State-specific Orbital Optimization Enhances Excited-States Calculation on Quantum Computers

Calculating the excited states of molecules presents a significant challenge for quantum computers, limiting their potential for simulating complex chemical processes. Guorui Zhu, Joel Bierman, Jianfeng Lu, and Yingzhou Li address this problem by developing a new method for optimising the orbitals used in these calculations. Their approach allows for state-specific orbital adjustments, offering greater flexibility and accuracy than existing techniques which typically use a single set of orbitals for all excited states. The team demonstrates that this optimisation scheme, when combined with a deflation method, substantially improves the accuracy of excited state calculations for molecules such as H4 and LiH, representing a key step towards reliable molecular simulations on near-term quantum computers.

This tailored approach allows for a more accurate description of the electronic structure and improves the overall fidelity of excited-state calculations by individually optimising orbitals for each excited state of interest. The core of this work is a variational algorithm that directly optimises molecular orbitals for a given excited state while simultaneously minimising the energy expectation value. This optimisation process leverages the unique capabilities of quantum computers to efficiently explore orbital configurations. The algorithm incorporates a penalty term to ensure physically meaningful solutions by enforcing orthogonality between occupied and virtual orbitals, and addresses state-specific symmetry breaking by allowing orbital rotations that adapt to the symmetry of each excited state. Numerical simulations on model molecular systems demonstrate a substantial improvement in the accuracy of calculated excited-state energies compared to conventional methods, particularly for systems exhibiting strong static correlation.

Variational Quantum Eigensolvers for Excited States

This research focuses on improving the efficiency and accuracy of variational quantum eigensolvers (VQEs) for calculating excited states of molecules. Researchers explored methods to improve the molecular orbitals used in VQE calculations, recognising that orbital quality significantly impacts results. The team investigated state-averaged and orthogonally constrained orbital optimisation, alongside orbital minimisation techniques to reduce qubit requirements, and derivative-free optimisation algorithms such as model-based optimisation and Powell’s method to avoid computationally expensive gradient calculations. The mathematical formalism involving creation and annihilation operators, known as second quantisation, is fundamental to the theoretical framework. This formalism expresses the quantum mechanical Hamiltonian in terms of these operators, simplifying Hamiltonian construction and facilitating mapping to qubit operators for implementation on quantum computers, leading to more efficient quantum circuits. This work combines orbital optimisation with derivative-free optimisation, develops efficient quantum circuits, and addresses the challenges of excited state calculations, ultimately reducing qubit requirements and improving accuracy.

State-Specific Orbitals Enhance Excited-State Accuracy

This research introduces a new state-specific orbital optimisation scheme designed to improve the accuracy of excited-state calculations for use on quantum computers. By allowing tailored orbitals for each electronic state, the method expands upon existing state-averaged approaches and offers greater flexibility in electronic structure calculations. Researchers successfully derived a gradient for the overlap between states generated using different orbitals, then employed gradient-based optimisation methods to refine these orbitals. Implementation within the Variational Quantum Deflation algorithm, and testing on molecules including H4 and LiH, demonstrates that the state-specific approach achieves higher accuracy than the state-averaged method. Future research directions include combining state-averaged and state-specific strategies, potentially allowing certain states to share common orbitals while others utilise individually optimised sets, which could be particularly useful for degenerate states and extend to practical settings such as efficient frozen-core calculations.