Efficient stabilizer entropies for quantum computers
| Autor: | Haug, Tobias, Lee, Soovin, Kim, M. S. |
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| Rok vydání: | 2023 |
| Předmět: | |
| DOI: | 10.48550/arxiv.2305.19152 |
| Popis: | Stabilizer entropies (SEs) are measures of nonstabilizerness or `magic' that quantify the degree to which a state is described by stabilizers. SEs are especially interesting due to their connections to scrambling, localization and property testing. However, practical applications have been limited so far as previously known measurement protocols for SEs scale exponentially with the number of qubits. Here, we introduce the Tsallis-$n$ SE as an efficient measure of nonstabilizerness for quantum computers. We find that the number of measurements is independent of the number of qubits for any integer index $n>1$ which ensures the scalability of the measure. The Tsallis SE is an efficient bound of various nonstabilizerness monotones which are intractable to compute beyond a few qubits. Using the IonQ quantum computer, we experimentally measure the Tsallis SE of random Clifford circuits doped with non-Clifford gates and give bounds for the stabilizer fidelity, stabilizer extent and robustness of magic. As applications, we provide efficient algorithms to measure $4n$-point out-of-time-order correlators and multifractal flatness. Our results open up the exploration of nonstabilizerness with quantum computers. 12 pages, 3 figures |
| Databáze: | OpenAIRE |
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