This PDF file contains the front matter associated with SPIE Proceedings Volume 7702, including the Title Page, Copyright information, Table of Contents, and the Conference Committee listing.

Quantum information theory is undergoing rapid development and recently there has been much progress in mapping out its relationship to low dimensional gravity, primarily through Chern-Simons topological quantum field theory and conformal field theory, with the prime application being topological quantum computation. Less attention has been paid to the relationship of quantum information theory to the long established and well tested theory of gravitational dynamics of 3+1 dimensional spacetime. Here we discuss this question in the weak field approximation of the 4-space metric tensor. The proposed approach considers a quantum algorithmic scheme suitable for simulating physical curved space dynamics that is traditionally described by the well known Einstein-Hilbert action. The quantum algorithmic approach builds upon Einstein's veirbein representation of gravity, which Einstein originally developed back in 1928 in his search for a unified field theory and, moreover, which is presently widely accepted as the preferred theoretical approach for representing dynamical relativistic Dirac fields in curved space. Although the proposed quantum algorithmic scheme is regular-lattice based it nevertheless recovers both the Einstein equation of motion as an effective field theory and invariance of the gravitational gauge field (i.e., the spin connection) with respect to Lorentz transformations as the local symmetry group in the low energy limit.

This paper gives a generalization of the AJL algorithm for quantum computation of the Jones polynomial to continuous ranges of values on the unit circle for the Jones parameter. We show that the Kauffman-Lomonaco 3-strand algorithm for the Jones polynomial is a special case of this generalization of the AJL algorithm.

Two-photon quantum imaging has so far demonstrated two peculiar features: (1) reproducing nonlocal images in "ghost" imaging type experiments and (2) improving imaging spatial resolution beyond the classical limit in quantum lithography type measurements. This article reports an experimental study on non-degenerate, two-color, biphoton ghost imaging which reproduced a nonlocal ghost image and simultaneously enhanced the angular resolving power of imaging by means of a greater field of view or by means of a greater imaging amplification compared with that of classical imaging.

Recent developments in the differential geometry of quantum computation are exposited. The quantum evolution is described in terms of the special unitary group of n-qubit unitary operators with unit determinant. The group manifold is taken to be Riemannian. In the present work, the lifted Jacobi equation and geodesic derivative are reviewed. This is applicable to investigations of conjugate points and the global characteristics of geodesic paths in the group manifold, and the determination of optimal quantum circuits for carrying out a quantum computation.

Recently a quantum algorithm for the Jones polynomial of virtual links was proposed by Kauffman and Dye via the implementation of the virtual braid group in anyonic topological quantum computation when the virtual crossings are considered as generalized swap gates. Also recently, a mathematical method for the computation of the Jones polynomial of a given virtual link in terms of the relative Tuttle polynomial of its face (Tait) graph with some suitable variable substitutions was proposed by Diao and Hetyei. The method of Diao and Hetyei is offered as an alternative to the ribbon graph approach according to which the Tutte polynomial of a given virtual link is computed in terms of the Bollobás- Riordan polynomial of the corresponding ribbon graph. The method of Diao and Hetyei can be considered as an extension of the celebrated Thistlethwaite theorem according to which invariant polynomials for knots and links are derived from invariant polynomials for graphs. Starting from these ideas we propose a quantum algorithm for the Jones polynomial of a given virtual link in terms of the generalized Tutte polynomials by exploiting the Thistlethwaite theorem and the Kauffman algorithm . Our method is claimed as the quantum version of the Diao-Hetyei method. Possible supersymmetric implementations of our algortihm are discussed jointly with its formulations using topological quantum lambda calculus.

A quantum lattice gas algorithm, based on interleaved unitary collide-stream operators, is used to study quantum turbulence of the ground state wave function of a Bose-Einstein condensate (BEC). The Gross-Pitaevskii equation is a Hamiltonian system for a compressible, inviscid quantum fluid. From simulations on a 5760³ grid it was observed that a multi-cascade existed for the incompressible kinetic energy spectrum with universal features: the large spatial scales exhibit a classical Kolmogorov k ^-5/3 spectrum while the very small scales exhibit a quantum Kelvin wave cascade k^-3 spectrum. Under certain conditions one can explicitly determine the Poincare recurrence of initial conditions as well as the intermittent destruction of the Kelvin wave cascade.

In the Riemannian geometry of quantum computation, the quantum evolution is described in terms of the special unitary group of n-qubit unitary operators with unit determinant. To elaborate on some aspects of the methodology, the generic Jacobi equation and lifted Jacobi equation, together with solutions on the group manifold, are explicitly derived. This is important for investigations of the global characteristics of geodesic paths in the group manifold, and the determination of optimal quantum circuits for carrying out a quantum computation.

Spinor Bose Einstein Condensates are intriguing because of their vast range of different topological vortices. These states occur when a BEC gas is trapped in an optical lattice rather than in a magnetic well (which would result in scalar BEC vortices). A spinor BEC states also occur in a quantum gas when several hyperfine states of the atom co-exist in the same trap. A unitary quantum lattice algorithm that is ideally parallelized to all available processors is used to solve the evolution of non-eigenstate Skyrmions in a coupled BEC system. The incompressible kinetic energy spectrum of the inner quantum vortex ring core rapidly deviates from the k^-3 spectrum found in the evolution of scalar BECs.

We propose the use of single-photon two-qubit quantum logic to physically simulate the optimal individual attack on Bennett-Brassard 1984 quantum key distribution protocol.The experimental setup does not require a quantum memory due to the physical simulation character of the proposal.

We present the characteristic performance of quantum key distribution over various fiber optic network topologies. The networks include the RING, BUS, and STAR. Quantum bit-error rate is determined for each network as function of number of users, and transmission distance. The trade off between number of users and transmission distance is presented. The model is compared with experiment results for bus network architecture for quantum key distribution.

Since, in general, non-orthogonal states cannot be cloned, any eavesdropping attempt in a Quantum Communication scheme using non-orthogonal states as carriers of information introduces some errors in the transmission, leading to the possibility of detecting the spy. Usually, orthogonal states are not used in Quantum Cryptography schemes since they can be faithfully cloned without altering the transmitted data. Nevertheless, L. Goldberg and L. Vaidman [Phys. Rev. Lett. 75 (7), pp. 12391243, 1995] proposed a protocol in which, even if the data exchange is realized using two orthogonal states, any attempt to eavesdrop is detectable by the legal users. In this scheme the orthogonal states are superpositions of two localized wave packets which travel along separate channels, i.e. two different paths inside a balanced Mach-Zehnder interferometer. Here we present an experiment realizing this scheme.

In quantum cryptography, the key can be directly distributed to the communicating parties through the communication channel. The security is guaranteed by the quantum properties of the channel. However, the transmitted key may contain errors due to the noise of the channel. Key integrity verification is an indispensable step in quantum cryptography and becomes an important problem in higher speed systems. Computing only one hash value for the key string does not provide an effective solution as it may lead to dropping all the bits once the hash values on both sides do not agree. In this paper, we introduce a new idea of using the technique of combinatorial group testing, which seems to be an unrelated topic, to design a scheme to identify the error bits to avoid dropping all the bits. Our scheme can precisely locate the error bits if the number of error bits is within the maximum set by the scheme while the overhead is insignificant based on our experiments (additional bits: 0.1% of the key; time for computing the hash values: 16ms; verification time: 22 ms). Also, even if the number of error bits is higher than the maximum set by the scheme, only some correct bits may be misclassified as error bits but not the vice versa. The results show that we can still keep the majority of the correct bits (e.g. the bits discarded due to misclassification is only 5% of the whole string even if the number of error bits is 10 times of the maximum).

The classical communication capacities of quantum Pauli channels with memory are known to exhibit a transition effect. We revisit this phenomenon from the standpoint of the functionally analogous task of Pauli channel memory identification. We treat the complete class of Pauli channels with memory and determine the maximum quantum Fisher information achievable both with pure separable channel probe states and with maximally entangled bipartite probe states. A comparison of these Fisher informations reveals four distinct classes of Pauli channels and shows that only those channels that exceed a certain parametric threshold exhibit a transition effect. For those Pauli channels that exhibit this effect, the memory threshold at which it occurs has a simple analytic expression.

Spontaneous downconversion yields photons for Quantum-Optical-Gate development though their generation is probabilistic. Optimized efficiency requires control over the spectral wavefunction, generally achieved via spectral filtering which sacrifices most downconverted photons. Selecting crystal parameters to address the issue has been demonstrated, but no natural media enable this for 800 nm applications with optimal detection. Synthesizing parameters with super-lattices of known crystals was also analyzed but two-crystal experiments were insufficient to exploit it. Prototype twelve-crystal-assemblies have now been fabricated and the first results are reported here. We review implications for further work and discuss how methods described here enhance efficiency in applications of entangled photons requiring multi-crystal sources, such as cluster states, entanglement swapping, and teleportation.

With the goal in mind of designing radars, interferometers and other sensors based on quantum entanglement the virtues of N00N states, plain M and M states (PMMSs) and linear combinations of M and M states (LCMMS) are considered. A derivation of the closed form expression for the detection operator that is optimal subject to constraints is provided. The raising and lowering properties of the detection operator and its square are developed. The expectations of the optimal detection operator and its square are derived. The expression for the visibility, the maximum expectation of the optimal detection operator, is developed. From the expectation of the square of the detection operator and the visibility, the phase error and the minimum phase error for the detection operator are derived. The optimal resolution for the maximum visibility and minimum phase error are found. For the visibility, comparisons between PMMSs, LCMMS and N00N states are provided. For the minimum phase error comparisons between LCMMS, PMMSs, N00N states, separate photon states (SPSs), the shot noise limit (SNL), and the Heisenberg limit (HL) are provided. A representative collection of computational results illustrating the superiority of LCMMS when compared to PMMSs and N00N states is given. It is found for a resolution 12 times the classical result LCMMS has visibility 11 times that of N00N states and four times that of PMMSs. For the same case, the minimum phase error for LCMMS is 10.7 times smaller than that of PMMS and 29.7 times smaller than that of N00N states.

The highly entangled four qubit cluster state can be used to perform an arbitrary single logical qubit rotation via the techniques of measurement-based quantum computation. In this paper, we explore the relationship between the entanglement in the cluster state and the ability of the state to accurately perform the desired logical rotation. This has important experimental ramifications as realistic cluster state experiments will always be subject to decoherence. We also note the exhibition of entanglement sudden death (ESD) and ask how severely its onset affects the utilization of the cluster state as a means of implementing the arbitrary single logical qubit rotation.

The intrinsic quantum properties shown in electrons and atoms allow us to explode a non-classic field for the information management. Through the Stern-Gerlach device (SG), the measurement of spin via a momentum is obtained with associated probabilities due to quantum principles. This paper studies the behavior of a three-particle coupled quantum system in which a spin particle is measured by the SG apparatus while the others are not. The response of the spin-1/2 uncharged particle because of the inhomogeneous magnetic field is also analyzed introducing as well non-linear variations of the magnetic field. The system solution will be determined by specials functions according to the variation field defined and three cases with Airy, Whittaker and Heun functions will be treated and supported by different simulations using symbolic computation with Maple.

Iqueye is a high speed astronomical photon counting device, tested at the ESO 3.5 m New Technology Telescope in La Silla (Chile). The optics splits the telescope pupil into four portions each feeding a Single Photon Avalanche Diode. A time-to-digital converter board time tags the pulses from the 4 channels, and the times sent to a storage device. The instrument is capable of running continuously up to a rate of 8 MHz, with an absolute rms accuracy better that 0.5 ns. The time is obtained by means of a rubidium clock referenced to UTC through the GPS signal. The paper describes the analysis performed on data taken on bright stars in order to perform 'quantum-like' measurements in the photon stream, namely the calculation of the second-order correlation functions g⁽²⁾(x,0) and g⁽²⁾(0,t). To this end, an ad hoc software correlator has been developed. Taking advantage of the pupil-splitting concept, the calculation of g(2)(x,0) has been made between the sub-apertures of the telescope, as a first step to verify the zero-baseline correlation coefficient in an Hanbury-Brown Twiss intensity interferometer [1]. Our experiment demonstrates the value of an Iqueye-like instrument applied to larger telescopes, like the four 8 m VLTs or the two 10m Keck telescopes, and even more the sub-pupils of the future 42 m E-ELT for a novel exploitation of the photon stream from celestial objects.

We exploit the remarkable phenomena of interference in physics together with aspects of number theory in order to factorize large numbers. In particular, the introduction of continuous truncated exponential sums (CTES) allows us to develop a new algorithm for factoring several large numbers by a single measurement of the periodicity of a CTES interferogram. Such an interferogram can be obtained by measuring the interference pattern produced by polychromatic light interacting with an interferometer with variable optical paths.

We present an experimental realization of a low-noise, phase-insensitive optical amplifier using a four-wave mixing interaction in hot Rb vapor. Performance near the quantum limit for a range of amplifier gains, including near unity, can be achieved. Such low-noise amplifiers are essential for so-called quantum cloning machines and are useful in quantum information networks and protocols. We demonstrate that amplification and ''cloning'' of one half of a two-mode squeezed state is possible while preserving entanglement. The inseparability criterion between the two original modes remains satisfied for small to large gains, while the EPR criterion is satisfied for a smaller range. This amplification of quantum correlations paves the way for optimal cloning of a bipartite entangled state.

Ideas from classical signal analysis and Khinchin's theorem suggest a different way to think about signals and quantum mechanics so that probability and noise are both treated in the same manner. This suggest connections between ideas of receivers and the Von Neuman theory of measurement. Weak values are connected to these ideas

The externally applied bias operation of linear mode avalanche photodetectors (APDs) is extended and compared to single photon avalanche photodetectors (SPADs). The minimum bias required for linear operation is calculated using the effective voltage field in the photodetector through Mach-Zehnder modulator (MZM) interference which allows for quantifiable incident peak and dc optical powers. This mode of operation allows for a quantifiable minimum bias on the diode, may enable a dualuse for single photon detectors at higher optical powers, and ensures RF signal conversion.

Whether or not neuronal signal properties can engage 'non-trivial', i.e. functionally significant, quantum properties, is the subject of an ongoing debate. Here we provide evidence that quantum coherence dynamics can play a functional role in ion conduction mechanism with consequences on the shape and associative character of classical membrane signals. In particular, these new perspectives predict that a specific neuronal topology (e.g. the connectivity pattern of cortical columns in the primate brain) is less important and not really required to explain abilities in perception and sensory-motor integration. Instead, this evidence is suggestive for a decisive role of the number and functional segregation of ion channel proteins that can be engaged in a particular neuronal constellation. We provide evidence from comparative brain studies and estimates of computational capacity behind visual flight functions suggestive for a possible role of quantum computation in biological systems.

We present a compiler for programming quantum architectures based on the Quantum Random Access Machine (QRAM) model. The QRAM model consists of a classical subsystem responsible for generating the quantum operations that are executed on a quantum subsystem. The compiler can also be applied to trade studies for optimizing the reliability and latency of quantum programs and to determine the required error correction resources. We use the Bacon-Shor [9, 1, 3] quantum error correcting code as an example quantum program that can be processed and analyzed by the compiler.

In this paper, we study a reliable architecture of a quantum computer and a new instruction set and machine language for the architecture, which can improve the performance and reduce the cost of the quantum computing. We also try to address some key issues in detail in the software-driven universal quantum computers.

Numerical simulation results are presented which suggest that a class of non-adiabatic rapid passage sweeps first realized experimentally in 1991, and which give rise to controllable quantum interference effects observed using NMR in 2003, should be capable of implementing a universal set of quantum gates G_u that operate with high-fidelity. G_u consists of the Hadamard and NOT gates, together with variants of the phase, π/8, and controlled-phase gates. Sweep parameter values are provided which simulations indicate will produce the different gates in G_u, and for each gate, yield an operation with error probability P_e < 10^-4. The simulations suggest that the universal gate set produced by these rapid passage sweeps show promise as possible elements of a fault-tolerant scheme for quantum computing.

The use of topological phases for the manipulation of electron spins in GaAs quantum dots is a promising candidate for solid state quantum computation and non-charged based logic devices for projected post-CMOS technology. A single electron can be trapped and its spin can be manipulated by moving the quantum dot adiabatically in a closed loop (Berry effect) through the application of gate potentials. In this paper, we present numerical simulations and analytical expressions for the transition probability of electron spins in single electron devices for a quantum dot. Using analytical and numerical techniques, we calculate the Berry Phase for both nondegenerate and degenerate cases. We show that the spin orbit coupling in III-V type semiconductors will enhance the transition probability of the electron spin over pure Dresselhaus or pure Rashba cases considered separately. Considering these mechanisms separately however, is useful in that an exact solution exists as determined by the Feynman disentangling technique. For the most general cases where the solution of the propagator becomes non-trivial, we carry out the numerical simulations of such propagator.

Analysis of the brain as a physical system, that has the capacity of generating a display of every day observed experiences and contains some knowledge of the physical reality which stimulates those experiences, suggests the brain executes a self-measurement process described by quantum theory. Assuming physical reality is a universe of interacting self-measurement loops, we present a model of space as a field of cells executing such self-measurement activities. Empty space is the observable associated with the measurement of this field when the mass and charge density defining the material aspect of the cells satisfy the least action principle. Content is the observable associated with the measurement of the quantum wave function ψ interpreted as mass-charge displacements. The illusion of space and its content incorporated into cognitive biological systems is evidence of self-measurement activity that can be associated with quantum operations.

The known Hawk and Dove game is analyzed from quantum mechanics with another two possible behaviors, Bully and Retaliator. The formalism used in the development of the strategies is not Dirac's due to its complex implementation in Computer Algebra System (CAS) but the matrix analysis is proposed. Both are completely alike in the results given, so the matrix method used is not less efficient than Dirac's. The classical game with the four strategies is also described and compared. As results of the quantum game, are presented pay-offs matrixes for possible players, the density matrix and its relation to quantum information and communication. Applications such as finances and biology are also presented and proposed.