Restoring broken symmetries using oracles

TL;DR

This paper introduces a quantum algorithm that restores symmetries in many-body systems without explicit projection, using oracles and ancillary qubits, demonstrated on the pairing model Hamiltonian.

Contribution

It presents a novel quantum method employing oracles for symmetry restoration in many-body systems, avoiding explicit projection procedures.

Findings

Successfully constructs oracles for symmetry operators

Restores symmetries via indirect measurements with a single ancilla

Achieves approximate ground state energy for pairing model

Abstract

We present a new method to perform variation after projection in many-body systems on quantum computers that does not require performing explicit projection. The technique employs the notion of ``oracle'', generally used in quantum search algorithms. We show how to construct the oracle and the projector associated with a symmetry operator. The procedure is illustrated for the parity, particle number, and total spin symmetries. The oracle is used to restore symmetry by indirect measurements using a single ancillary qubit. An Illustration of the technique is made to obtain the approximate ground state energy for the pairing model Hamiltonian.