@article{Haug:2024:10.1103/physrevlett.132.240602,
author = {Haug, T and Lee, S and Kim, MS},
doi = {10.1103/physrevlett.132.240602},
journal = {Physical Review Letters},
title = {Efficient quantum algorithms for stabilizer entropies},
url = {http://dx.doi.org/10.1103/physrevlett.132.240602},
volume = {132},
year = {2024}
}

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TY  - JOUR
AB  - Stabilizer entropies (SEs) are measures of nonstabilizerness or “magic” that quantify the degree to whicha state is described by stabilizers. SEs are especially interesting due to their connections to scrambling,localization and property testing. However, applications have been limited so far as previously knownmeasurement protocols for SEs scale exponentially with the number of qubits. Here, we efficiently measureSEs for integer R´enyi index n > 1 via Bell measurements. The SE of N-qubit quantum states can bemeasured with OðnÞ copies and OðnNÞ classical computational time, where for even n we additionallyrequire the complex conjugate of the state. We provide efficient bounds of various nonstabilizernessmonotones that are intractable to compute beyond a few qubits. Using the IonQ quantum computer, wemeasure SEs of random Clifford circuits doped with non-Clifford gates and give bounds for the stabilizerfidelity, stabilizer extent, and robustness of magic. We provide efficient algorithms to measure Clifford averaged 4n-point out-of-time-order correlators and multifractal flatness. With these measures we study thescrambling time of doped Clifford circuits and random Hamiltonian evolution depending on nonstabilizer ness. Counterintuitively, random Hamiltonian evolution becomes less scrambled at long times, which wereveal with the multifractal flatness. Our results open up the exploration of nonstabilizerness with quantumcomputers.
AU  - Haug,T
AU  - Lee,S
AU  - Kim,MS
DO  - 10.1103/physrevlett.132.240602
PY  - 2024///
SN  - 0031-9007
TI  - Efficient quantum algorithms for stabilizer entropies
T2  - Physical Review Letters
UR  - http://dx.doi.org/10.1103/physrevlett.132.240602
UR  - http://hdl.handle.net/10044/1/112426
VL  - 132
ER  - 

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