A random-basis, minimum-of-means stabilizer certification protocol accepts good states and rejects bad states with error probabilities exponentially small in qubit number under a wide fidelity gap.
Validating and Certifying Stabilizer States
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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.
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Verifying a stabilizer state with few observables but many shots
A random-basis, minimum-of-means stabilizer certification protocol accepts good states and rejects bad states with error probabilities exponentially small in qubit number under a wide fidelity gap.