Related papers: More on Optical Holonomic Quantum Computer
We describe an approach to the quantization of (2+1)--dimensional gravity with topology R x T^2 and negative cosmological constant, which uses two quantum holonomy matrices satisfying a q--commutation relation. Solutions of diagonal and…
We prove that quantum computation is polynomially equivalent to classical probabilistic computation with an oracle for estimating the value of simple sums, quadratically signed weight enumerators. The problem of estimating these sums can be…
Geometric and holonomic quantum computation utilizes intrinsic geometric properties of quantum-mechanical state spaces to realize quantum logic gates. Since both geometric phases and quantum holonomies are global quantities depending only…
Universal quantum computing requires an architecture that supports both linear circuits and, crucially, strong nonlinear resources. For quantum photonic systems, integrating such nonlinearities with scalable linear circuitry has been a…
One-way quantum computing allows any quantum algorithm to be implemented easily using just measurements. The difficult part is creating the universal resource, a cluster state, on which the measurements are made. We propose a radically new…
The Hilbert space formalism of quantum mechanics is reviewed with emphasis on applications to quantum computing. Standard interferomeric techniques are used to construct a physical device capable of universal quantum computation. Some…
The theory of quantum computation can be constructed from the abstract study of anyonic systems. In mathematical terms, these are unitary topological modular functors. They underlie the Jones polynomial and arise in Witten-Chern-Simons…
A consistent realization of the quantum operators corresponding to the canonically conjugate phase and number variables is proposed, resorting to the irreducible unitary representations of the Lie algebra su(1,1), as proposed by Kastrup.
We describe a generalization of the cluster-state model of quantum computation to continuous-variable systems, along with a proposal for an optical implementation using squeezed-light sources, linear optics, and homodyne detection. For…
Single photons provide excellent quantum information carriers, but current schemes for preparing, processing and measuring them are inefficient. For example, down-conversion provides heralded, but randomly timed single photons, while…
We introduce a scheme for linear optics quantum computation, that makes no use of teleported gates, and requires stable interferometry over only the coherence length of the photons. We achieve a much greater degree of efficiency and a…
In topological quantum computation the geometric details of a particle trajectory are irrelevant; only the topology matters. Taking this one step further, we consider a model of computation that disregards even the topology of the particle…
We show that an $n$-dimensional Riemannian manifold with $n$-nonnegative or $n$-nonpositive curvature operator of the second kind has restricted holonomy $SO(n)$ or is flat. The result does not depend on completeness and can be improved…
We show that the Knill Laflamme Milburn method of quantum computation with linear optics gates can be interpreted as a one-way, measurement based quantum computation of the type introduced by Briegel and Rausendorf. We also show that the…
Quantum computers with Kerr-nonlinear parametric oscillators (KPOs) have recently been proposed by the author and others. Quantum computation using KPOs is based on quantum adiabatic bifurcations of the KPOs, which lead to quantum…
We suggest a new method for quantum optical control with nanoscale resolution. Our method allows for coherent far-field manipulation of individual quantum systems with spatial selectivity that is not limited by the wavelength of radiation…
Continuous-variables (CV) quantum optics is a natural formalism for neural networks (NNs) due to its ability to reproduce the information processing of such trainable interconnected systems. In quantum optics, Gaussian operators induce…
We prove that universal quantum computation can be realized---using only linear optics and $\chi^{(2)}$ (three-wave mixing) interactions---in any $(n+1)$-dimensional qudit basis of the $n$-pump-photon subspace. First, we exhibit a strictly…
We consider quantum holonomy of some three-dimensional general covariant non-Abelian field theory in Landau gauge and confirm a previous result partially proven. We show that quantum holonomy retains metric independence after explicit gauge…
Due to its geometric nature, holonomic quantum computation is fault-tolerant against certain types of control errors. Although proposed more than a decade ago, the experimental realization of holonomic quantum computation is still an open…