Quantum Parametric Resonance of a dissipative oscillator: fading and persistent memory in the long-time evolution

The evolution of a quantum oscillator, with periodically varying frequency and damping, is studied in the two cases of parametric resonance (PR) producing a limited, or unlimited stretching of the wave function. The different asymptotic behaviors of the energy distribution, show the non trivial interplay between PR and the initial quantum state. In the first case, the oscillator's mean energy tends asymptotically to a fully classical value, independent of the initial state, with vanishing relative quantum fluctuations. In the second case, the memory of the initial state persists over arbitrary long time scales, both in the mean value and in the large quantum fluctuations of the energy.Comment: 20 pages, 2 figure

Quantum Metropolis Sampling

The original motivation to build a quantum computer came from Feynman who envisaged a machine capable of simulating generic quantum mechanical systems, a task that is believed to be intractable for classical computers. Such a machine would have a wide range of applications in the simulation of many-body quantum physics, including condensed matter physics, chemistry, and high energy physics. Part of Feynman's challenge was met by Lloyd who showed how to approximately decompose the time-evolution operator of interacting quantum particles into a short sequence of elementary gates, suitable for operation on a quantum computer. However, this left open the problem of how to simulate the equilibrium and static properties of quantum systems. This requires the preparation of ground and Gibbs states on a quantum computer. For classical systems, this problem is solved by the ubiquitous Metropolis algorithm, a method that basically acquired a monopoly for the simulation of interacting particles. Here, we demonstrate how to implement a quantum version of the Metropolis algorithm on a quantum computer. This algorithm permits to sample directly from the eigenstates of the Hamiltonian and thus evades the sign problem present in classical simulations. A small scale implementation of this algorithm can already be achieved with today's technologyComment: revised versio

Revivals of Coherence in Chaotic Atom-Optics Billiards

We investigate the coherence properties of thermal atoms confined in optical dipole traps where the underlying classical dynamics is chaotic. A perturbative expression derived for the coherence of the echo scheme of [Andersen et. al., Phys. Rev. Lett. 90, 023001 (2003)] shows it is a function of the survival probability or fidelity of eigenstates of the motion of the atoms in the trap. The echo coherence and the survival probability display "system specific" features, even when the underlying classical dynamics is chaotic. In particular, partial revivals in the echo signal and the survival probability are found for a small shift of the potential. Next, a "semi-classical" expression for the averaged echo signal is presented and used to calculate the echo signal for atoms in a light sheet wedge billiard. Revivals in the echo coherence are found in this system, indicating they may be a generic feature of dipole traps

Witnessing eigenstates for quantum simulation of Hamiltonian spectra

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 provide a new quantum approach which combines variational methods and phase estimation to approximate eigenvalues for both ground and excited states. This protocol is experimentally verified on a programmable silicon quantum photonic chip, a mass-manufacturable platform, which embeds entangled state generation, arbitrary controlled-unitary operations, and projective measurements. Both ground and excited states are experimentally found with fidelities >99%, and their eigenvalues are estimated with 32-bits of precision. We also investigate and discuss the scalability of the approach and study its performance through numerical simulations of more complex Hamiltonians. This result shows promising progress towards quantum chemistry on quantum computers.Comment: 9 pages, 4 figures, plus Supplementary Material [New version with minor typos corrected.