Quantum-Classical Hybrid Computation of Electron Transfer in a Cryptochrome Protein via VQE-PDFT and Multiscale Modeling

TL;DR

This paper introduces VQE-PDFT, a quantum-classical hybrid method combining quantum circuits and density functionals to accurately model electron transfer in biological systems, validated through simulations and hardware experiments.

Contribution

The work develops a novel hybrid framework integrating VQE with MC-PDFT, reducing quantum resource needs and enabling applications in complex biological systems.

Findings

VQE-PDFT achieves results comparable to conventional MC-PDFT on benchmark datasets.

Shallow-depth ansatz circuits enable practical quantum simulations of biological electron transfer.

Hardware experiments demonstrate feasibility and analyze noise impacts on quantum measurements.

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,aquantum-classical hybrid framework that integrates 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 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 the 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.