This PDF file contains the front matter associated with SPIE Proceedings Volume 6976, including the Title Page, Copyright information, Table of Contents, Introduction (if any), and the Conference Committee listing.

We are developing solid-state quantum repeaters for long-distance, secure quantum communication networks. These repeaters will combine long-range quantum entanglement, produced by optical measurements, with local few-qubit quantum processing and storage nodes. So far we have demonstrated all the key elements of the local quantum processors using nitrogen-vacancy (NV) color centers in diamond. These include multi-qubit entanglement, long storage times, and robustness against multiple re-initialization steps. Significantly, all these local operations were demonstrated at room temperature. Finally, we estimate that single shot readout should be achievable with optical plasmon wire coupling which would open the door to room-temperature few-qubit quantum computers.

Interference patterns produced by binomially splitting atom states in a double well optical lattice can be used to probe many important properties of this system, including double well tilt (and tilt inhomogeneities), the on-site interaction energy U, atom number distribution across the lattice, vibrational excitation, and lattice state coherence, making atom interferometry a powerful tool to analyze and characterize the structure and states of optical lattice systems, an essential task if they are to realize their potential for quantum information and for a variety of other proposed uses.

There is increasing interest in development of high speed, low noise and readily fieldable near infrared (NIR) single photon detectors. InGaAs/InP Avalanche photodiodes (APD) operated in Geiger mode (GM) are a leading choice for NIR due to their preeminence in optical networking. After-pulsing is, however, a primary challenge to operating InGaAs/InP single photon detectors at high frequencies1. After-pulsing is the effect of charge being released from traps that trigger false ("dark") counts. To overcome this problem, hold-off times between detection windows are used to allow the traps to discharge to suppress after-pulsing. The hold-off time represents, however, an upper limit on detection frequency that shows degradation beginning at frequencies of ~100 kHz in InGaAs/InP. Alternatively, germanium (Ge) single photon avalanche photodiodes (SPAD) have been reported to have more than an order of magnitude smaller charge trap densities than InGaAs/InP SPADs², which allowed them to be successfully operated with passive quenching² (i.e., no gated hold off times necessary), which is not possible with InGaAs/InP SPADs, indicating a much weaker dark count dependence on hold-off time consistent with fewer charge traps. Despite these encouraging results suggesting a possible higher operating frequency limit for Ge SPADs, little has been reported on Ge SPAD performance at high frequencies presumably because previous work with Ge SPADs has been discouraged by a strong demand to work at 1550 nm. NIR SPADs require cooling, which in the case of Ge SPADs dramatically reduces the quantum efficiency of the Ge at 1550 nm. Recently, however, advantages to working at 1310 nm have been suggested which combined with a need to increase quantum bit rates for quantum key distribution (QKD) motivates examination of Ge detectors performance at very high detection rates where InGaAs/InP does not perform as well. Presented in this paper are measurements of a commercially available Ge APD operated at relatively short GM hold-off times to examine whether there are potential advantages to using Ge for 1310 nm single photon detection. A weaker after-pulsing dependence on frequency is observed offering initial indications of the potential that Ge APDs might provide better high frequency performance.

We note the separation of a quantum description of an experiment into a statement of results (as probabilities) and an explanation of these results (in terms of linear operators). The inverse problem of choosing an explanation to fit given results is analyzed, leading to the conclusion that any quantum description comes as an element of a family of related descriptions, entailing multiple statements of results and multiple explanations. Facing this multiplicity opens avenues for exploration and consequences that are only beginning to be explored. Among the consequences are these: (1) statements of results impose topologies on control parameters, without resort to any quantum explanation; (2) an endless source of distinct explanations forces an open cycle of exploration and description bringing more and more control parameters into play, and (3) ambiguity of description is essential to the concept of invariance in physics.

The measurement of discrete quantum systems is a vital ingredient for quantum information processors. These systems, being fragile in nature, are characterized by a perturbation or collapse of their states whenever they are measured due to measurement-induced decoherence. We propose a quantum measurement model that allows for the extraction of information from any superposed quantum system without inducing a total collapse. The methodology used involves the coupling of a quantum probe through suitable interactions that create a partial entanglement between probe and quantum system. This entanglement in turn transfers information about the quantum system to the probe. Therefore, by making measurements on the probe rather than the superposed quantum system itself, we avert a total collapse to the quantum system.

In this paper, we consider the control of two qubit systems in the presence of a weak measurement. In particular we consider how Hamiltonian feedback can be applied to two qubit systems, both in the case where only one qubit is measured, and in the case where a joint measurement is made of both qubits. We consider how the rate of entanglement can be increased by using a joint measurement and feedback, and also how information can be gathered about one qubit by measuring the other.

We define quantum state disturbance in terms of Hilbert-Schmidt (HS) distance, finding according to this definition that measurements and unitary operations drive qubit states along straight lines and circles, respectively, in HS geometry. We establish conditions for additive disturbance; the straigh-line signature of quantum measurement is a direct consequence of this additivity. Also, state disturbance defined by HS distance is contrapuntally related to information gain measured by state discrimination probability. We use these quantifiers of state disturbance and information gain to elaborate the trade-off between the two. Explicitly identified in this trade-off between information gain and state disturbance is the mechanism-the measurement strength-that mediates the trade-off.

Decoherence of phases and dissipation of amplitudes can lead to loss of entanglement between two systems. In particular, an initially set-up entanglement of two qubits can end after a finite time in "sudden death". We show how local, unitary actions by the individual qubits can change this fate. In particular, the sudden death can even be averted all together.

The objective of this paper is to give experimentalists a quantum manual for implementing the Aharonov-Jones- Landau algorithm on an architecture of their choice. In particular, we explicitly apply this algorithm to a number of knot examples.

In this work, we study methods of entropy and relative entropy estimation for classical and quantum information sources. We show that algorithms and methods for classical entropy estimation can be effectively used in constructing algorithms for quantum entropy estimation. Specifically, we look at the entropy estimation for a broad class of stationary ergodic processes and obtain important bounds on estimator's variance and mathematical expectation as well as analyze their asymptotic behavior.

We study representations of the braid group to SU(2) and their relationships with topological quantum computation.

A heuristic mapping onto links and knots of Feynman diagrams in quantum electrodynamics at infinitesimal distances is investigated. This model map is formulated by treating the asymptotic photon propagator as composite electron and positron propagators, and exploiting Feynman's picture of positrons as electrons moving backward in time. The mapping is applied to the calculation in Feynman gauge of the divergent part of the inverse charge renormalization constant to sixth order in the bare charge of the electron as an illustration of Kreimer's classification of the divergent part of Feynman diagrams in terms of transcendental numbers and knots. In particular, I elucidate the mapping of a vacuum polarization graph with two crossed photo propagators onto the trefoil knot.

Three possible quantum algorithms, for the computation of the Bollobás-Riordan-Tutte polynomial of a given ribbon graph, are presented and discussed. The first possible algorithm is based on the spanning quasi-trees expansion for generalized Tutte polynomials of generalized graphs and on a quantum version of the Binary Decision Diagram (BDD) for quasi-trees . The second possible algorithm is based on the relation between the Kauffman bracket and the Tutte polynomial; and with an application of the recently introduced Aharonov-Arad-Eban-Landau quantum algorithm. The third possible algorithm is based on the relation between the HOMFLY polynomial and the Tutte polynomial; and with an application of the Wocjan-Yard quantum algorithm. It is claimed that these possible algorithms may be more efficient that the best known classical algorithms. These three algorithms may have interesting applications in computer science at general or in computational biology and bio-informatics in particular. A line for future research based on the categorification project is mentioned.

We introduce the concept of memory of an instrument into quantum mechanics. The connection between quantum memory and contextuality arises via the lack of the Markov property of instrumentation. Also, a further connection is made between memory and gauge transformations that arises in the definition of distance relative to measurement.

We have establish a more rigorous formulation of the AV-formula by illustrating how it can be derived from the Projection Theorem. This connection with the Projection Theorem enables us to establish an additional formula as well as show how to calculate the higher powers of the observable in terms of the formulas for Â|Ψ⟩ and Â|Ψ⊥⟩. Additionally discussed the relevance of the expression to weak values from the formulas for a post selection state |ζ⟩.

The ground state wave function for a Bose Einstein condensate is well described by the Gross-Pitaevskii equation. A Type-II quantum algorithm is devised that is ideally parallelized even on a classical computer. Only 2 qubits are required per spatial node. With unitary local collisions, streaming of entangled states and a spatially inhomogeneous unitary gauge rotation one recovers the Gross-Pitaevskii equation. Quantum vortex reconnection is simulated - even without any viscosity or resistivity (which are needed in classical vortex reconnection).

It is often believed that quantum entanglement plays an important role in the speed-up of quantum algorithms. In addition, a few research groups have found that Majorization behavior may also play an important role in some quantum algorithms. In some of our previous work we showed that for a simple spin 1/2 system, consisting of two or three qubits, the value of a Groverian entanglement (a rather useful measure of entanglement) varies inversely with the temperature. In practical terms this means that more iterations of the Grover's algorithm may be needed when a quantum computer is working at finite temperature. That is, the performance of a quantum algorithm suffers due to temperature-dependent changes on the density matrix of the system. Most recently, we have been interested in the behavior of Majorization for the same types of quantum system, and we are trying to determine the relationship between Groverian entanglement and Majorization at finite temperature. As Majorization entails the probability distribution arising out of the evolving quantum state from the probabilities of the final outcomes, our study will reveal how Majorization affects the evolution of Grover's algorithm at finite temperature.

In this paper we raise questions about the reality of computational quantum parallelism. Such questions are important because while quantum theory is rigorously established, the hypothesis that it supports a more powerful model of computation remains speculative. More specifically, we suggest the possibility that the seeming computational parallelism offered by quantum superpositions is actually effected by gate-level parallelism in the reversible implementation of the quantum operator. In other words, when the total number of logic operations is analyzed, quantum computing may not be more powerful than classical. This fact has significant public policy implications with regard to the relative levels of effort that are appropriate for the development of quantumparallel algorithms and associated hardware (i.e., qubit-based) versus quantum-scale classical hardware.

An expository review is given of recent developments in the differential geometry of quantum computation. Descriptions are given of the appropriate Riemannian geometry of the special unitary unimodular group in 2ⁿ- dimensions, including the choice of metric, connection, curvature tensor, and optimal geodesics for achieving minimal complexity quantum computations.

We review our schemes of subwavelength interferometric lighthography based on classical lights, and show the procedures to obtain arbitrary subwavelength 2D patterns by multiple exposures. The first scheme is by correlating wave vector and frequency in a narrow band, multiphoton detection process. The second scheme is by preparing the system in a position dependent trapping state via phase shifted standing wave patterns.