439 research outputs found
Efficient quantum algorithm for preparing molecular-system-like states on a quantum computer
We present an efficient quantum algorithm for preparing a pure state on a
quantum computer, where the quantum state corresponds to that of a molecular
system with a given number of electrons occupying a given number of
spin orbitals. Each spin orbital is mapped to a qubit: the states and
of the qubit represent, respectively, whether the spin orbital is
occupied by an electron or not. To prepare a general state in the full Hilbert
space of qubits, which is of dimension %, controlled-NOT
gates are needed, i.e., the number of gates scales \emph{exponentially} with
the number of qubits. We make use of the fact that the state to be prepared
lies in a smaller Hilbert space, and we find an algorithm that requires at most
gates, i.e., scales \emph{polynomially} with the number
of qubits , provided . The algorithm is simulated numerically for
the cases of the hydrogen molecule and the water molecule. The numerical
simulations show that when additional symmetries of the system are considered,
the number of gates to prepare the state can be drastically reduced, in the
examples considered in this paper, by several orders of magnitude, from the
above estimate.Comment: 11 pages, 8 figures, errors are corrected, Journal information adde
Conversion of terahertz wave polarization at the boundary of a layered superconductor due to the resonance excitation of oblique surface waves
We predict a complete TM-TE transformation of the polarization of terahertz
electromagnetic waves reflected from a strongly anisotropic boundary of a
layered superconductor. We consider the case when the wave is incident on the
superconductor from a dielectric prism separated from the sample by a thin
vacuum gap. The physical origin of the predicted phenomenon is similar to the
Wood anomalies known in optics, and is related to the resonance excitation of
the oblique surface waves. We also discuss the dispersion relation for these
waves, propagating along the boundary of the superconductor at some angle with
respect to the anisotropy axis, as well as their excitation by the
attenuated-total-reflection method.Comment: 4 pages, 5 figure
Self-induced tunable transparency in layered superconductors
We predict a novel nonlinear electromagnetic phenomenon in layered
superconducting slabs irradiated from one side by an electromagnetic plane
wave. We show that the reflectance and transmittance of the slab can vary over
a wide range, from nearly zero to one, when changing the incident wave
amplitude. Thus changing the amplitude of the incident wave can induce either
the total transmission or reflection of the incident wave. In addition, the
dependence of the superconductor transmittance on the incident wave amplitude
has an unusual hysteretic behavior with jumps. This remarkable nonlinear effect
(self-induced transparency) can be observed even at small amplitudes, when the
wave frequency is close to the Josephson plasma frequency .Comment: 9 pages, 7 figure
Surface Josephson plasma waves in layered superconductors
We predict the existence of surface waves in layered superconductors in the
THz frequency range, below the Josephson plasma frequency . This wave
propagates along the vacuum-superconductor interface and dampens in both
transverse directions out of the surface (i.e., towards the superconductor and
towards the vacuum). This is the first prediction of propagating surface waves
in any superconductor. These predicted surface Josephson plasma waves are
important for different phenomena, including the complete suppression of the
specular reflection from a sample (Wood's anomalies) and a huge enhancement of
the wave absorption (which can be used as a THz detector).Comment: 4 pages, 2 figure
Weak and strong measurement of a qubit using a switching-based detector
We analyze the operation of a switching-based detector that probes a qubit's
observable that does not commute with the qubit's Hamiltonian, leading to a
nontrivial interplay between the measurement and free-qubit dynamics. In order
to obtain analytic results and develop intuitive understanding of the different
possible regimes of operation, we use a theoretical model where the detector is
a quantum two-level system that is constantly monitored by a macroscopic
system. We analyze how to interpret the outcome of the measurement and how the
state of the qubit evolves while it is being measured. We find that the answers
to the above questions depend on the relation between the different parameters
in the problem. In addition to the traditional strong-measurement regime, we
identify a number of regimes associated with weak qubit-detector coupling. An
incoherent detector whose switching time is measurable with high accuracy can
provide high-fidelity information, but the measurement basis is determined only
upon switching of the detector. An incoherent detector whose switching time can
be known only with low accuracy provides a measurement in the qubit's energy
eigenbasis with reduced measurement fidelity. A coherent detector measures the
qubit in its energy eigenbasis and, under certain conditions, can provide
high-fidelity information.Comment: 20 pages (two-column), 6 figure
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