Toward a resource-optimized dynamic quantum algorithm via non-iterative auxiliary subspace corrections

Area of Science:

• Quantum computing
• Computational chemistry
• Electronic structure theory

Background:

• Current quantum algorithms for electronic structure theory dynamically build ansatzs using many-body operators.
• Increasing ansatz complexity for accuracy leads to deep quantum circuits, especially for highly correlated systems.
• Deep circuits pose significant resource challenges for quantum computation.

Purpose of the Study:

• To develop a novel theoretical framework to reduce quantum circuit depth in electronic structure calculations.
• To enhance the efficiency and accuracy of quantum algorithms for molecular systems.
• To address the limitations of current threshold-based dynamic ansatz construction.

Main Methods:

• Segregating the ansatz into a dynamically selected core 'principal' component and an 'auxiliary' component.
• Performing computations on the principal component using shallow-depth circuits.
• Incorporating the effect of the auxiliary component via cost-efficient, non-iterative energy corrections.
• Developing a formalism for analytical prediction of auxiliary parameters from principal ones.
• Employing non-iterative auxiliary subspace correction techniques.

Main Results:

• The proposed framework significantly reduces quantum circuit depth.
• Non-iterative auxiliary subspace corrections recover substantial electronic correlations without additional quantum resources.
• The method ensures requisite accuracy by efficiently folding in the auxiliary component's effects.
• Numerical validation on strongly correlated molecular systems demonstrates resource efficiency and accuracy.

Conclusions:

• The novel theoretical framework offers a resource-efficient approach to quantum electronic structure calculations.
• This method effectively mitigates the issue of rapidly proliferating circuit depth in highly correlated systems.
• The segregation and correction strategy provides a pathway to more feasible and accurate quantum chemistry simulations.