For the solution of time-dependent nonlinear differential equations, we present variational quantum algorithms (VQAs) that encode both space and time in qubit registers. The spacetime encoding enables us to obtain the entire time evolution from a single ground-state computation. We describe a general procedure to construct efficient quantum circuits for the cost function evaluation required by VQAs. To mitigate the barren plateau problem during the optimization, we propose an adaptive multigrid strategy. The approach is illustrated for the nonlinear Burgers equation. We classically optimize quantum circuits to represent the desired ground-state solutions, run them on IBM Q System One and Quantinuum System Model H1, and demonstrate that current quantum computers are capable of accurately reproducing the exact results.

Electron-hole pairs in organic photovoltaics efficiently dissociate although their Coulomb-binding energy exceeds thermal energy at room temperature. The vibronic coupling of electronic states to structured vibrational environments containing multiple underdamped modes is thought to assist charge separation. However, non-perturbative simulations of such large, spatially extended, electronic-vibrational (vibronic) systems remain an unmet challenge which current methods bypass by considering effective one-dimensional Coulomb potentials or unstructured environments where the effect of underdamped modes is ignored. Here we address this challenge with a non-perturbative simulation tool and investigate the charge separation dynamics in one, two and three-dimensional donor-acceptor networks to identify under what conditions underdamped vibrational motion induces efficient long-range charge separation. The resulting comprehensive picture of ultrafast charge separation differentiates electronic or vibronic couplings mechanisms for a wide range of driving forces and identifies the role of entropic effects in extended systems. This provides a toolbox for the design of efficient charge separation pathways in artificial nanostructures.

The simulation of quantum systems currently constitutes one of the most promising applications of quantum computers. However, the integration of more general partial differential equations (PDEs) for models of classical systems that are not governed by the laws of quantum mechanics remains a fundamental challenge. Current approaches such as the Variational Quantum Linear Solver (VQLS) method can accumulate large errors and the associated quantum circuits are difficult to optimize. A recent method based on the Feynmann-Kitaev formalism of quantum dynamics has been put forth, where the full evolution of the system can be retrieved after a single optimization of an appropriate cost function. This spacetime formulation alleviates the accumulation of errors, but its application is restricted to quantum systems only. In this work, we introduce an extension of this formalism applicable to the non-unitary dynamics of classical systems including for example, the modeling of diffusive transport or heat transfer. In addition, we demonstrate how PDEs with non-linear elements can also be integrated to incorporate turbulent phenomena.

Recent developments in qubit engineering make circuit quantum electrodynamics devices promising candidates for the study of Bloch oscillations (BOs) and Landau–Zener (LZ) transitions. In this work, a hybrid circuit chain with alternating site energies under external electric fields is employed to study Bloch–Zener oscillations (BZOs), i.e. coherent superpositions of BOs and LZ transitions. We couple each of the tunable qubits in the chain to dispersionless optical phonons and build an extended Holstein polaron model with the purpose of investigating vibronic effects in the BZOs. We employ an extension of the Davydov ansatz in combination with the Dirac–Frenkel time-dependent variational principle to simulate the dynamics of the qubit chain under the influence of high-frequency quantum harmonic oscillators. Band gaps emerge due to energy differences in site energies at alternating qubit sites, and are shown to play key roles in tuning band structures and time periodic reconstructions of the wave patterns. In the absence of qubit–phonon interactions, the qubits undergo either standard BZOs or breathing modes, depending on whether the initial wave packet is formed by a broad or narrow Gaussian wave packet, respectively. The BZOs can get localized in space if the band gaps are sufficiently large. In the presence of qubit–phonon coupling, the periodic behavior of BZOs can be washed out and undergo dynamic localization. The influence of an ohmic bath on the dynamics of BZOs is investigated by means of a Markovian master equation approach. Finally, we calculate the von Neumann entropy as a measure of the entanglement between qubits and phonons.

A method for the systematic construction of few-body damped harmonic oscillator networks accurately reproducing the effect of general bosonic environments in open quantum systems is presented. Under the sole assumptions of a Gaussian environment and regardless of the system coupled to it, an algorithm to determine the parameters of an equivalent set of interacting damped oscillators obeying a Markovian quantum master equation is introduced. By choosing a suitable coupling to the system and minimizing an appropriate distance between the two-time correlation function of this effective bath and that of the target environment, the error induced in the reduced dynamics of the system is brought under rigorous control. The interactions among the effective modes provide remarkable flexibility in replicating non-Markovian effects on the system even with a small number of oscillators, and the resulting Lindblad equation for the system and the modes may therefore be integrated at a very reasonable computational cost using standard methods for Markovian problems, even in strongly nonperturbative coupling regimes and at arbitrary temperatures including zero. We apply the method to an exactly solvable problem in order to demonstrate its accuracy, and present two studies based on current research in the context of coherent transport in biological aggregates and organic photovoltaics as more realistic examples of its use and potential; performance and versatility are highlighted, and theoretical and numerical advantages over existing methods, as well as possible future improvements, are discussed.

Charge and energy transfer in biological and synthetic organic materials are strongly influenced by the coupling of electronic states to a highly structured dissipative environment. Nonperturbative simulations of these systems require a substantial computational effort, and current methods can only be applied to large systems if environmental structures are severely coarse grained. Time evolution methods based on tensor networks are fundamentally limited by the times that can be reached due to the buildup of entanglement in time, which quickly increases the size of the tensor representation, i.e., the bond dimension. In this Letter, we introduce a dissipation-assisted matrix product factorization (DAMPF) method that combines a tensor network representation of the vibronic state within a pseudomode description of the environment where a continuous bosonic environment is mapped into a few harmonic oscillators under Lindblad damping. This framework is particularly suitable for a tensor network representation, since damping suppresses the entanglement growth among oscillators and significantly reduces the bond dimension required to achieve a desired accuracy. We show that dissipation removes the "time-wall" limitation of existing methods, enabling the long-time simulation of large vibronic systems consisting of 10-50 sites coupled to 100-1000 underdamped modes in total and for a wide range of parameter regimes. For these reasons, we believe that our formalism will facilitate the investigation of spatially extended systems with applications to quantum biology, organic photovoltaics, and quantum thermodynamics.

The measured multi-dimensional spectral response of different light harvesting complexes exhibits oscillatory features which suggest an underlying coherent energy transfer. However, making this inference rigorous is challenging due to the difficulty of isolating excited state coherences in highly congested spectra. In this work, we provide a coherent control scheme that suppresses ground state coherences, thus making rephasing spectra dominated by excited state coherences. We provide a benchmark for the scheme using a model dimeric system and numerically exact methods to analyze the spectral response. We argue that combining temporal and spectral control methods can facilitate a second generation of experiments that are tailored to extract desired information and thus significantly advance our understanding of complex open many-body structure and dynamics.

Self-assembled supramolecular aggregates are excellent candidates for the design of efficient excitation transport devices. Both artificially prepared and natural photosynthetic aggregates in plants and bacteria present an important degree of disorder that is supposed to hinder excitation transport. Besides, molecular excitations couple to nuclear motion affecting excitation transport in a variety of ways. We present an exhaustive study of exciton dynamics in disordered nanorings with long-range interactions under the influence of a phonon bath taking the LH2 system of purple bacteria as a model. Nuclear motion is explicitly taken into account by employing the Davydov ansatz description of the polaron and quantum dynamics are obtained using a time-dependent variational method. We reveal an optimal exciton-phonon coupling that suppresses disorder-induced localization and facilitate excitation de-trapping. This excitation transfer enhancement, mediated by environmental phonons, is attributed to energy relaxation toward extended, low-energy excitons provided by the precise LH2 geometry with anti-parallel dipoles and long-range interactions. An analysis of localization and spectral statistics is followed by dynamic measures of coherence and localization, transfer efficiency and superradiance. Linear absorption, 2D photon-echo spectra and diffusion measures of the exciton are examined to monitor the diffusive behavior as a function of the strengths of disorder and exciton-phonon coupling.

We study the effect of disorder on spectral properties of tubular chlorosomes in green sulfur bacteria Cf. aurantiacus. Employing a Frenkel-exciton Hamiltonian with diagonal and off-diagonal disorder consistent with spectral and structural studies, we analyze excitonic localization and spectral statistics of the chlorosomes. A size-dependent localization-delocalization crossover is found to occur as a function of the excitonic energy. The crossover energy region coincides with the more optically active states with maximized superradiance and is, consequently, more conducive for energy transfer.

Photosynthesis is one of the most essential biological processes in which specialized pigment-protein complexes absorb solar photons, and with a remarkably high efficiency, guide the photo-induced excitation energy toward the reaction center to subsequently trigger its conversion to chemical energy. In this work, we review the principles of optimal energy transfer in various natural and artificial light harvesting systems. We begin by presenting the guiding principles for optimizing the energy transfer efficiency in systems connected to dissipative environments, with particular attention paid to the potential role of quantum coherence in light harvesting systems. We will comment briefly on photo-protective mechanisms in natural systems that ensure optimal functionality under varying ambient conditions. For completeness, we will also present an overview of the charge separation and electron transfer pathways in reaction centers. Finally, recent theoretical and experimental progress on excitation energy transfer, charge separation, and charge transport in artificial light harvesting systems is delineated, with organic solar cells taken as prime examples.