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 $m$ of electrons occupying a given number $n$ of spin orbitals. Each spin orbital is mapped to a qubit: the states $| 1 >$ and $| 0>$ 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 $n$ qubits, which is of dimension $2^{n}$%, $O(2^{n})$ 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 $O(2^{m+1} n^{m}/{m!})$ gates, i.e., scales \emph{polynomially} with the number of qubits $n$, provided $n\gg m$. 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

Speed limits for quantum gates in multi-qubit systems

We use analytical and numerical calculations to obtain speed limits for various unitary quantum operations in multiqubit systems under typical experimental conditions. The operations that we consider include single-, two-, and three-qubit gates, as well as quantum-state transfer in a chain of qubits. We find in particular that simple methods for implementing two-qubit gates generally provide the fastest possible implementations of these gates. We also find that the three-qubit Toffoli gate time varies greatly depending on the type of interactions and the system's geometry, taking only slightly longer than a two-qubit controlled-NOT (CNOT) gate for a triangle geometry. The speed limit for quantum-state transfer across a qubit chain is set by the maximum spin-wave speed in the chain.Comment: 7 pages (two-column), 2 figures, 2 table

On the Mass Eigenstate Composition of the 8B Neutrinos from the Sun

The present data of gallium experiments provide indirectly the only experimental limit on the fraction of $\nu_2$ mass eigenstate for the $^8$B neutrinos from the Sun. However, if to use the experimental data alone, the fraction of $\nu_2$ and, consequently, $sin^2\theta_{sol}$ still is allowed to be varied within a rather broad range. The further experimental efforts are needed to clear this point.Comment: 13 pages, 1 figure, 1 table. Corrected version, published in JCAP04(2007)00

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 $\omega$ is close to the Josephson plasma frequency $\omega_J$.Comment: 9 pages, 7 figure

Brane Configurations for Nonsupersymmetric Meta-Stable Vacua in SQCD with Adjoint Matter

We present the configurations of intersecting branes in type IIA string theory corresponding to the meta-stable supersymmetry breaking vacua(hep-th/0608063) in the four-dimensional N=1 supersymmetric Yang-Mills theory coupled massive flavors with adjoint matter where the superpotential has three deformed terms.Comment: 15pp, 3 figures; The last two sentences in page 7 corrected; The last figure added;improved pages 10 and 11;figures corrected;the references to colors improved in the text and to appear in CQ