An Efficient Quantum Algorithm and Circuit to Generate Eigenstates of SU(2) and SU(3) Representations

TL;DR

This paper introduces a resource-efficient quantum algorithm and circuit design for generating eigenstates of SU(2) and SU(3) representations, including highly entangled states, using the Schur transform with polynomial resources.

Contribution

It provides the first explicit quantum circuits for eigenstate generation of SU(2) and SU(3), with a method that can be extended to higher groups.

Findings

Efficient polynomial-resource quantum algorithm for SU(2) and SU(3) eigenstates.

Explicit quantum circuits for generating highly entangled states.

Generalization potential to higher symmetry groups.

Abstract

This thesis presents an efficient quantum algorithm and explicit circuits for generating eigenstates of arbitrary SU(2) and SU(3) representations. These include a wide variety of highly entangled states. The algorithm uses Schur transform that rotates the input computational basis states to the output Schur basis states with resources polynomial in number of qudits n. Using the fact that quantum logic is reversible, we accomplish the desired result using the inverse Schur transform. The algorithm can be easily generalized to any arbitrary higher groups.