A Feasible Approach for Automatically Differentiable Unitary Coupled-Cluster on Quantum Computers

TL;DR

This paper introduces an efficient, encoding-independent method for computing gradients of unitary coupled-cluster operators on quantum computers, significantly reducing computational costs compared to standard approaches.

Contribution

The authors develop a new framework for gradient evaluation that is computationally affordable and independent of encoding, enabling practical quantum chemistry applications.

Findings

Gradient evaluation requires only four expectation values, reducing cost from exponential to polynomial.

For real wavefunctions, the cost is further reduced to two expectation values.

Implemented in open-source package tequila, demonstrating initial applications in electronic states.

Abstract

We develop computationally affordable and encoding independent gradient evaluation procedures for unitary coupled-cluster type operators, applicable on quantum computers. We show that, within our framework, the gradient of an expectation value with respect to a parameterized n-fold fermionic excitation can be evaluated by four expectation values of similar form and size, whereas most standard approaches based on the direct application of the parameter-shift-rule come with an associated cost of O(2^(2n)) expectation values. For real wavefunctions, this cost can be further reduced to two expectation values. Our strategies are implemented within the open-source package tequila and allow blackboard style construction of differentiable objective functions. We illustrate initial applications for electronic ground and excited states.