Generalization of group-theoretic coherent states for variational calculations

TL;DR

This paper develops a new class of quantum states based on group-theoretic coherent states, enabling efficient evaluation of observables and increased entanglement for variational quantum calculations.

Contribution

It introduces a method to generate entangled states from group-theoretic coherent states using quadratic operators, expanding their applicability in quantum variational methods.

Findings

Allows efficient computation of observable expectation values.

Generates entanglement beyond original coherent states.

Applicable to various Lie groups and quantum systems.

Abstract

We introduce new families of pure quantum states that are constructed on top of the well-known Gilmore-Perelomov group-theoretic coherent states. We do this by constructing unitaries as the exponential of operators quadratic in Cartan subalgebra elements and by applying these unitaries to regular group-theoretic coherent states. This enables us to generate entanglement not found in the coherent states themselves, while retaining many of their desirable properties. Most importantly, we explain how the expectation values of physical observables can be evaluated efficiently. Examples include generalized spin-coherent states and generalized Gaussian states, but our construction can be applied to any Lie group represented on the Hilbert space of a quantum system. We comment on their applicability as variational families in condensed matter physics and quantum information.