A Hybrid Quantum Encoding Algorithm of Vector Quantization for Image Compression

Many classical encoding algorithms of Vector Quantization (VQ) of image compression that can obtain global optimal solution have computational complexity O(N). A pure quantum VQ encoding algorithm with probability of success near 100% has been proposed, that performs operations 45sqrt(N) times approximately. In this paper, a hybrid quantum VQ encoding algorithm between classical method and quantum algorithm is presented. The number of its operations is less than sqrt(N) for most images, and it is more efficient than the pure quantum algorithm. Key Words: Vector Quantization, Grover's Algorithm, Image Compression, Quantum AlgorithmComment: Modify on June 21. 10pages, 3 figure

Black Holes in Six-dimensional Conformal Gravity

We study conformally-invariant theories of gravity in six dimensions. In four dimensions, there is a unique such theory that is polynomial in the curvature and its derivatives, namely Weyl-squared, and furthermore all solutions of Einstein gravity are also solutions of the conformal theory. By contrast, in six dimensions there are three independent conformally-invariant polynomial terms one could consider. There is a unique linear combination (up to overall scale) for which Einstein metrics are also solutions, and this specific theory forms the focus of our attention in this paper. We reduce the equations of motion for the most general spherically-symmetric black hole to a single 5th-order differential equation. We obtain the general solution in the form of an infinite series, characterised by 5 independent parameters, and we show how a finite 3-parameter truncation reduces to the already known Schwarzschild-AdS metric and its conformal scaling. We derive general results for the thermodynamics and the first law for the full 5-parameter solutions. We also investigate solutions in extended theories coupled to conformally-invariant matter, and in addition we derive some general results for conserved charges in cubic-curvature theories in arbitrary dimensions.Comment: 28 pages. References adde

An ω\omega Deformation of Gauged STU Supergravity

Four-dimensional ${\cal N}=2$ gauged STU supergravity is a consistent truncation of the standard ${\cal N}=8$ gauged $SO(8)$ supergravity in which just the four $U(1)$ gauge fields in the Cartan subgroup of $SO(8)$ are retained. One of these is the graviphoton in the ${\cal N}=2$ supergravity multiplet and the other three lie in three vector multiplets. In this paper we carry out the analogous consistent truncation of the newly-discovered family of $\omega$-deformed ${\cal N}=8$ gauged $SO(8)$ supergravities, thereby obtaining a family of $\omega$-deformed STU gauged supergravities. Unlike in some other truncations of the deformed ${\cal N}=8$ supergravity that have been considered, here the scalar potential of the deformed STU theory is independent of the $\omega$ parameter. However, it enters in the scalar couplings in the gauge-field kinetic terms, and it is non-trivial because of the minimal couplings of the fermion fields to the gauge potentials. We discuss the supersymmetry transformation rules in the $\omega$-deformed supergravities, and present some examples of black hole solutions.Comment: 31 pages. Derivation of the range of \omega corrected; discussion of supersymmetry of solutions extended, and a reference adde

AdS Dyonic Black Hole and its Thermodynamics

We obtain spherically-symmetric and $\R^2$-symmetric dyonic black holes that are asymptotic to anti-de Sitter space-time (AdS), which are solutions in maximal gauged four-dimensional supergravity, with just one of the U(1) fields carrying both the electric and magnetic charges $(Q,P)$. We study the thermodynamics, and find that the usually-expected first law does not hold unless P=0, Q=0 or P=Q. For general values of the charges, we find that the first law requires a modification with a new pair of thermodynamic conjugate variables. We show that they describe the scalar hair that breaks some of the asymptotic AdS symmetries.Comment: 21 pages, typos corrected, discussion of Euclidean action adde

Correlation Functions in ω\omega-Deformed N=6 Supergravity

Gauged N=8 supergravity in four dimensions is now known to admit a deformation characterized by a real parameter $\omega$ lying in the interval $0\le\omega\le \pi/8$. We analyse the fluctuations about its anti-de Sitter vacuum, and show that the full N=8 supersymmetry can be maintained by the boundary conditions only for $\omega=0$. For non-vanishing $\omega$, and requiring that there be no propagating spin s>1 fields on the boundary, we show that N=3 is the maximum degree of supersymmetry that can be preserved by the boundary conditions. We then construct in detail the consistent truncation of the N=8 theory to give $\omega$-deformed SO(6) gauged N=6 supergravity, again with $\omega$ in the range $0\le\omega\le \pi/8$. We show that this theory admits fully N=6 supersymmetry-preserving boundary conditions not only for $\omega=0$, but also for $\omega=\pi/8$. These two theories are related by a U(1) electric-magnetic duality. We observe that the only three-point functions that depend on $\omega$ involve the coupling of an SO(6) gauge field with the U(1) gauge field and a scalar or pseudo-scalar field. We compute these correlation functions and compare them with those of the undeformed N=6 theory. We find that the correlation functions in the $\omega=\pi/8$ theory holographically correspond to amplitudes in the U(N)_k x U(N)_{-k} ABJM model in which the U(1) Noether current is replaced by a dynamical U(1) gauge field. We also show that the $\omega$-deformed N=6 gauged supergravities can be obtained via consistent reductions from the eleven-dimensional or ten-dimensional type IIA supergravities.Comment: 38 pages, one figur

Electrolysis-based diaphragm actuators

This work presents a new electrolysis-based microelectromechanical systems (MEMS) diaphragm actuator. Electrolysis is a technique for converting electrical energy to pneumatic energy. Theoretically electrolysis can achieve a strain of 136 000% and is capable of generating a pressure above 200 MPa. Electrolysis actuators require modest electrical power and produce minimal heat. Due to the large volume expansion obtained via electrolysis, small actuators can create a large force. Up to 100 µm of movement was achieved by a 3 mm diaphragm. The actuator operates at room temperature and has a latching and reversing capability