Validating and Certifying Stabilizer States

TL;DR

This paper introduces a measurement scheme for validating and certifying the fidelity of n-qubit stabilizer states efficiently, using a minimal number of measurements and providing explicit fidelity bounds.

Contribution

It presents a new measurement protocol for stabilizer state validation and derives explicit worst-case fidelity bounds that can be certified with polynomial resources.

Findings

Validation scheme uses n Pauli measurements realizable with single-qubit gates

Explicit worst-case fidelity expression derived for stabilizer states

High-probability certification with O(n^2) copies of the state

Abstract

We propose a measurement scheme that validates the preparation of an $n$-qubit stabilizer state. The scheme involves a measurement of $n$ Pauli observables, a priori determined from the stabilizer state and which can be realized using single-qubit gates. Based on the proposed validation scheme, we derive an explicit expression for the worst-case fidelity, i.e., the minimum fidelity between the stabilizer state and any other state consistent with the measured data. We also show that the worst-case fidelity can be certified, with high probability, using ${\cal O}(n^2)$ copies of the state.