# Quantum algorithm for spectral projection by measuring an ancilla iteratively

## TL;DR

This paper introduces a quantum algorithm that projects a system onto eigenstates of any Hermitian operator using iterative ancilla measurements, useful for quantum annealing and simulating many-body systems.

## Contribution

It presents a novel iterative spectral projection algorithm utilizing ancilla measurements, applicable to quantum annealing and many-body quantum simulations.

## Key findings

- Algorithm successfully projects onto eigenstates following the Born rule.
- Simulation demonstrates effectiveness in driving spin chains to ground states.
- Potential integration as a subroutine in quantum optimization procedures.

## Abstract

We propose a quantum algorithm for projecting a quantum system to eigenstates of any Hermitian operator, provided one can access the associated control-unitary evolution for the ancilla and the system, as well as the measurement of the controlling ancillary qubit. Such a Hadamard-test like primitive is iterated so as to achieve the spectral projection, and the distribution of the projected eigenstates obeys the Born rule. This algorithm can be used as a subroutine in the quantum annealing procedure by measurement to drive the system to the ground state of a final Hamiltonian, and we simulate this for quantum many-body spin chains.