Twirling Operations to Produce Energy Eigenstates of a Hamiltonian by Classically Emulated Quantum Simulation

TL;DR

This paper introduces a method using ancilla qubits and entanglement to generate energy eigenstates of a Hamiltonian, demonstrated on the Schwinger model, with potential for broad applicability in finite-dimensional quantum systems.

Contribution

The authors present a novel, simple procedure employing classical emulation and entanglement to produce specific energy eigenstates of a Hamiltonian.

Findings

Successfully applied to the (1+1)-D massless Schwinger model

Can produce any energy eigenstate with proper initial state selection

Applicable to Hamiltonians with finite-dimensional Hilbert spaces

Abstract

We propose a simple procedure to produce energy eigenstates of a Hamiltonian with discrete eigenvalues. We use ancilla qubits and quantum entanglement to separate an energy eigenstate from the other energy eigenstates. We exhibit a few examples derived from the (1+1)-dimensional massless Schwinger model. Our procedure in principle will be applicable for a Hamiltonian with a finite dimensional Hilbert space. Choosing an initial state properly, we can in principle produce any energy eigenstate of the Hamiltonian.