Quantum Dynamics Simulation of a Small Quantum System Embedded in a Classical Environment

1996 ◽  
pp. 157-179 ◽  
Author(s):  
H. J. C. Berendsen ◽  
J. Mavri
Keyword(s):  
Quantum System ◽  
Quantum Dynamics ◽  
Dynamics Simulation ◽  
Small Quantum

scholarly journals Tangible reduction in learning sample complexity with large classical samples and small quantum system

2021 ◽  
Vol 20 (8) ◽  
Author(s):  
Wooyeong Song ◽  
Marcin Wieśniak ◽  
Nana Liu ◽  
Marcin Pawłowski ◽  
Jinhyoung Lee ◽  
...  
Keyword(s):  
Quantum System ◽  
Learning Sample ◽  
Sample Complexity ◽  
Small Quantum

New method of quantum dynamics simulation based on the quantum tomography

2003 ◽  
Vol 319 (3-4) ◽  
pp. 217-224 ◽  
Author(s):  
A.S. Arkhipov ◽  
Yu.E. Lozovik
Keyword(s):  
Quantum Dynamics ◽  
Quantum Tomography ◽  
New Method ◽  
Dynamics Simulation ◽  
Simulation Based

Constrained quantum dynamics and coarse-grained description of a quantum system of nonlinear oscillators

2012 ◽  
Vol T149 ◽  
pp. 014011
Author(s):  
Milan Radonjić ◽  
Slobodan Prvanović ◽  
Nikola Burić
Keyword(s):  
Quantum System ◽  
Quantum Dynamics ◽  
Nonlinear Oscillators ◽  
Coarse Grained

scholarly journals A random walk approach to quantum algorithms

2006 ◽  
Vol 364 (1849) ◽  
pp. 3407-3422 ◽  
Author(s):  
Vivien M Kendon
Keyword(s):  
Random Walk ◽  
Quantum Dynamics ◽  
Quantum Computer ◽  
Quantum Algorithms ◽  
Quantum Walk ◽  
Quantum Random Walk ◽  
Small Quantum ◽  
Starting Point ◽  
Quantum Version ◽  
Speed Up

The development of quantum algorithms based on quantum versions of random walks is placed in the context of the emerging field of quantum computing. Constructing a suitable quantum version of a random walk is not trivial; pure quantum dynamics is deterministic, so randomness only enters during the measurement phase, i.e. when converting the quantum information into classical information. The outcome of a quantum random walk is very different from the corresponding classical random walk owing to the interference between the different possible paths. The upshot is that quantum walkers find themselves further from their starting point than a classical walker on average, and this forms the basis of a quantum speed up, which can be exploited to solve problems faster. Surprisingly, the effect of making the walk slightly less than perfectly quantum can optimize the properties of the quantum walk for algorithmic applications. Looking to the future, even with a small quantum computer available, the development of quantum walk algorithms might proceed more rapidly than it has, especially for solving real problems.

scholarly journals Open Quantum Dynamics Theory on the Basis of Periodical System-Bath Model for Discrete Wigner Function

2021 ◽  
Author(s):  
Yuki Iwamoto ◽  
Yoshitaka Tanimura
Keyword(s):  
Distribution Function ◽  
Quantum Dynamics ◽  
Degrees Of Freedom ◽  
Wigner Distribution ◽  
Equations Of Motion ◽  
Heat Bath ◽  
Planck Equation ◽  
Mesh Size ◽  
Dynamics Simulation ◽  
Open Quantum

Abstract Discretizing distribution function in a phase space for an efficient quantum dynamics simulation is non-trivial challenge, in particular for a case that a system is further coupled to environmental degrees of freedom. Such open quantum dynamics is described by a reduced equation of motion (REOM) most notably by a quantum Fokker-Planck equation (QFPE) for a Wigner distribution function (WDF). To develop a discretization scheme that is stable for numerical simulations from the REOM approach, we find that a two-dimensional (2D) periodically invariant system-bath (PISB) model with two heat baths is an ideal platform not only for a periodical system but also for a system confined by a potential. We then derive the numerically ''exact'' hierarchical equations of motion (HEOM) for a discrete WDF in terms of periodically invariant operators in both coordinate and momentum spaces. The obtained equations can treat non-Markovian heat-bath in a non-perturbative manner at finite temperatures regardless of the mesh size. The stability of the present scheme is demonstrated in a high-temperature Markovian case by numerically integrating the discrete QFPE with by a coarse mesh for a 2D free rotor and harmonic potential systems for an initial condition that involves singularity.

scholarly journals Can small quantum systems learn

2017 ◽  
Vol 17 (7&8) ◽  
pp. 568-594
Author(s):  
Nathan Wiebe ◽  
Christopher Grandade
Keyword(s):  
Quantum Mechanics ◽  
Fault Tolerance ◽  
Bayesian Inference ◽  
Quantum System ◽  
Lower Bounds ◽  
State Vector ◽  
Quantum Systems ◽  
Posterior Distributions ◽  
Quantum Devices ◽  
Small Quantum

We examine the question of whether quantum mechanics places limitations on the ability of small quantum devices to learn. We specifically examine the question in the context of Bayesian inference, wherein the prior and posterior distributions are encoded in the quantum state vector. We conclude based on lower bounds from Grover’s search that an efficient blackbox method for updating the distribution is impossible. We then address this by providing a new adaptive form of approximate quantum Bayesian inference that is polynomially faster than its classical anolog and tractable if the quantum system is augmented with classical memory or if the low–order moments of the distribution are protected through redundant preparation. This work suggests that there may be a connection between fault tolerance and the capacity of a quantum system to learn from its surroundings.

scholarly journals Massively Parallel Classical Logic via Coherent Dynamics of an Ensemble of Quantum Systems with Dispersion in Size

2020 ◽  
Author(s):  
Hugo Gattuso ◽  
Raphael D. Levine ◽  
Francoise Remacle
Keyword(s):  
Quantum System ◽  
Quantum Dynamics ◽  
Algebraic Theory ◽  
Laser Pulses ◽  
Quantum Systems ◽  
Individual Variability ◽  
Expectation Values ◽  
Charge Transfer Excitons ◽  
Simultaneous Reading ◽  
Size Dispersion

Quantum parallelism can be implemented on a classical ensemble of discrete level quantum systems. The nano systems are not quite identical and the ensemble represents their individual variability. An underlying Lie algebraic theory is developed using the closure of the algebra to demonstrate the parallel information processing at the level of the ensemble. The ensemble is addressed by a sequence of laser pulses. In the Heisenberg picture of quantum dynamics the coherence between the N levels of a given quantum system can be handled as an observable. Thereby there are N2 logic variables per N level system. This is how massive parallelism is achieved in that there are N2 potential outputs for a quantum system of N levels. The use of an ensemble allows simultaneous reading of such outputs. Due to size dispersion the expectation values of the observables can differ somewhat from system to system. We show that for a moderate variability of the systems one can average the N2 expectation values over the ensemble while retaining closure and parallelism. This allows directly propagating in time the ensemble averaged values of the observables. Results of simulations of electronic excitonic dynamics in an ensemble of quantum dot, QD, dimers are presented. The QD size and interdot distance in the dimer are used to parametrize the Hamiltonian. The dimer N levels include local and charge transfer excitons within each dimer. The well-studied physics of semi-conducting QDs suggests that the dimer coherences can be probed at room temperature

Quantum dynamics simulation of the ultrafast photoionization of Li2

2001 ◽  
Vol 114 (3) ◽  
pp. 1259-1271 ◽  
Author(s):  
Lorenzo Pesce ◽  
Zohar Amitay ◽  
Radoslaw Uberna ◽  
Stephen R. Leone ◽  
Mark Ratner ◽  
...  
Keyword(s):  
Quantum Dynamics ◽  
Dynamics Simulation
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