Quantum many-body linear algebra, Hamiltonian moments, and a coupled-cluster inspired framework

Area of Science:

• Quantum computing
• Computational chemistry
• Linear algebra

Background:

• Developing efficient quantum algorithms for linear algebra is crucial for scientific discovery.
• Current methods often rely on perturbation theory, which has limitations.
• Quantum many-body approximations offer a potential avenue for improvement.

Purpose of the Study:

• To propose a general strategy for creating quantum many-body approximations for linear algebra primitives.
• To introduce a coupled-cluster inspired framework for approximate Hamiltonian moments.
• To demonstrate the application of this framework in ground state estimation algorithms.

Main Methods:

• Developing a general strategy for quantum many-body approximations.
• Implementing a coupled-cluster inspired framework to calculate approximate Hamiltonian moments.
• Applying these approximations to linear algebra algorithms for ground state estimation.

Main Results:

• The coupled-cluster inspired framework successfully produces approximate Hamiltonian moments.
• Numerical examples show differences in ground-state energies compared to many-body perturbation theory.
• The strategy provides a viable alternative to perturbation theory for quantum algorithms.

Conclusions:

• Quantum many-body approximations beyond perturbation theory are feasible.
• This work offers a new route for designing advanced quantum algorithms.
• The proposed strategy can enhance the efficiency and accuracy of quantum linear algebra computations.