Quantum Equation of Motion for Computing Molecular Excitation Energies on Noisy Quantum Processors
This paper presents an innovative approach for computing molecular excitation energies by extending classical electronic structure methodologies to quantum computing. The research primarily focuses on adapting the equation of motion (EOM) method, a classical technique, to a quantum algorithm, yielding an approach referred to as quantum EOM (qEOM). This method demonstrates promise in accurately calculating excitation energies for molecular systems while mitigating errors due to the inherent noise found in current quantum hardware.
Overview of Contributions
The authors propose an adaptation of the well-established EOM method to a variational quantum eigensolver (VQE) framework, extending its application for computing excited states. The qEOM method is particularly suited for handling the challenges associated with correlated molecular systems, offering a viable alternative to conventional classical calculations which suffer from poor scaling with system size. The methodology is tested through extensive numerical simulations and experiments on IBM's quantum processors, making it a practical contribution to quantum chemistry on noisy intermediate-scale quantum (NISQ) devices.
Methodology
- Adaptation of EOM to qEOM: The theoretical foundation relies on expressing excited states as excitations from a ground state wave function and utilizing commutators to derive excitation energies. The qEOM utilizes double commutators to ensure Hermiticity, resulting in real-valued energy differences and enhancing algorithm stability.
- Algorithm Implementation: The authors implemented the qEOM in Qiskit to enable realistic simulations on IBM's quantum devices. They performed statevector simulations and mitigated hardware noise to evaluate qEOM on small molecules like H₂, LiH, and H₂O.
- Reduction of Circuit Complexity: In the case of LiH, a reduction in active space from 10 to 4 qubits was achieved, coupled with optimization of the unitary coupled cluster (UCC) quantum circuits. This reduced the circuit complexity significantly without substantial loss in accuracy.
Numerical and Experimental Results
- Simulation Accuracy: Testing on molecular systems such as H₂, LiH, and H₂O demonstrated that qEOM can produce excitation energies within chemical accuracy. The performance on both simulated and real-device experiments showed qEOM’s robustness against varied levels of noise.
- Experimental Implementation: Using IBM's 20-qubit superconducting processor, the research exhibited stable calculations of LiH excitation energies through advanced error mitigation strategies. These techniques reduced extrapolated energy errors by an order of magnitude, underscoring the method’s experimental viability.
Implications and Future Directions
The successful demonstration of qEOM shows significant potential for future applications in quantum chemistry, particularly in photochemistry where accurate excited-state calculations are critical. The method’s robustness and efficient measurement scaling could accelerate the practical integration of quantum algorithms in standard chemical simulations.
This research contributes to bridging the gap between theoretical quantum algorithms and their experimental implementation on NISQ devices. Future work could involve extending the approach to other chemical systems and exploring more efficient error correction mechanisms to further enhance the accuracy and scalability of quantum computations in chemical applications.