Related papers: Symbolic Quantum State Representation and its Simu…
Phase space quasi-probability functions provide powerful representations of quantum states and operators, as well as criteria for assessing quantum computational resources. In discrete, odd-dimensional systems (qudits), protocols involving…
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…
We provide a scheme for efficient simulation of a broad class of quantum optics experiments. Our efficient simulation extends the continuous variable Gottesman-Knill theorem to a large class of non-Gaussian mixed states, thereby identifying…
We define quantum phase in terms of inverses of annihilation and creation operators. We show that like Susskind - Glogower phase operators, the measured phase operators and the unitary phase operators can be defined in terms of the inverse…
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 sketch a group-theoretical framework, based on the Heisenberg-Weyl group, encompassing both quantum and classical statistical descriptions of mechanical systems. We re-define in group-theoretical terms the kinematical arena and the…
In this paper, we review the theory of time space-harmonic polynomials developed by using a symbolic device known in the literature as the classical umbral calculus. The advantage of this symbolic tool is twofold. First a moment…
The current shift in the quantum optics community towards large-size experiments -- with many modes and photons -- necessitates new classical simulation techniques that go beyond the usual phase space formulation of quantum mechanics. To…
In this second paper on loop quantization of Gowdy model, we introduce the kinematical Hilbert space on which appropriate holonomies and fluxes are well represented. The quantization of the volume operator and the Gauss constraint is…
Rational functions are exceptionally powerful tools in scientific computing, yet their abilities to advance quantum algorithms remain largely untapped. In this paper, we introduce effective implementations of rational transformations of a…
We extensively discuss the Hong-Ou-Mandel experiment taking an original phase-space-based perspective. For this, we analyze time and frequency variables as quantum continuous variables in perfect analogy with position and momentum of…
In this work, we consider fixed $1/2$ spin particles interacting with the quantized radiation field in the context of quantum electrodynamics (QED). We investigate the time evolution operator in studying the reduced propagator (interaction…
We investigate the simulation of fermionic systems on a quantum computer. We show in detail how quantum computers avoid the dynamical sign problem present in classical simulations of these systems, therefore reducing a problem believed to…
To simulate the quantum systems at classical or quantum computers, it is necessary to reduce continuous observables (e.g. coordinate and momentum or energy and time) to discrete ones. In this work we consider the continuous observables…
It is known that ab initio molecular dynamics based on the electron ground state eigenvalue can be used to approximate quantum observables in the canonical ensemble when the temperature is low compared to the first electron eigenvalue gap.…
In this paper we are discussing the question how a continuous quantum system can be simulated by mean field fluctuations of a finite number of qubits. On the kinematical side this leads to a convergence result which states that…
The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics,…
Photons are the elementary quantum excitations of the electromagnetic field. Quantization is usually constructed on the basis of an expansion in eigenmodes, in the form of plane waves. Since they form a basis, other electromagnetic…
Gaussian wave packets (GWPs) are well suited as basis functions to describe the time evolution of arbitrary wave functions in systems with nonsingular smooth potentials. They are less so in atomic systems on account of the singular behavior…
High-dimensional quantum information processing promises capabilities beyond the current state of the art, but addressing individual information-carrying modes presents a significant experimental challenge. Here we demonstrate effective…