Quantum Resource Assay for the Grid-Based Simulation of the Photodynamics of Pyrazine

Abstract

We establish and analyse the performance and resource requirements of an end-to-end fault-tolerant quantum algorithm for computing the absorption spectrum and population dynamics of photoexcited pyrazine. The quantum circuit construction consists of initial state preparation using uniformly controlled rotations, the time-dependent Hamiltonian propagation based on the grid-based Split Operator Quantum Fourier Transform (SO-QFT) method, and cost-effective measurements including statistical and canonical phase estimation. We use classical emulations to validate the quantum resources required for the task, and propose generalised formulae for the qubit count and gate depth calculation. Simulating the vibronic dynamics of pyrazine in a low-dimensional abstraction requires 17-qubit circuits with a gate depth of $\mathcal{O}(10^5)$, whereas a full-dimensional simulation of pyrazine in 24 modes requires at least 97-qubit circuits with a gate depth of $\mathcal{O}(10^6)$. Our work provides a foundational framework for understanding high-dimensional wavepacket-based quantum simulations of photo-induced dynamics and vibronic spectra, anticipating future applications in the simulation of even larger molecular systems on fault-tolerant quantum computers.

Figures (24)

• Figure 1: Schematic overview of the proposed end-to-end quantum algorithmic framework, comprising three main stages: state preparation, time evolution, and signal processing. Each component is discussed in detail in Sections \ref{['State preparation']}- \ref{['signal processing']}.
• Figure 2: Quantum circuit of time evolution for one time step $dt$.
• Figure 3: Autocorrelation measurement at a single time step using an ancillary qubit.
• Figure 4: Spectrum signal measurements using canonical QPE techniques, with $m$ qubits in the time register.
• Figure 5: Maximum values of the probability density at the boundaries of the simulation box for each normal mode as a function of time. The persistently low amplitudes indicate that the chosen simulation size is sufficient to contain the evolving wavefunction.