Related papers: An algorithm for the optical equivalence theorem
We construct a hybrid quantum-classical approach for the $K$-Nearest Neighbour algorithm, where the information is embedded in a phase-distributed multimode coherent state with the assistance of a single photon. The task of finding the…
Motivated by some well-known results in the phase space description of quantum optics and quantum information theory, we aim to describe the formalism of quantum field theory by explicitly considering the holomorphic representation for a…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
Implementing general functions of operators is a powerful tool in quantum computation. It can be used as the basis for a variety of quantum algorithms including matrix inversion, real and imaginary-time evolution, and matrix powers. Quantum…
The effective formulas reducing the two-dimensional Hermite polynomials to the classical (one-dimensional) orthogonal polynomials are given. New one-parameter generating functions for these polynomials are derived. Asymptotical formulas for…
By virtue of the technique of integration within an ordered product (IWOP) of operators and the bipartite entangled state representation we derive some new identities about operator Hermite polynomials in both single- and two-variable, we…
We propose an optical parallel computation similar to quantum computation that can be realized by introducing pseudorandom phase sequences into classical optical fields with two orthogonal modes. Based on the pseudorandom phase sequences,…
Some $q-$analogues of the normal ordering of the operator $(X+sD)^n$ on the polynomials are derived.
Why do we need quantization to describe vision? What are the quadrature operators of the electromagnetic field? Is it possible to measure them? What are the characteristic functions useful for? In this brief tutorial we provide the…
We introduce the entangled coherent state representation, which provides a powerful technique for efficiently and elegantly describing and analyzing quantum optics sources and detectors while respecting the photon number superselection rule…
The coherent states for a set of quadratic Hamiltonians in the trap regime are constructed. A matrix technique which allows to identify directly the creation and annihilation operators will be presented. Then, the coherent states as…
A new class of states of light is introduced that is complementary to the well-known squeezed states. The construction is based on the general solution of the three-term recurrence relation that arises from the saturation of the…
We propose and investigate an optical scheme for probabilistic implementation of an arbitrary single-mode quantum operation that can be expressed as a function of photon number operator. The scheme coherently combines multiple photon…
Though quantum algorithm acts as an important role in quantum computation science, not only for providing a great vision for solving classically unsolvable problems, but also due to the fact that it gives a potential way of understanding…
The photon distribution function of a discrete series of excitations of squeezed coherent states is given explicitly in terms of Hermite polynomials of two variables. The Wigner and the coherent-state quasiprobabilities are also presented…
Predicting observables in equilibrium states is a central yet notoriously hard question in quantum many-body systems. In the physically relevant thermodynamic limit, certain mathematical formulations of this task have even been shown to…
We suggest a method to prepare any chosen superposition a0 |0> + a1 |1> of the vacuum and one-photon states. The method is based on a conditional double-interferometer fed by an one-photon state and a coherent state. The scheme involves…
Some properties and relations satisfied by the polynomial solutions of a bispectral problem are studied. Given a finite order differential operator, under certain restrictions, its polynomial eigenfunctions are explicitly obtained, as well…
We propose a formalization of generic algorithms that includes analog algorithms. This is achieved by reformulating and extending the framework of abstract state machines to include continuous-time models of computation. We prove that every…
An algorithm to classify a general Hermitian matrix according to its signature (positive semi-definite, negative or indefinite) is presented. It builds on the Quantum Phase Estimation algorithm, which stores the sign of the eigenvalues of a…