Imaginary time evolution with quantum nondemolition measurements: multi-qubit interactions via measurement nonlinearities

TL;DR

This paper introduces a method using quantum nondemolition measurements to perform imaginary time evolution, enabling deterministic state preparation and multi-qubit interactions through measurement nonlinearities.

Contribution

It proposes a measurement-based imaginary time evolution scheme utilizing QND measurements to generate multi-qubit interactions and prepare complex entangled states.

Findings

Demonstrates how QND measurements can drive systems toward energy eigenstates.

Shows conversion of single-qubit QND Hamiltonians into multi-qubit interactions.

Successfully prepares a four-qubit cluster state using only collective measurements.

Abstract

We show that quantum nondemolition (QND) measurements can be used to realize measurement-based imaginary time evolution. In our proposed scheme, repeated weak QND measurements are used to estimate the energy of a given Hamiltonian. Based on this estimated energy, adaptive unitary operations are applied such that only the targeted energy eigenstates are fixed points of the evolution. In this way, the system is deterministically driven towards the desired state. The nonlinear nature of the QND measurement, which allows for producing interactions between systems, is explicitly derived in terms of measurement operators. We show that for suitable interaction times, single qubit QND Hamiltonians can be converted to effective multi-qubit imaginary time operations. We illustrate our techniques with the example of preparing a four qubit cluster state, which is prepared using only collective single qubit QND measurements and single qubit adaptive operations.