Beating the efficiency of both quantum and classical simulations with semiclassics

Abstract

While rigorous quantum dynamical simulations of many-body systems are extremely difficult (or impossible) due to the exponential scaling with dimensionality, corresponding classical simulations completely ignore quantum effects. Semiclassical methods are generally more efficient but less accurate than quantum methods, and more accurate but less efficient than classical methods. We find a remarkable exception to this rule by showing that a semiclassical method can be both more accurate and faster than a classical simulation. Specifically, we prove that for the semiclassical dephasing representation the number of trajectories needed to simulate quantum fidelity is independent of dimensionality and also that this semiclassical method is even faster than the most efficient corresponding classical algorithm. Analytical results are confirmed with simulations of quantum fidelity in up to 100 dimensions with 2^1700-dimensional Hilbert space.

5 pages, 4 figures

References in corpus (5)

• Dynamics of Loschmidt echoes and fidelity decay
• Decoherence, Entanglement and Irreversibility in Quantum Dynamical Systems with Few Degrees of Freedom
• Dephasing representation of quantum fidelity for general pure and mixed states
• On the stability of classical chaotic motion under system's perturbations
• Decay of the classical Loschmidt echo in integrable systems

Cited by in corpus (13)

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• Measuring nonadiabaticity of molecular quantum dynamics with quantum fidelity and with its efficient semiclassical approximation
• Evaluation of the importance of spin-orbit couplings in the nonadiabatic quantum dynamics with quantum fidelity and with its efficient "on-the-fly" ab initio semiclassical approximation
• Improving the accuracy and efficiency of time-resolved electronic spectra calculations: Cellular dephasing representation with a prefactor
• Path integral approach to the quantum fidelity amplitude
• Sampling strategies for the Herman-Kluk propagator of the wavefunction
• Role of the sampling weight in evaluating classical time autocorrelation functions
• Breaking the exponential wall in classical simulations of fidelity
• Refined approach to cellularization: going from Heller's thawed Gaussian approximation to the Herman--Kluk propagator