Daniel S. Abrams, Colin P. Williams
quantum algorithms for numerical integrals and
Computational Synthesis of any N-Qubit Pure or Mixed State (2008)
Future quantum information processing devices will require the use of exotic quantum states, such as specially crafted entangled states, to achieve certain desired computations on demand. Thus far,...
Linear Optics and Projective Measurements for Fun and Profit (2008)
Pieter Kok, Hwang Lee, Colin P. Williams, Jonathan P. Dowling
The technique of projective measurements in linear optics can provide apparent, efficient nonlinear interaction between photons, which is technically problematic otherwise. We present an application...
Quantum Recurrent Networks for Simulating Stochastic Processes (2008)
Michail Zak, Colin P. Williams
Abstract. We introduce the concept of quantum recurrent networks by incorporating classical feedback loops into conventional quantum networks. We show that the dynamical evolution of such networks,...
Non-unitary probabilistic quantum computing (2006)
Gingrich, Robert M., Williams, Colin P.
We present a method for designing quantum circuits that perform non-unitary quantum computations on n-qubit states probabilistically, and give analytic expressions for the success probability and...
NASA/JPL
Random matrix model of adiabatic quantum computing (2005)
Mitchell, David R., Adami, Christoph, Lue, Waynn, Williams, Colin P.
We present an analysis of the quantum adiabatic algorithm for solving hard instances of 3-SAT (an NP-complete problem) in terms of random matrix theory (RMT). We determine the global regularity of...
Zak, Michail, Williams, Colin P.
The capacity of classical neurocomputers is limited by the number of classical degrees of freedom which is roughly proportional to the size of the computer. By Contrast, a Hypothetical quantum...
A Random Matrix Model of Adiabatic Quantum Computing (2004)
Mitchell, David R., Adami, Christoph, Lue, Waynn, Williams, Colin P.
We present an analysis of the quantum adiabatic algorithm for solving hard instances of 3-SAT (an NP-complete problem) in terms of Random Matrix Theory (RMT). We determine the global regularity of...
Realization of a General Three-Qubit Quantum Gate (2004)
Vatan, Farrokh, Williams, Colin P.
We prove that a generic three-qubit quantum logic gate can be implemented using at most 98 one-qubit rotations about the $y$- and $z$-axes and 40 CNOT gates, beating an earlier bound of 64 CNOT gates.
From Linear Optical Quantum Computing to Heisenberg-Limited Interferometry (2003)
Lee, Hwang, Kok, Pieter, Williams, Colin P., Dowling, Jonathan P.
The working principles of linear optical quantum computing are based on photodetection, namely, projective measurements. The use of photodetection can provide efficient nonlinear interactions between...
Non-Unitary Probabilistic Quantum Computing (2003)
Robert M. Gingrich, Colin P. Williams
We present a method for designing quantum circuits that perform non-unitary quantum computations on n-quhit states prohabilistically, and give analytic expressions for the suc-cess probability and...
Practical quantum repeaters with linear optics and double-photon guns (2002)
Kok, Pieter, Williams, Colin P., Dowling, Jonathan P.
We show how to create practical, efficient, quantum repeaters, employing double-photon guns, for long-distance optical quantum communication. The guns create polarization-entangled photon pairs on...
Quantum interferometric optical lithography:towards arbitrary two-dimensional patterns (2000)
Kok, Pieter, Boto, Agedi N., Abrams, Daniel S., Williams, Colin P., Braunstein, Samuel L., Dowling, Jonathan P.
As demonstrated by Boto et al. [Phys. Rev. Lett. 85, 2733 (2000)], quantum lithography offers an increase in resolution below the diffraction limit. Here, we generalize this procedure in order to...
Quantum Clock Synchronization Based on Shared Prior Entanglement (2000)
Jozsa, Richard, Abrams, Daniel S., Dowling, Jonathan P., Williams, Colin P.
We demonstrate that two spatially separated parties (Alice and Bob) can utilize shared prior quantum entanglement, and classical communications, to establish a synchronized pair of atomic clocks. In...
Boto, Agedi N., Kok, Pieter, Abrams, Daniel S., Braunstein, Samuel L., Williams, Colin P., Dowling, Jonathan P.
Classical, interferometric, optical lithography is diffraction limited to writing features of a size lambda/2 or greater, where lambda is the optical wavelength. Using nonclassical photon number...
Fast quantum algorithms for numerical integrals and stochastic processes (1999)
Abrams, Daniel S., Williams, Colin P.
We discuss quantum algorithms that calculate numerical integrals and descriptive statistics of stochastic processes. With either of two distinct approaches, one obtains an exponential speed increase...
Maxwell Duality, Lorentz Invariance, and Topological Phase (1999)
Dowling, Jonathan P., Williams, Colin P., Franson, J. D.
We discuss the Maxwell electromagnetic duality relations between the Aharonov-Bohm, Aharonov-Casher, and He-McKellar-Wilkens topological phases, which allows a unified description of all three...
Generalized Quantum Search with Parallelism (1999)
Gingrich, Robert, Williams, Colin P., Cerf, Nicolas
We generalize Grover's unstructured quantum search algorithm to enable it to use an arbitrary starting superposition and an arbitrary unitary matrix simultaneously. We derive an exact formula for the...
Automated Design of Quantum Circuits (1999)
Abstract. In order to design a quantum circuit that performs a desired quantum computation, it is necessary to find a decomposition of the unitary matrix that represents that computation in terms of...
Quantum Wavelet Transforms: Fast Algorithms and Complete Circuits (1998)
Fijany, Amir, Williams, Colin P.
The quantum Fourier transform (QFT), a quantum analog of the classical Fourier transform, has been shown to be a powerful tool in developing quantum algorithms. However, in classical computing there...
Using Deep Structure to Locate Hard Problems (1992)
One usually writes A.I. programs to be used on a range of examples which, although similar in kind, differ in detail. This paper shows how to predict where, in a space of problem instances, the...
Model approximation via dimension reduction (1992)
Ulf Dieckmann, Colin P. Williams
In the initial stages of refining a mathematical model of a real-world dynamical system, one is often confronted with many more variables and coupled differential equations than one intuitively feels...