Efficient discrete-time simulations of continuous-time quantum query algorithms

The continuous-time query model is a variant of the discrete query model in which queries can be interleaved with known operations (called "driving operations") continuously in time. Interesting algorithms have been discovered in this model, such as an algorithm for evaluating nand trees more efficiently than any classical algorithm. Subsequent work has shown that there also exists an efficient algorithm for nand trees in the discrete query model; however, there is no efficient conversion known for continuous-time query algorithms for arbitrary problems. We show that any quantum algorithm in the continuous-time query model whose total query time is T can be simulated by a quantum algorithm in the discrete query model that makes O[T log(T) / log(log(T))] queries. This is the first upper bound that is independent of the driving operations (i.e., it holds even if the norm of the driving Hamiltonian is very large). A corollary is that any lower bound of T queries for a problem in the discrete-time query model immediately carries over to a lower bound of \Omega[T log(log(T))/log (T)] in the continuous-time query model.Comment: 12 pages, 6 fig

Quantum Circuit Placement

We study the problem of the practical realization of an abstract quantum circuit when executed on quantum hardware. By practical, we mean adapting the circuit to particulars of the physical environment which restricts/complicates the establishment of certain direct interactions between qubits. This is a quantum version of the classical circuit placement problem. We study the theoretical aspects of the problem and also present empirical results that match the best known solutions that have been developed by experimentalists. Finally, we discuss the efficiency of the approach and scalability of its implementation with regards to the future development of quantum hardware.Comment: 15 pages, 4 figures. Improved theory and software implementation, new experimental result

Interface bonding of a ferromagnetic/semiconductor junction : a photoemission study of Fe/ZnSe(001)

We have probed the interface of a ferromagnetic/semiconductor (FM/SC) heterojunction by a combined high resolution photoemission spectroscopy and x-ray photoelectron diffraction study. Fe/ZnSe(001) is considered as an example of a very low reactivity interface system and it expected to constitute large Tunnel Magnetoresistance devices. We focus on the interface atomic environment, on the microscopic processes of the interface formation and on the iron valence-band. We show that the Fe contact with ZnSe induces a chemical conversion of the ZnSe outermost atomic layers. The main driving force that induces this rearrangement is the requirement for a stable Fe-Se bonding at the interface and a Se monolayer that floats at the Fe growth front. The released Zn atoms are incorporated in substitution in the Fe lattice position. This formation process is independent of the ZnSe surface termination (Zn or Se). The Fe valence-band evolution indicates that the d-states at the Fermi level show up even at submonolayer Fe coverage but that the Fe bulk character is only recovered above 10 monolayers. Indeed, the Fe 1-band states, theoretically predicted to dominate the tunneling conductance of Fe/ZnSe/Fe junctions, are strongly modified at the FM/SC interface.Comment: 23 pages, 5 figures, submitted to Physical review

Independent sets of maximum weight in apple-free graphs

We present the first polynomial-time algorithm to solve the maximum weight independent set problem for apple-free graphs, which is a common generalization of several important classes where the problem can be solved efficiently, such as claw-free graphs, chordal graphs, and cographs. Our solution is based on a combination of two algorithmic techniques (modular decomposition and decomposition by clique separators) and a deep combinatorial analysis of the structure of apple-free graphs. Our algorithm is robust in the sense that it does not require the input graph G to be apple-free; the algorithm either finds an independent set of maximum weight in G or reports that G is not apple-free

Resonant tunneling magnetoresistance in epitaxial metal-semiconductor heterostructures

We report on resonant tunneling magnetoresistance via localized states through a ZnSe semiconducting barrier which can reverse the sign of the effective spin polarization of tunneling electrons. Experiments performed on Fe/ZnSe/Fe planar junctions have shown that positive, negative or even its sign-reversible magnetoresistance can be obtained, depending on the bias voltage, the energy of localized states in the ZnSe barrier and spatial symmetry. The averaging of conduction over all localized states in a junction under resonant condition is strongly detrimental to the magnetoresistance

Approximating Fractional Time Quantum Evolution

An algorithm is presented for approximating arbitrary powers of a black box unitary operation, $\mathcal{U}^t$, where $t$ is a real number, and $\mathcal{U}$ is a black box implementing an unknown unitary. The complexity of this algorithm is calculated in terms of the number of calls to the black box, the errors in the approximation, and a certain `gap' parameter. For general $\mathcal{U}$ and large $t$, one should apply $\mathcal{U}$ a total of $\lfloor t \rfloor$ times followed by our procedure for approximating the fractional power $\mathcal{U}^{t-\lfloor t \rfloor}$. An example is also given where for large integers $t$ this method is more efficient than direct application of $t$ copies of $\mathcal{U}$. Further applications and related algorithms are also discussed.Comment: 13 pages, 2 figure

Study of the performance of a large scale water-Cherenkov detector (MEMPHYS)

MEMPHYS (MEgaton Mass PHYSics) is a proposed large-scale water Cherenkov experiment to be performed deep underground. It is dedicated to nucleon decay searches, neutrinos from supernovae, solar and atmospheric neutrinos, as well as neutrinos from a future Super-Beam or Beta-Beam to measure the CP violating phase in the leptonic sector and the mass hierarchy. A full simulation of the detector has been performed to evaluate its performance for beam physics. The results are given in terms of "Migration Matrices" of reconstructed versus true neutrino energy, taking into account all the experimental effects.Comment: Updated after JCAP's referee's comment

Future large-scale water-Cherenkov detector

MEMPHYS (MEgaton Mass PHYSics) is a proposed large-scale water-Cherenkov experiment to be performed deep underground. It is dedicated to nucleon decay searches and the detection of neutrinos from supernovae, solar, and atmospheric neutrinos, as well as neutrinos from a future beam to measure the CP violating phase in the leptonic sector and the mass hierarchy. This paper provides an overview of the latest studies on the expected performance of MEMPHYS in view of detailed estimates of its physics reach, mainly concerning neutrino beams