The role of quantum coherence loss in mixed quantum-classical dynamical systems is explored in the context of the theory of quantum decoherence introduced recently by Bittner and Rossky [J. Chem. Phys. 103, 8130 (1995)]. This theory, which is based upon the consistent histories interpretation of quantum mechanics, introduces decoherence in the quantum subsystem by carefully considering the relevant time and length scales over which one must consider the effects of phase interference between alternative histories of the classical subsystem. Such alternative histories are an integral part of any quantum-classical computational scheme which employs transitions between discrete quantum states; consequently, the coherences between alternative histories have a profound effect on the transition probability between quantum states. In this paper, we review the Bittner–Rossky theory and detail a computational algorithm suitable for large-scale quantum molecular dynamics simulations which implements this theory. Application of the algorithm towards the relaxation of a photoexcited aqueous electron compare well to previous estimates of the excited state survival time as well as to the experimental measurements.
The role of quantum coherence loss in mixed quantum-classical dynamical systems is explored in the context of the theory of quantum decoherence introduced recently by Bittner and Rossky [J. Chem. Phys. 103, 8130 (1995)]. This theory, which is based upon the consistent histories interpretation of quantum mechanics, introduces decoherence in the quantum subsystem by carefully considering the relevant time and length scales over which one must consider the effects of phase interference between alternative histories of the classical subsystem. Such alternative histories are an integral part of any quantum-classical computational scheme which employs transitions between discrete quantum states; consequently, the coherences between alternative histories have a profound effect on the transition probability between quantum states. In this paper, we review the Bittner–Rossky theory and detail a computational algorithm suitable for large-scale quantum molecular dynamics simulations which implements this theory. Application of the algorithm towards the relaxation of a photoexcited aqueous electron compare well to previous estimates of the excited state survival time as well as to the experimental measurements.
Abstract In this Perspective, we discuss how quantum computers may advance the simulation of nonadiabatic molecular dynamics, a framework central to describing excited-state processes in photochemistry, biology, and materials science. Classical approaches span from exponentially scaling full quantum dynamics to more approximate mixed quantum–classical techniques such as surface hopping and Ehrenfest dynamics. Hybrid quantum–classical algorithms – particularly those based on the variational quantum eigensolver – offer a transformative alternative by providing access to the key electronic properties needed to drive nonadiabatic molecular dynamics simulations, including energies, gradients, and nonadiabatic couplings. We examine recent proof-of-principle quantum simulations of reduced model systems which, despite being restricted to small molecules and limited active spaces due to constraints of qubit number and device noise, already showcase the potential of quantum devices to capture phenomena such as conical intersections and ultrafast relaxation. Although practical applications are not yet feasible in the present noisy intermediate-scale quantum era, these efforts underline the conceptual and methodological advances of quantum algorithms paving the way for large-scale quantum simulations of nonadiabatic processes. Framed within the 2025 International Year of Quantum Science and Technology, such progress exemplifies how quantum computing may open new horizons for chemistry and beyond.
We address the issue of quantum decoherence in mixed quantum-classical simulations. We demonstrate that restricting the classical paths to a single path among all the quantum paths affects a coarse graining of the quantum paths. Such coarse graining causes the quantum paths to lose coherence as the various possible classical paths associated with each quantum state diverge. This defines a reduction mapping of the quantum density matrix, and we derive a quantum master equation suitable for mixed quantum-classical systems. The equation includes two terms: first, the ordinary quantum Liouvillian which is parametrized by a single classical path, and second, a quantum decoherence term that includes both a coherence time and length scale which are determined by the dynamics of the classical paths. Model calculations for electronic coherence loss in nonadiabatic mixed quantum-classical dynamics are presented as examples. For a model charge transfer chemical reaction with nonadiabatic transitions, application of the present formulation reveals that nonadiabaticity is diminished as the decoherence timescale becomes shorter and adiabatic dynamics are recovered in the limit of rapid decoherence.
In this work, we explore the implementation possibility of quantum simulation for quantum molecular dynamics, in particular for reaction dynamics, though several implementations have already reported through quantum-classical mixed simulations ({\it Acc. Chem. Res.} {\bf 54} (2021), 4229 and {\it J. Phys. Chem. Lett.} {\bf xx} (2026), XXXX). To analyze this aspect, we examine (1) the conjugacy relation between quantum simulator and the target molecular system, (2) the wave function correspondence in quantum algorithm and classical algorithm for multi-dimensional dynamics, (3) problems arisen from real-valued classical algorithms, and finally (4) geometric phase arisen from the separation among the degrees of freedom (DOFs). As is well known, the aforementioned first and second points play fundamental roles in quantum simulation of quantum many-body systems, and the third and fourth points are theoretical issues that might introduce problems in classical and quantum computing. In this work, we mainly focus on the third and fourth points by analysis of the first two points by reviewing previously reported quantum-classical mixed implementations of quantum simulation. We also consider gauge freedom in high-dimensional quantum molecular dynamics that has been introduced recently, and then discuss possibility of advantages and disadvantages of quantum simulation for molecular reaction dynamics.
We introduce a general theory of electronic decoherence for molecules in the condensed phase that captures contributions coming from pure dephasing effects, electronic transitions among diabatic states, and their interference. The theory is constructed by taking advantage of a recently developed [ J. Phys. Chem. Lett. 2017 , 8 , 4289 - 4294 ] general expression for decoherence times that is based on an early time expansion of the purity dynamics and extends early electronic decoherence models based on pure dephasing ideas. Using this theory, we construct the decoherence time for the displaced harmonic oscillator model amended with constant and linear diabatic couplings, which is a widely used model of the photoexcited dynamics of molecules. The validity of the short-time expansion is demonstrated by the quantitative agreement of the theory with exact numerical computations of the decoherence dynamics obtained using the hierarchical equation of motion method. These developments offer a rigorous understanding of early time electronic decoherence processes that accompany basic molecular events and demonstrate that electronic transitions among diabatic states play a major role in the decoherence dynamics.
Electronic decoherence processes in molecules and materials are usually thought and modeled via schemes for the system-bath evolution in which the bath is treated either implicitly or approximately. Here we present computations of the electronic decoherence dynamics of a model many-body molecular system described by the Su-Schrieffer-Heeger Hamiltonian with Hubbard electron-electron interactions using an exact method in which both electronic and nuclear degrees of freedom are taken into account explicitly and fully quantum mechanically. To represent the electron-nuclear Hamiltonian in matrix form and propagate the dynamics, the computations employ the Jordan-Wigner transformation for the fermionic creation/annihilation operators and the discrete variable representation for the nuclear operators. The simulations offer a standard for electronic decoherence that can be used to test approximations. They also provide a useful platform to answer fundamental questions about electronic decoherence that cannot be addressed through approximate or implicit schemes. Specifically, through simulations, we isolate basic mechanisms for electronic coherence loss and demonstrate that electronic decoherence is possible even for one-dimensional nuclear bath. Furthermore, we show that (i) decreasing the mass of the bath generally leads to faster electronic decoherence; (ii) electron-electron interactions strongly affect the electronic decoherence when the electron-nuclear dynamics is not pure-dephasing; (iii) classical bath models with initial conditions sampled from the Wigner distribution accurately capture the short-time electronic decoherence dynamics; (iv) model separable initial superpositions often used to understand decoherence after photoexcitation are only relevant in experiments that employ delta-like laser pulses to initiate the dynamics. These insights can be employed to interpret and properly model coherence phenomena in molecules.
Simulation of quantum dynamics for many-body systems is an open area of research. For interacting many-body quantum systems, the computer memory necessary to perform calculations has an astronomical value, so that approximated models are needed to reduce the required computational resources. A useful approximation that can often be made is that of quantum-classical dynamics, where the majority of the degrees are treated classically, while a few of them must be treated quantum mechanically. When energy is exchanged very quickly between the quantum subsystem and classical environment, the dynamics is nonadiabatic. Most theories for nonadiabatic dynamics are unsatisfactory, as they fail to properly describe the quantum backreaction of the subsystem on the environment. However, an approach based on the quantum-classical Liouville equation solves this problem. Even so, nonadiabatic dynamics is difficult to implement on a computer, and longer simulation times are often inaccessible due to statistical error. There is thus a need for improved algorithms for nonadiabatic dynamics. In this thesis, two algorithms that utilise the quantum-classical Liouville equation will be qualitatively and quantitatively compared. In addition, stochastic sampling schemes for nonadiabatic transitions will be studied, and a new sampling scheme is introduced [D. A. Uken et al., Phys. Rev. E. 88, 033301 (2013)] which proves to have a dramatic advantage over existing techniques, allowing far longer simulation times to be calculated reliably.