with the envelope evolution of mode The unitary operator of transformation should transform nonlinear mode structures in linear ones (in time-frequency domain), and thus allow the use of classical Fourier filtering techniques.
Collapses interrupt or outright replace the unitary evolution of the quantum state.
Then, we make use of the Trotter expansion [2 4] to decompose the unitary evolution of the simulated system in a sequence of quantum gates.
Modulo some philosophical concerns about the meaning of time reversal (Albert 2000, Callender 2000, Earman 2002), the equation governing the unitary evolution of the quantum state is time reversal invariant.
These interpretations fall broadly into two types, depending on their view of the unitary evolution of the quantum state (e.g., evolution according to the Schroedinger equation): they either say that there is something more than the quantum state, or that the unitary evolution is not entirely correct.
In this paper, we give an algorithm for the control of the unitary evolution operator for the system of two spin 12's interacting through Heisenberg interaction.
(It should be noted that 'quantum computing,' in the standard modern sense, is based on the predictability of the unitary evolution, and does not, as yet, go into the question of how reduction occurs).
The Trotter formula is an approximation of the unitary evolution (e^{-iHt}), where H is the simulated Hamiltonian, consisting of M quantum gates (e^{-iH_{i}t}) that fulfill the condition (H=sum_{i}^{M} H_{i}), being (H_{i}) the natural interaction terms of the controllable system.
The question of whether black hole evolution is unitary raises the issue of how the unitary evolution of standard quantum mechanics serves to guarantee that no experiment can reveal a violation of energy conservation or of microcausality.
Von Neumann's axioms of quantum mechanics involve two processes: unitary evolution of the wave function, which is predictable, and the measurement or reduction operation, which introduces unpredictability.
In Figure 9, we show a plot of these populations considering a perfect unitary evolution of the Fermi-Hubbard model versus the evolution associated with the digital decomposition, where l is the number of Trotter steps.
