Many-body approach to projective solution of generalized operators: Formulation and application to quantum computing

Area of Science:

• Quantum Chemistry
• Computational Physics
• Many-Body Theory

Background:

• Coupled-cluster (CC) methods are standard for accurate electronic structure calculations.
• Higher-order excitations are crucial for precise energy determination but computationally expensive.
• Existing quantum algorithms face challenges with resource requirements and noise sensitivity.

Purpose of the Study:

• To introduce a novel many-body approach for calculating generalized operator amplitudes.
• To develop a formalism that accounts for higher-order excitations efficiently.
• To enhance the performance and noise resilience of quantum eigensolvers.

Main Methods:

• Utilized a double-exponential coupled-cluster (CC) ansatz with generalized operators.
• Developed a projection-based formalism to manage redundancy and optimize operators.
• Integrated the method with the projective quantum eigensolver (PQE) framework for iterative decoupling.
• Employed residual minimization for optimizing the quantum eigensolver.

Main Results:

• Achieved accuracy comparable to disentangled unitary coupled cluster with singles, doubles, and triples (UCCSDT).
• Required an order of magnitude fewer quantum resources compared to UCCSDT.
• Demonstrated significantly improved noise resilience against stochastic and hardware noise compared to other PQE methods and variational quantum eigensolver (VQE).

Conclusions:

• The developed many-body approach offers a resource-efficient and noise-resilient alternative for quantum electronic structure calculations.
• This method enhances the practical applicability of quantum computation for molecular systems.
• The findings pave the way for more accurate and robust quantum simulations in chemistry and physics.