A stochastic approach to unitary coupled cluster.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Quantum Computing Algorithms

Background:

• Unitary Coupled Cluster (UCC) is a quantum chemistry method adapted for quantum computers.
• The complexity of UCC wavefunctions (Ansatz) hinders current quantum implementations.
• Quantum Monte Carlo methods provide sparse wavefunctions suitable for stochastic approaches.

Purpose of the Study:

• To develop a stochastic solution for the Unitary Coupled Cluster (UCC) problem.
• To enable efficient UCC calculations on quantum computers by addressing Ansatz size limitations.
• To explore a novel, scalable quantum computational chemistry approach.

Main Methods:

• Utilizing the coupled cluster Monte Carlo framework.
• Developing cluster selection schemes to represent UCC wavefunction structure.
• Solving projected equations for both UCC and its Trotterized approximation.
• Employing stochastic methods to handle wavefunction sparsity.

Main Results:

• The stochastic UCC approach scales polynomially with system size.
• A non-variational projected energy estimator is naturally produced.
• For small systems (e.g., two electrons), results align with Full Configuration Interaction (FCI).
• For larger systems (N2), projected energy converges to coupled cluster, while expectation values differ.

Conclusions:

• Stochastic UCC offers a scalable and efficient alternative for quantum computations.
• The projected energy estimator provides a valuable, non-variational metric.
• This method bridges the gap between quantum Monte Carlo sparsity and UCC computational demands.