Validating and Certifying Stabilizer States

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 $\mathcal{O}(n^2)$ copies of the state.

V2: Authors update, experimental results added

References in corpus (5)

• Demonstration of a small programmable quantum computer with atomic qubits
• Experimental Comparison of Two Quantum Computing Architectures
• Direct Fidelity Estimation from Few Pauli Measurements
• The Learnability of Quantum States
• Proceedings of the 15th International Conference on Quantum Physics and Logic

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• SYK model based $\beta$ regime dependent two-qubit dynamical wormhole-inspired teleportation protocol simulation
• Sampling and the complexity of nature