem of time by relating it to change. We argue using quantum information theory that the Hamiltonian constraint in quantum gravity cannot probe change, so it cannot be used to…
The quantum marginal problem asks, given a set of reduced quantum states of a multipartite system, whether there exists a joint quantum state consistent with these reduced states. The quantum marginal problem is known to be hard to solve in…
In optimal quantum-mechanical evolutions, motion can take place along paths of minimal length within an optimal time frame. Alternatively, optimal evolutions may occur along established paths without any waste of energy resources and…
One among the possible realizations of non-Hermitian systems is based on open quantum systems by omitting quantum jumping terms in the master equation. This is a good approximation at short times where the effects of quantum jumps can be…
We study the effects of non-hermitian perturbation on a quantum kicked model exhibiting a localization transition. Using an exact renormalization scheme, we show that the critical line separating the extended and localized phases approaches…
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…
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…
Unitarity is a cornerstone of quantum theory, ensuring the conservation of probability and information. Although non-Hermitian Hamiltonians are typically associated with open or dissipative systems, pseudo-Hermitian quantum mechanics shows…
The time evolution of a finite fermion system towards statistical equilibrium is investigated using analytical solutions of a nonlinear partial differential equation that had been derived earlier from the Boltzmann collision term. The…
Variational quantum time evolution allows us to simulate the time dynamics of quantum systems with near-term compatible quantum circuits. Due to the variational nature of this method the accuracy of the simulation is a priori unknown. We…
Applying the theory of self-adjoint extensions of Hermitian operators to Koopman von Neumann classical mechanics, the most general set of probability distributions is found for which entropy is conserved by Hamiltonian evolution. A new…
In orthodox quantum theory the observables of spacelike separated quantum systems commute. I shall call this the commutation constraint. It severely limits quantum theory's explanatory power. For instance, the constraint cannot be met in…
We present a general theoretical framework for finding the time-optimal unitary evolution of the quantum systems when the Hamiltonian is subject to arbitrary constraints. Quantum brachistochrone (QB) is such a framework based on the…
We develop further the approach to upper and lower bounds in quantum dynamics via complex analysis methods which was introduced by us in a sequence of earlier papers. Here we derive upper bounds for non-time averaged outside probabilities…
The generic bound of quantum speed limit time (the minimal evolution time) for a qubit system interacting with structural environment is investigated. We define a new bound for the quantum speed limit. It is shown that the non-Markovianity…
Optimal simultaneous control of position and momentum can be achieved by maximizing the probabilities of finding their experimentally observed values within two well-defined intervals. The assumption that particles move along straight lines…