Related papers: Quantum computers in phase space

This work presents a selective review of results concerning the mathematical interface between the classical and quantum aspects encountered in problems such as the nuclear mean-field dynamics or quantum Brownian motion. It is shown that…

We derive an analytical expression of a Wigner function that approximately describes the time evolution of the one-dimensional motion of a particle in a nonharmonic potential. Our method involves two exact frame transformations, accounting…

We derive a quantum version of the classical-optics Wiener-Khintchine theorem within the framework of detection of phase-space displacements with a suitably designed quantum ruler. A phase-pace based quantum mutual coherence function is…

The Gibbs canonical state, as a maximum entropy density matrix, represents a quantum system in equilibrium with a thermostat. This state plays an essential role in thermodynamics and serves as the initial condition for nonequilibrium…

In the usual formulation of quantum mechanics, groups of automorphisms of quantum states have ray representations by unitary and antiunitary operators on complex Hilbert space, in accordance with Wigner's Theorem. In the phase-space…

For classical canonical transformations, one can, using the Wigner transformation, pass from their representation in Hilbert space to a kernel in phase space. In this paper it will be discussed how the time-dependence of the uncertainties…

Using the remarkable mathematical construct of Eugene Wigner to visualize quantum trajectories in phase space, quantum processes can be described in terms of a quasi-probability distribution analogous to the phase space probability…

We devise a classical algorithm which efficiently computes the quantum expectation values arising in a class of continuous variable quantum circuits wherein the final quantum observable | after the Heisenberg evolution associated with the…

The representation of quantum states via phase-space functions constitutes an intuitive technique to characterize light. However, the reconstruction of such distributions is challenging as it demands specific types of detectors and detailed…

We propose a method for classical simulation of finite-dimensional quantum systems, based on sampling from a quasiprobability distribution, i.e., a generalized Wigner function. Our construction applies to all finite dimensions, with the…

This dissertation serves as a general introduction to Wigner functions, phase space, and quantum metrology but also strives to be useful as a how-to guide for those who wish to delve into the realm of using continuous variables, to describe…

A quantum state can be written in phase space, but the resulting object is not generally the probability density of a positive stochastic process on ordinary phase space. We spell this out for Wigner dynamics. If a positive phase-space…

In this work we present the formal background used to develop the methods used in earlier works to extend the truncated Wigner representation of quantum and atom optics in order to address multi-time problems. The truncated Wigner…

We formulate continuous time quantum walks (CTQW) in a discrete quantum mechanical phase space. We define and calculate the Wigner function (WF) and its marginal distributions for CTQWs on circles of arbitrary length $N$. The WF of the CTQW…

We analyze and further develop a new method to represent the quantum state of a system of $n$ qubits in a phase space grid of $N\times N$ points (where $N=2^n$). The method, which was recently proposed by Wootters and co--workers (Gibbons…

We analyse some features of the class of discrete Wigner functions that was recently introduced by Gibbons et al. to represent quantum states of systems with power-of-prime dimensional Hilbert spaces [Phys. Rev. A 70, 062101 (2004)]. We…

We review recent developments in the theory of quantum dynamics in ultra-cold atomic physics, including exact techniques, but focusing on methods based on phase-space mappings that are appli- cable when the complexity becomes exponentially…

We present an experimental scanning-based tomography approach for near-term quantum devices. The underlying method has previously been introduced in an ensemble-based NMR setting. Here we provide a tutorial-style explanation along with…

We show that quantum circuits where the initial state and all the following quantum operations can be represented by positive Wigner functions can be classically efficiently simulated. This is true both for continuous-variable as well as…

A quantum computer directly manipulates information stored in the state of quantum mechanical systems. The available operations have many attractive features but also underly severe restrictions, which complicate the design of quantum…