Optimization of the Qubit Coupled Cluster Ansatz on Classical Computers

Area of Science:

• Quantum computing
• Computational chemistry
• Electronic structure theory

Background:

• Quantum computing is driving the development of new electronic structure methods.
• Quantum hardware limitations necessitate quantum-inspired algorithms for classical implementation.
• Efficient algorithms are crucial for exploiting the potential of quantum-inspired methods.

Purpose of the Study:

• To introduce two novel schemes for optimizing amplitudes in the iterative qubit coupled cluster (iQCC) method.
• To enhance the efficiency and accuracy of quantum-inspired electronic structure calculations.
• To enable larger and more complex molecular systems to be studied.

Main Methods:

• Developed a variational quantum eigensolver-type approach approximating the qubit coupled cluster (QCC) unitary with polynomial expansions.
• Introduced a second scheme to limit the expansion space of the QCC unitary for memory control.
• Applied these schemes to optimize QCC amplitudes for molecular systems.

Main Results:

• The polynomial approximation scheme offers tunable computational complexity and smooth energy landscapes for gradient-based optimization.
• The expansion space limitation scheme provides memory control and enables energy extrapolation.
• Both schemes allow for more generators in the QCC form, reducing iterations and improving accuracy.
• Successfully tested on dinitrogen, water, and Ir(F2ppy)3 molecular systems.

Conclusions:

• The proposed amplitude optimization schemes significantly improve the performance of the iQCC method.
• These advancements facilitate more accurate and efficient quantum-inspired electronic structure calculations.
• The methods pave the way for tackling larger molecular systems on current and future hardware.