Quantum State Certification via Effective Parent Hamiltonians from Local Measurement Data

TL;DR

This paper presents a new method for certifying quantum states using local measurements and parent Hamiltonians, enabling efficient and scalable verification of multipartite entanglement on quantum hardware.

Contribution

The authors introduce a tomography-free certification framework based on parent Hamiltonians, validated experimentally on IBM quantum devices for large multipartite states.

Findings

Certify genuine multipartite entanglement up to 6 qubits for W states.

Establish positive fidelity bounds for states up to 13 qubits.

Largest witness-certified demonstrations on programmable quantum processors.

Abstract

The preparation and certification of quantum states is a fundamental challenge across quantum information technology. We introduce a tomography-free state certification method that lower-bounds the fidelity by estimating expectation values of engineered parent-Hamiltonian terms from local measurement data. We apply this framework to construct a parent Hamiltonian that enables certification and variational optimization across the Dicke-state family, which includes the single-excitation $W_n$ state. We experimentally validate the framework on IBM quantum hardware, certifying genuine multipartite entanglement for $W_n$ states up to six qubits and establishing positive lower bounds on the state fidelity up to thirteen qubits. For Dicke states with two- and three-excitations, we certify genuine multipartite entanglement up to seven qubits. Within this stringent certification framework, these results constitute among the largest witness-certified demonstrations of such states on a programmable quantum processor.