Qubit-Efficient Quantum Chemistry with the ADAPT Variational Quantum Eigensolver and Double Unitary Downfolding

Area of Science:

• Quantum chemistry
• Computational physics
• Quantum computing

Background:

• Accurate quantum simulations are crucial for understanding chemical systems.
• Developing efficient quantum algorithms is key for advancing computational chemistry.
• Unitary downfolding methods aim to reduce the complexity of quantum many-body problems.

Purpose of the Study:

• To assess the accuracy of double unitary coupled cluster (DUCC) effective Hamiltonians for quantum simulation.
• To investigate the ability of DUCC Hamiltonians to capture dynamical correlation energy beyond an active space.
• To evaluate the performance of DUCC Hamiltonians when combined with the adaptive variational quantum eigensolver (ADAPT-VQE).

Main Methods:

• Combining double unitary coupled cluster (DUCC) theory with the adaptive variational quantum eigensolver (ADAPT-VQE).
• Benchmarking DUCC effective Hamiltonians against established methods for recovering dynamical correlation energy.
• Analyzing the impact of strong correlation, commutator truncation, higher-body terms, and approximate amplitudes on Hamiltonian accuracy.

Main Results:

• DUCC effective Hamiltonians show promise in recovering dynamical correlation energy outside the active space.
• The combination of DUCC Hamiltonians with ADAPT-VQE demonstrates comparable ground-state convergence to standard active space Hamiltonians.
• Accuracy improvements were observed without a corresponding increase in the computational resources required on quantum processors.

Conclusions:

• DUCC effective Hamiltonians offer a pathway to more accurate quantum simulations in chemistry.
• Integrating DUCC with ADAPT-VQE provides a powerful hybrid quantum-classical approach for electronic structure calculations.
• This work highlights the potential of unitary downfolding techniques to enhance the efficiency and accuracy of quantum computational chemistry.