# Quantum-classical hybrid computation of electron transfer in a cryptochrome protein via VQE-PDFT and multiscale modeling

## TL;DR

This paper introduces a quantum-classical hybrid method to accurately model electron transfer in cryptochrome proteins, achieving results consistent with experiments.

## Contribution

The novel VQE-PDFT framework combines quantum computing with classical methods to efficiently model electron correlations in biological systems.

## Key findings

- VQE-PDFT achieves results comparable to conventional MC-PDFT with reduced quantum resources.
- Electron transfer rates in ErCRY4 protein align with experimental measurements using the hybrid framework.
- Noise impact was analyzed on a 13-qubit superconducting device, demonstrating hardware feasibility.

## Abstract

Accurate calculation of strongly correlated electronic systems requires proper treatment of both static and dynamic correlations, which remains challenging for conventional methods. To address this, we present VQE-PDFT, a quantum-classical hybrid framework that integrates the variational quantum eigensolver with multiconfiguration pair-density functional theory (MC-PDFT). This framework strategically employs quantum circuits for multiconfigurational wavefunction representation while utilizing density functionals for correlation energy evaluation. The hybrid strategy maintains accurate treatment of static and dynamic correlations while reducing quantum resource requirements compared to highly expressive quantum algorithms. Benchmark validation, performed via a noiseless quantum circuit simulator, on the charge-transfer dataset confirmed that VQE-PDFT achieved results comparable to conventional MC-PDFT. Building upon this, we developed shallow-depth hardware-efficient ansatz circuits and integrated them into a QM/MM multiscale architecture to enable applications in complex biological systems. This extended framework, when applied to electron transfer in the European robin cryptochrome protein ErCRY4 with noiseless simulations, yielded transfer rates that aligned well with experimental measurements. Finally, as a proof-of-concept hardware demonstration, we executed reduced-density-matrix measurements for a single protein conformation on a 13-qubit superconducting device and showed the impact of noise through a comprehensive error analysis.

We leveraged superconducting quantum hardware within a VQE-PDFT framework to obtain critical active space energy differences in ErCRY4, facilitating reliable multiscale modeling of its electron transfer rates consistent with experimental data.