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Coherent states of the two dimensional harmonic oscillator are constructed as superpositions of energy and angular momentum eigenstates. It is shown that these states are Gaussian wave-packets moving along a classical trajectory, with a…
In a quantum measurement setting, it is known that environment-induced decoherence theory describes the emergence of effectively classical features of the quantum system-measuring apparatus composite system when the apparatus is allowed to…
We analyze the application of the history state formalism to quantum walks. The formalism allows one to describe the whole walk through a pure quantum history state, which can be derived from a timeless eigenvalue equation. It naturally…
It is a common belief among field theorists that path integrals can be computed exactly only in a limited number of special cases, and that most of these cases are already known. However recent developments, which generalize the WKBJ method…
A self-adjoint operator with dimensions of time is explicitly constructed, and it is shown that its complete and orthonormal set of eigenstates can be used to define consistently a probability distribution of the time of arrival at a…
We study the correspondence between phase-space localization of quantum (quasi-)energy eigenstates and classical correlation decay, given by Ruelle-Pollicott resonances of the Frobenius-Perron operator. It will be shown that scarred…
We obtain sufficient conditions for the efficient simulation of a continuous variable quantum algorithm or process on a classical computer. The resulting theorem is an extension of the Gottesman-Knill theorem to continuous variable quantum…
We represent both the states and the evolution of a quantum computer in phase space using the discrete Wigner function. We study properties of the phase space representation of quantum algorithms: apart from analyzing important examples,…
The Newton-Wigner states and operator are widely accepted to provide an adequate notion of spatial localization of a particle in quantum field theory on a spacelike hypersurface. Replacing the spacelike with a timelike hypersurface, we…
The efficient calculation of Hamiltonian spectra, a problem often intractable on classical machines, can find application in many fields, from physics to chemistry. Here, we introduce the concept of an "eigenstate witness" and through it…
In the covariant canonical approach to classical physics, each point in phase space represents an entire classical trajectory. Initial data at a fixed time serve as coordinates for this ``timeless'' phase space, and time evolution can be…
The conventional phase space of classical physics treats space and time differently, and this difference carries over to field theories and quantum mechanics (QM). In this paper, the phase space is enhanced through two main extensions.…
We propose a scheme to deal with certain time-dependent non-Hermitian Hamiltonian operators $H(t)$ that generate a real phase in their time-evolution. This involves the use of invariant operators $I_{PH}(t)$ that are pseudo-Hermitian with…
We investigate the computational power of creating steady-states of quantum dissipative systems whose evolution is governed by time-independent and local couplings to a memoryless environment. We show that such a model allows for efficient…
For a time-dependent classical quadratic oscillator we introduce pairs of real and complex invariants that are linear in position and momentum. Each pair of invariants realize explicitly a canonical transformation from the phase space to…
Discovering pragmatic and efficient approaches to construct $\varepsilon$-approximations of quantum operators such as real (imaginary) time-evolution propagators in terms of the basic quantum operations (gates) is challenging. Prior…
Identifying phase transition points is a fundamental challenge in condensed matter physics, particularly for transitions driven by quantum interference effects, such as Anderson and many-body localization. Recent studies have demonstrated…
Classical phase-space variables are normally chosen to promote to quantum operators in order to quantize a given classical system. While classical variables can exploit coordinate transformations to address the same problem, only one set of…
The domain of application of quantization methods is traditionally restricted to smooth classical observables. We show that the coherent states or "anti-Wick" quantization enables us to construct fairly reasonable quantum versions of…
Solving the electronic structure problem on a universal-gate quantum computer within the variational quantum eigensolver (VQE) methodology requires constraining the search procedure to a subspace defined by relevant physical symmetries.…