Related papers: Constructions of Optimal-Speed Quantum Evolutions:…
By a quantum speed limit one usually understands an estimate on how fast a quantum system can evolve between two distinguishable states. The most known quantum speed limit is given in the form of the celebrated Mandelstam-Tamm inequality…
Consider the set of all Hamiltonians whose largest and smallest energy eigenvalues, E_max and E_min, differ by a fixed energy \omega. Given two quantum states, an initial state |\psi_I> and a final state |\psi_F>, there exist many…
It is known that the continuous-time variant of Grover's search algorithm is characterized by quantum search frameworks that are governed by stationary Hamiltonians, which result in search trajectories confined to the two-dimensional…
We investigate the evolution of a single qubit subject to a continuous unitary dynamics and an additional interrupting influence which occurs periodically. One may imagine a dynamically evolving closed quantum system which becomes open at…
We introduce the concept of interpolation in quantum evolution and present a general framework to find the energy optimal Hamiltonian for a quantum system evolving among a given set of middle states using variational and geometric methods.…
Under broad conditions, evolutions due to two different Hamiltonians are shown to lead at some moment to orthogonal states. For two spin-1/2 systems subject to precession by different magnetic fields the achievement of orthogonalization is…
We consider the simulation of the dynamics of one nonlocal Hamiltonian by another, allowing arbitrary local resources but no entanglement nor classical communication. We characterize notions of simulation, and proceed to focus on…
We introduce an iterative method to search for time-optimal Hamiltonians that drive a quantum system between two arbitrary, and in general mixed, quantum states. The method is based on the idea of progressively improving the efficiency of…
We examine the time evolution of an asymmetric Hubbard dimer, which has a different on-site interaction on the two sites. The Hamiltonian has a time-dependent hopping term, which can be employed to describe an electric field (which creates…
Quantum mechanics establishes a fundamental bound for the minimum evolution time between two states of a given system. Known as the quantum speed limit (QSL), it is a useful tool in the context of quantum control, where the speed of some…
We argue that a quantum annealer at very long annealing times is likely to experience a quasistatic evolution, returning a final population that is close to a Boltzmann distribution of the Hamiltonian at a single (freeze-out) point during…
We study the dynamics of a two-level system described by a slowly varying Hamiltonian and weakly coupled to the Ohmic environment. We follow the Bloch--Redfield perturbative approach to include the effect of the environment on qubit…
A non-Hermitian operator may serve as the Hamiltonian for a unitary quantum system, if we can modify the Hilbert space of state vectors of the system so that it turns into a Hermitian operator. If this operator is time-dependent, the…
We investigate the quantum dynamics of a one-dimensional tight-binding lattice driven by a spatially quadratic and time-periodic potential. Both Hermitian ($J_1 = J_2$) and non-Hermitian ($J_1 \neq J_2$) hopping regimes are analyzed. Within…
We analyze the influence of relativistic effects on the minimum evolution time between two orthogonal states of a quantum system. Defining the initial state as an homogeneous superposition between two Hamiltonian eigenstates of an electron…
We propose, formulate and examine novel quantum systems and behavioral phases in which momentary choices of the system's memories interact in order to source the internal interactions and unitary time evolutions of the system. In a closed…
In quantum adiabatic evolution algorithms, the quantum computer follows the ground state of a slowly varying Hamiltonian. The ground state of the initial Hamiltonian is easy to construct; the ground state of the final Hamiltonian encodes…
I report a tight upper bound of the maximum speed of evolution from one quantum state $\rho$ to another $\rho'$ with fidelity $F(\rho,\rho')$ less than or equal to an arbitrary but fixed value under the action of a time-independent…
The requirement of Hermiticity of a Quantum Mechanical Hamiltonian, for the description of physical processes with real eigenvalues which has been challenged notably by Carl Bender, is examined for the case of a Fock space Hamilitonian…
We present the method of describing an evolution in quantum cosmology in the framework of the reduced phase space quantization of loop cosmology. We apply our method to the flat Friedman-Robertson-Walker model coupled to a massless scalar…