Résultats de recherche pour « Mixed quantum-classical dynamics »

Mixed quantum-classical spin systems have been proposed in spin chain theory and, more recently, in magnon spintronics. However, current models of quantum-classical dynamics beyond mean-field approximations typically suffer from long-standing consistency issues, and, in some cases, invalidate Heisenberg's uncertainty principle. Here, we present a fully Hamiltonian theory of quantum-classical spin dynamics that appears to be the first to ensure an entire series of consistency properties, including positivity of both the classical and the quantum density, so that Heisenberg's principle is satisfied at all times. We show how this theory may connect to recent energy-balance considerations in measurement theory and we present its Poisson bracket structure explicitly. After focusing on the simpler case of a classical Bloch vector interacting with a quantum spin observable, we illustrate the extension of the model to systems with several spins, and restore the presence of orbital degrees of freedom.

This paper proposes a method to simulate nonadiabatic dynamics initiated by thermal light, including solar radiation, in the frame of mixed quantum-classical (MQC) methods, like surface hopping. The method is based on the Chenu-Brumer approach, which treats the thermal radiation as an ensemble of coherent pulses. It is composed of three steps, 1) sampling initial conditions from a broad blackbody spectrum, 2) propagation of the dynamics using conventional methods, and 3) ensemble averaging considering the field and realization time of the pulses. The application of MQC dynamics with pulse ensemble (MQC-PE) to a model system of nucleic acid photophysics showed the emergence of a stationary excited-state population. In another test case, modeling retinal isomerization, MQC-PE revealed that even when the underlying photophysics occurs within 200 fs, it may take tens of microseconds of continuous solar irradiation to activate a molecule photochemically. Such emergent long timescales may impact our understanding of biological and technological phenomena occurring under solar radiation.

We consider the dynamics of interacting quantum and classical systems in the Heisenberg representation. Unlike the usual construction in standard quantum mechanics, mixed quantum-classical systems involve the interplay of unitary operators acting on the quantum observables and the Lagrangian trajectories sweeping the classical degrees of freedom. This interplay reflects an intricate structure which is made particularly challenging by the backreaction excerpted on the classical trajectories by the quantum degrees of freedom. While the backreaction is underestimated in the common Ehrenfest model, more recent methodologies succeed in capturing this important effect by resorting to Koopman wavefunctions in classical mechanics. Luckily, both Ehrenfest and Koopman models enjoy a variational framework which is exploited here to unfold the geometric structure underlying quantum-classical coupling. A special role is played by the action of the diffeomorphic Lagrangian paths on a non-Abelian pure-gauge potential which comprises statistical correlations. After presenting the treatment in the simple case of Ehrenfest dynamics, we move on to the Koopman model and present the role of the backreaction terms therein. Finally, we compare both models in the context of pure-dephasing systems.

This paper proposes a method to simulate nonadiabatic dynamics initiated by thermal light, including solar radiation, in the frame of mixed quantum-classical (MQC) methods, like surface hopping. The method is based on the Chenu-Brumer approach, which treats the thermal radiation as an ensemble of coherent pulses. It is composed of three steps, 1) sampling initial conditions from a broad blackbody spectrum, 2) dynamics propagation using conventional methods, and 3) ensemble averaging considering the field and realization time of the pulses. The application of MQC dynamics with pulse ensemble (MQC-PE) to a model system of nucleic acid photophysics showed the emergence of a steady excited-state population. In another test case, modeling retinal photophysics, MQC-PE predicted that although the photoisomerization occurs within 200 fs, it may take tens of microseconds of continuous solar irradiation to photoactivate a single retinal. Such emergent long timescales may impact our understanding of biological and technological phenomena occurring under solar radiation.

A recent proposal for mixed dynamics of classical and quantum ensembles is shown, in contrast to other proposals, to satisfy the minimal algebraic requirements proposed by Salcedo for any consistent formulation of such dynamics. Generalised Ehrenfest relations for the expectation values of classical and quantum observables are also obtained. It is further shown that additional desirable requirements, related to separability, may be satisfied under the assumption that only the configuration of the classical component is directly accessible to measurement, eg, via a classical pointer. Although the mixed dynamics is formulated in terms of ensembles on configuration space, thermodynamic mixtures of such ensembles may be defined which are equivalent to canonical phase space ensembles on the classical sector. Hence, the formulation appears to be both consistent and physically complete.

Recent developments in quantum computing are highly promising, particularly in the realm of quantum chemistry. Due to the noisy nature of currently available quantum hardware, hybrid quantum-classical algorithms have emerged as a reliable option for near-term simulations. Mixed quantum-classical dynamics methods effectively capture nonadiabatic effects by integrating classical nuclear dynamics with quantum chemical computations of the electronic properties. However, these methods face challenges due to the high computational cost of the quantum chemistry part. To mitigate the computational demand, we propose a method where the required electronic properties are computed through a hybrid quantum-classical approach on combination of classical and quantum hardware. This framework employs the variational quantum eigensolver and variational quantum deflation algorithms to obtain ground and excited state energies, gradients, nonadiabatic coupling vectors, and transition dipole moments. These quantities are used to propagate the nonadiabatic molecular dynamics using the Tully’s fewest switches surface hopping method, although the implementation is also compatible with other molecular dynamics approaches. The approach, implemented by integrating the molecular dynamics program package SHARC with the TEQUILA quantum computing framework, is validated by studying the cis-trans photoisomerization of methanimine and the electronic relaxation of ethylene. The results show qualitatively accurate molecular dynamics that align with experimental findings and other computational studies. This work is expected to mark a significant step towards achieving a "quantum advantage" for realistic chemical simulations.

We consider the interaction dynamics of a classical oscillator and a quantum two-level system for different pure-dephasing Hamiltonians of the type $\widehat{H}(q,p)=H_C(q,p)\boldsymbol{1}+H_I(q,p)\widehatσ_z$. This type of systems represents a severe challenge for popular hybrid quantum-classical descriptions. For example, in the case of the common Ehrenfest model, the classical density evolution is shown to decouple entirely from the pure-dephasing quantum dynamics. We focus on a recently proposed hybrid wave equation that is based on Koopman's wavefunction description of classical mechanics. This model retains quantum-classical correlations whenever a coupling potential is present. Here, several benchmark problems are considered and the results are compared with those arising from fully quantum dynamics. A good agreement is found for a series of study cases involving harmonic oscillators with linear and quadratic coupling, as well as time-varying coupling parameters. In all these cases the classical evolution coincides exactly with the oscillator dynamics resulting from the fully quantum description. In the special case of time-independent coupling involving a classical oscillator with varying frequency, the quantum Bloch rotation exhibits peculiar features that escape from the hybrid description. In addition, nonlinear corrections to the harmonic Hamiltonian lead to an overall growth of decoherence at long times, which is absent in the fully quantum treatment.

The problem of Phase Estimation (or Amplitude Estimation) admits a quadratic quantum speedup. Wang, Higgott and Brierley [2019, Phys. Rev. Lett. 122 140504] have shown that there is a continuous trade-off between quantum speedup and circuit depth (by defining a family of algorithms known as $α$-QPE). In this work, we show that the scaling of $α$-QPE can be naturally and succinctly derived within the framework of Quantum Singular Value Transformation (QSVT). From the QSVT perspective, a greater number of coherent oracle calls translates into a better polynomial approximation to the sign function, which is the key routine for solving Phase Estimation. The better the approximation to the sign function, the fewer samples one needs to determine the sign accurately. With this idea, we simplify the proof of $α$-QPE, while providing a new interpretation of the interpolation parameters, and show that QSVT is a promising framework for reasoning about classical-quantum interpolations.

We derive the L-MFE method to incorporate Lindblad jump operator dynamics into the mean-field Ehrenfest (MFE) approach. We map the density matrix evolution of Lindblad dynamics onto pure state coefficients using trajectory averages. We use simple assumptions to construct the L-MFE method that satisfies this exact mapping. This establishes a method that exactly reproduces Lindblad decay dynamics using a wavefunction description, with deterministic changes of the magnitudes of the quantum expansion coefficients, while only adding on a stochastic phase. We further demonstrate that when including nuclei in the Ehrenfest dynamics, the L-MFE method gives semi-quantitatively accurate results, with the accuracy limited by the accuracy of the approximations present in the semiclassical MFE approach. This work provides a general framework to incorporate Lindblad dynamics into semiclassical or mixed quantum-classical simulations.