Quantum Algorithm for Vibronic Dynamics: Case Study on Singlet Fission Solar Cell Design

TL;DR

This work addresses the challenge of simulating fully quantum non-adiabatic vibronic dynamics, which are essential for understanding photo-induced processes but intractable with classical methods. It introduces a scalable digital quantum algorithm based on a product-form (Trotter) time-evolution of a general vibronic Hamiltonian, including an explicit fragmentation and block-diagonalization strategy that extends beyond two electronic states and leverages a caching scheme to reduce arithmetic costs. The authors provide complexity scaling, discuss efficient initial-state preparation and observable extraction (notably electronic-state populations and spectra), and demonstrate the method’s relevance by outlining a proof-of-principle pipeline for designing singlet fission chromophores, with concrete resource estimates for representative SF models. The work thereby offers a pathway to accelerate materials discovery for SF-based solar cells by enabling accurate quantum non-adiabatic dynamics previously limited to small systems, while acknowledging challenges in obtaining accurate vibronic couplings from electronic structure calculations.

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 $2.76 \times 10^6$ Toffoli gates. While a $4$-state, $246$-mode model describing charge transfer at an anthracene-fullerene interface requires $1053$ qubits and $2.66 \times 10^7$ Toffoli gates.

Figures (5)

• Figure 1: Proof-of-principle integration of our quantum algorithm into a materials discovery workflow. (A) Following the initialization or modification of a molecule, electronic structure calculations are performed, leveraging either quantum or classical resources to construct the vibronic model. For vibronic Hamiltonians employed in ultrafast photochemistry, this procedure typically includes geometry optimization, a normal-mode analysis following the calculation of the Hessian, and excited-state calculations at points along normal mode displacements. (B) The non-adiabatic dynamics for the vibronic Hamiltonian are performed on a quantum computer using the algorithm presented in Section \ref{['sec:algorithm']}, producing observable quantities such as diabatic state populations and photoabsorption spectra. (C) The interpretation of the output observables is used to inform a change to molecular candidates to optimize properties such as transition rates and excited-state lifetimes.
• Figure 2: a) Fragmentation of the vibronic potential $V$ for the $N=4$ case. b) Illustrative examples of the Clifford block-diagonalization for fragments $H_1$ and $H_3$. $\texttt{Had}_i$ denotes application of Hadamard gate on qubit $i$, and $\texttt{CNOT}_{ij}$ denotes a CNOT controlled by qubit $i$ and targetting qubit $j$.
• Figure 3: Example circuit implementation for a term of the form $\sum_j \ket{j}\bra{j}\otimes \exp\left(i \Delta^2 c_{(1,1)}^{(j,j)} x_0x_1\right)$. Where $\delta$ is the fixed point precision used to represent the coefficients in the Hamiltonian, and Mult denotes a quantum arithmetic multiplication gate as described in Ref. su2021fault.
• Figure 4: A proof-of-principle SF chromophore design pipeline utilizing the iterative workflow from \ref{['fig:workflow']}, with stages for (A) singlet fission, (B) triplet separation, and (C) charge transfer optimization. (A): A set of candidate SF chromophores is assessed based on the theoretical rate of singlet fission. Depicted is a set of anthracene derivatives generated via functional group and heteroatom substitutions (left) and a pictorial description of the SF process (right), where a singlet exciton state (red) converts to two triplets (blue) localized at the ends of the chromophore. (B): Following the selection of an SF chromophore, covalent linking strategies are optimized to enable efficient triplet separation. Various bridges and conformational arrangements would be assessed (left) to provide the most rapid triplet separation, where a triplet-pair local to a single SF chromophore converts to two triplets isolated to individual chromophores (right). (C): Finally, the charge transfer rate could be optimized using different chromophore/acceptor strategies, such as chromophore/acceptor covalent linking (left), in analogy to the optimization of step (B), to ensure efficient transfer from a triplet exciton to a charge-separated state at the acceptor interface (right).
• Figure 5: A simplified orbital depiction of the processes relevant to the performance of a SF chromophore layer, including a) the fission of a photoexcited singlet into two adjacent triplet excitons, b) separation of the spin-coupled triplet pair, and c) charge transfer from an excitonic donor to an acceptor at the chromophore-acceptor interface.

Theorems & Definitions (2)

• Theorem 1
• proof : Proof of \ref{['thm:complexity']}