Quantum Circuits for General Multiqubit Gates

We consider a generic elementary gate sequence which is needed to implement a general quantum gate acting on n qubits -- a unitary transformation with 4^n degrees of freedom. For synthesizing the gate sequence, a method based on the so-called cosine-sine matrix decomposition is presented. The result is optimal in the number of elementary one-qubit gates, 4^n, and scales more favorably than the previously reported decompositions requiring 4^n-2^n+1 controlled NOT gates.Comment: 4 pages, 3 figure

Response functions of an artificial Anderson atom in the atomic limit

We consider the spin and pseudospin (charge) response functions of the exactly soluble Anderson atom model. We demonstrate, in particular, that a deviation from the magnetic Curie-law behaviour, appropriate for a free spin one-half, increases with increasing asymmetry and temperature. In general, oscillator strength is transferred from the spin degrees of freedom to the pseudospin modes. We also consider the negative-U Anderson atom and demonstrate that the pseudospin modes are the relevant low-energy excitations in this case. Especially, the roles of the spin and charge excitations are interchanged upon reversal of the intrasite Coulomb repulsion, U.Comment: 23 pages, 12 figures. Accepted for publication in J. Low Temp. Phy

Precessional motion of a vortex in a finite-temperature Bose-Einstein condensate

We study the precessing motion of a vortex in a Bose-Einstein condensate of atomic gases. In addition to the former zero-temperature studies, finite temperature systems are treated within the Popov and semiclassical approximations. Precessing vortices are discussed utilizing the rotating frame of reference. The relationship between the sign of the lowest excitation energy and the direction of precession is discussed in detail.Comment: 6 pages, 9 figures. More discussion in Sec.III. Reference is update

Anderson Model in a Superconductor: Φ\Phi-Derivable Theory

We introduce a new $\Phi$-derivable approach for the Anderson impurity model in a BCS superconductor. The regime of validity of this conserving theory extends well beyond that of the Hartree-Fock approximation. This is the first generalization of the U-perturbation theory to encompass a superconductor.Comment: 11 pages and 4 figures. Accepted for publication in Journal of Physics: Condensed Matter as a Letter to the Edito

Conoscopic interferometry of wafers for surface-acoustic wave devices

We show that in interpreting the conoscopic interference fringes, one should exercise care in employing approximate expressions which fail for certain crystal cuts. In this paper, we study 64°- and 128°-rotated Y-cut and Z-cut LiNbO3 wafers. We show that the error made in using the approximate formulae for the samples is more than 25% and that one has to use exact formulae in order to attain quantitative agreement with the experimental data.Peer reviewe

Quantum circuits with uniformly controlled one-qubit gates

Uniformly controlled one-qubit gates are quantum gates which can be represented as direct sums of two-dimensional unitary operators acting on a single qubit. We present a quantum gate array which implements any n-qubit gate of this type using at most 2^{n-1} - 1 controlled-NOT gates, 2^{n-1} one-qubit gates and a single diagonal n-qubit gate. The circuit is based on the so-called quantum multiplexor, for which we provide a modified construction. We illustrate the versatility of these gates by applying them to the decomposition of a general n-qubit gate and a local state preparation procedure. Moreover, we study their implementation using only nearest-neighbor gates. We give upper bounds for the one-qubit and controlled-NOT gate counts for all the aforementioned applications. In all four cases, the proposed circuit topologies either improve on or achieve the previously reported upper bounds for the gate counts. Thus, they provide the most efficient method for general gate decompositions currently known.Comment: 8 pages, 10 figures. v2 has simpler notation and sharpens some result

Realization of Arbitrary Gates in Holonomic Quantum Computation

Among the many proposals for the realization of a quantum computer, holonomic quantum computation (HQC) is distinguished from the rest in that it is geometrical in nature and thus expected to be robust against decoherence. Here we analyze the realization of various quantum gates by solving the inverse problem: Given a unitary matrix, we develop a formalism by which we find loops in the parameter space generating this matrix as a holonomy. We demonstrate for the first time that such a one-qubit gate as the Hadamard gate and such two-qubit gates as the CNOT gate, the SWAP gate and the discrete Fourier transformation can be obtained with a single loop.Comment: 8 pages, 6 figure