Filtering states with total spin on a quantum computer

TL;DR

This paper introduces quantum algorithms for projecting a general wave function onto total spin eigenstates, enabling extraction of spin components and degeneracy lifting, with applications in physics and quantum information.

Contribution

It proposes novel quantum algorithms for total spin filtering that can project states onto specific spin subspaces and resolve degeneracies, advancing quantum state analysis techniques.

Findings

Algorithms successfully project onto total spin eigenstates

State collapses to specific spin eigenstates after measurement

Potential applications in many-body physics and quantum information

Abstract

Starting from a general wave function described on a set of spins/qubits, we propose several quantum algorithms to extract the components of this state on eigenstates of the total spin ${\bf S}^2$ and its azimuthal projection $S_z$. The method plays the role of total spin projection and gives access to the amplitudes of the initial state on a total spin basis. The different algorithms have various degrees of sophistication depending on the requested tasks. They can either solely project onto the subspace with good total spin or completely uplift the degeneracy in this subspace. After each measurement, the state collapses to one of the spin eigenstates that could be used for post-processing. For this reason, we call the method Total Quantum Spin filtering (TQSf). Possible applications ranging from many-body physics to random number generators are discussed.