Abstract Vibronic interactions between nuclear motion and electronic states are critical for the accurate modeling of photochemistry. However, accurate simulations of fully quantum non-adiabatic dynamics are often prohibitively expensive for classical methods beyond small systems. In this work, we present a quantum algorithm based on product formulas for simulating time evolution under a general vibronic Hamiltonian in real space, capable of handling an arbitrary number of electronic states and vibrational modes. We develop the first trotterization scheme for vibronic Hamiltonians beyond two electronic states and introduce an array of optimization techniques for the exponentiation of each fragment in the product formula, resulting in a remarkably low cost of implementation. To demonstrate practical relevance, we outline a proof-of-principle integration of our algorithm into a materials discovery pipeline for designing more efficient singlet fission-based organic solar cells. We estimate that 100 fs of propagation using a second-order Trotter product formula for a 6-state, 21-mode model of exciton transport at an anthracene dimer requires 154 qubits and 2.76 × 106 Toffoli gates. While a 4-state, 246-mode model describing charge transfer at an anthracene-fullerene interface requires 1053 qubits and 2.66 × 107 Toffoli gates.
Abstract Vibronic interactions between nuclear motion and electronic states are critical for the accurate modeling of photochemistry. However, accurate simulations of fully quantum non-adiabatic dynamics are often prohibitively expensive for classical methods beyond small systems. In this work, we present a quantum algorithm based on product formulas for simulating time evolution under a general vibronic Hamiltonian in real space, capable of handling an arbitrary number of electronic states and vibrational modes. We develop the first trotterization scheme for vibronic Hamiltonians beyond two electronic states and introduce an array of optimization techniques for the exponentiation of each fragment in the product formula, resulting in a remarkably low cost of implementation. To demonstrate practical relevance, we outline a proof-of-principle integration of our algorithm into a materials discovery pipeline for designing more efficient singlet fission-based organic solar cells. We estimate that 100 fs of propagation using a second-order Trotter product formula for a 6-state, 21-mode model of exciton transport at an anthracene dimer requires 154 qubits and 2.76 × 106 Toffoli gates. While a 4-state, 246-mode model describing charge transfer at an anthracene-fullerene interface requires 1053 qubits and 2.66 × 107 Toffoli gates.
Non-adiabatic dynamics at molecule-metal interfaces govern diverse and technologically important phenomena, from heterogeneous catalysis to dye-sensitized solar energy conversion and charge transport across molecular junctions. Realistic modeling of such dynamics necessitates taking into account various charge and energy transfer channels involving the coupling of nuclear motion with a very large number of electronic states, leading to prohibitive cost using classical computational methods. In this work we introduce a generalization of the Anderson-Newns Hamiltonian and develop a highly optimized quantum algorithm for simulating the non-adiabatic dynamics of realistic molecule-metal interfaces. Using the PennyLane software platform, we perform resource estimations of our algorithm, showing its remarkably low implementation cost for model systems representative of various scientifically and industrially relevant molecule-metal systems. Specifically, we find that time evolution for models including 100 metal orbitals, 8 molecular orbitals, and 20 nuclear degrees of freedom, requires only 271 qubits and 7.9×107 Toffoli gates for 1000 Trotter steps, suggesting non-adiabatic molecule-metal dynamics as a fruitful application of first-generation fault-tolerant quantum computers.
Simulating vibrational dynamics is essential for understanding molecular structure, unlocking useful applications such as vibrational spectroscopy for high-fidelity chemical detection. Quantum algorithms for vibrational dynamics are emerging as a promising alternative to resource-demanding classical approaches, but this domain is largely underdeveloped compared with quantum simulations of electronic structure. In this work, we describe in detail three distinct forms of the vibrational Hamiltonian: canonical bosonic quantization, real space representation, and the Christiansen second-quantized form. Leveraging the Lie algebraic properties of each, we develop efficient fragmentation schemes to enable the use of Trotter product formulas for simulating time evolution. We introduce circuits required to implement time evolution in each form and highlight factors that contribute to the simulation cost, including the choice of vibrational coordinates. Using a perturbative approach for the Trotter error, we obtain tight estimates of the T gate cost for the simulation of time evolution in each form, enabling their quantitative comparison. Combining tight Trotter error estimates and efficient fragmentation schemes, we find that for the CH 4 molecule with 9 vibrational modes, time evolution for approximately 1.8 ps may be simulated using as few as 36 qubits and approximately 3 × 10 8 T gates─an order-of-magnitude speedup over state-of-the-art algorithms. Finally, we present calculations of vibrational spectra using each form to demonstrate the fidelity of our algorithms. This work presents a unified and highly optimized framework that makes simulating vibrational dynamics an attractive use case for quantum computers.
Solar cell technology has reached a limiting efficiency, now known as the Shockley-Queisser efficiency limit, and researchers are investigating novel strategies like quantum mechanics to surpass this limit. Restriction is imposed by the fact that singlet fission singlet fission , a quantum process, doubles the number of charge carriers charge carriers per photon generated, which results in giving two low-energy excitons from one high-energy photon. But classical simulations would find it inherently difficult to avoid the cryptic nature of its underlying quantum structure, that is, based in coherence, spin states, and environmental influence. The principle of quantum mechanics enables the development of special quantum simulation quantum simulation as a revolutionary way of performing and improving singlet fission research. The material can be screened, the electrical structure studied, and the device or optoelectronic optimized while keeping the material quantum coherent. Hybrid quantum-classical approaches reduce the computational burdens of existing hardware, while sophisticated algorithms such as quantum phase estimation and variational quantum eigensolvers are used to accurately model molecular energetics. To efficiently simulate singlet fission in molecular systems (both simple models, such as linear H 4 molecules, as well as more complicated materials), this work relies on the PDS( K ) energy functional framework. Such a technique alleviates quantum resource limits by carrying out fewer Pauli string measurements, shorter qubits, and using commutativity principles to simplify calculation. Researchers thus find potential materials by modeling quantum states and excitonic transitions and improve device topologies to find the most efficient paths for converting that energy. But there are still distances to go, from producing stable, affordable materials to scaling up quantum technology. This, however, demonstrates that quantum simulation can propel solar cells to entirely novel heights, where they can be paired with existing science, such as perovskite solar cells. The potential for lower energy expenses and environmental gains are business implications. This is a revolutionary development in device engineering, quantum computing, and material discovery material discovery – the bellwether for the future of sustainable energy. Long-lasting solar cells result from quantum hardware and algorithms progressing alongside quantum theory and experimental testing, culminating in ultraefficient processes. So, quantum simulation represents an important breakthrough with respect to the efforts needed to solve the world’s energy problems and to promote an environmentally friendly and energy-secure future.
We develop a powerful tree tensor network states method that is capable of simulating exciton-phonon quantum dynamics of larger molecular complexes and open quantum systems with multiple bosonic environments. We interface this method with ab initio density functional theory to study singlet exciton fission (SF) in a pentacene dimer. With access to the full vibronic many-body wave function, we track and assign the contributions of different symmetry classes of vibrations to SF and derive energy surfaces, enabling us to dissect, understand, and describe the strongly coupled electronic and vibrational dynamics, relaxation, and reduced state cooling. This directly exposes the rich possibilities of exploiting the functional interplay of molecular symmetry, electronic structure and vibrational dynamics in SF material design. The described method can be similarly applied to other complex (bio-) molecular systems, characterised by a rich manifold of electronic states and vibronic coupling driving non-adiabatic dynamics.
Abstract Quantum simulation offers a route to study open-system molecular dynamics in non-perturbative regimes by programming the interactions among electronic, vibrational, and environmental degrees of freedom on similar energy scales. Trapped-ion systems possess this capability, with their native spins, phonons, and tunable dissipation integrated within a single platform. Here, we demonstrate an open-system quantum simulation of charge and exciton transfer in a multi-mode linear vibronic coupling model. Employing tailored spin-phonon interactions alongside reservoir engineering techniques, we emulate a system with two dissipative vibrational modes coupled to donor and acceptor electronic sites and follow its non-equilibrium dynamics. We continuously tune the system from the charge transfer (CT) regime to the vibrationally assisted exciton transfer (VAET) regime by controlling the vibronic coupling strengths. We find that degenerate modes enhance CT and VAET rates at large energy gaps, while non-degenerate modes activate slow-mode pathways that reduce the energy-gap dependence, thus enlarging the window for efficient transfer. These results show that the presence of one additional vibration introduces interfering vibrationally assisted pathways and reshapes non-perturbative quantum excitation transfer. Our work establishes a scalable route to simulating chemically relevant, many-mode vibronic processes with engineered environments, guiding the design of next-generation organic photovoltaics and molecular electronics.
In this work we propose an approach for implementing time-evolution of a quantum system using product formulas. The quantum algorithms we develop have provably better scaling (in terms of gate complexity and circuit depth) than a naive application of well-known Trotter formulas, for systems where the evolution is determined by a Hamiltonian with different energy scales (i.e., one part is "large" and another part is "small"). Our algorithms generate a decomposition of the evolution operator into a product of simple unitaries that are directly implementable on a quantum computer. Although the theoretical scaling is suboptimal compared with state-of-the-art algorithms (e.g., quantum signal processing), the performance of the algorithms we propose is highly competitive in practice. We illustrate this via extensive numerical simulations for several models. For instance, in the strong-field regime of the 1D transverse-field Ising model, our algorithms achieve an improvement of one order of magnitude in both the system size and evolution time that can be simulated with a fixed budget of 1000 arbitrary 2-qubit gates, compared with standard Trotter formulas.