Speaker
Description
Classical shadows are a powerful method for learning many properties of quantum states in a sample-efficient manner, by making use of randomized measurements. Random local Pauli measurements [1] and shallow shadows [2–4] provide optimal protocols for estimating expectation values of local observables.
On the contrary, the Clifford global-twirling protocol [1] is optimal for estimating global quantities such as pure-state fidelity or the system's purity. However, this protocol may be difficult to implement in practice, due to the need to apply a global random unitary U.
In this work, we are interested in classical shadow protocols based on Brownian quantum circuits [5], which may be implemented using two-qubit gates only. We put forward a very simple approximate estimation scheme which, for a deep enough circuit, performs similarly to the global-twirling protocol, without the need to apply global unitary operators. We support this scheme with a systematic numerical study of its validity and performance.
[1] H.-Y. Huang, R. Kueng, and J. Preskill, Nature Phys. 16, 1050 (2020).
[2] A. A. Akhtar, H.-Y. Hu, and Y.-Z. You, Quantum 7, 1026 (2023).
[3] C. Bertoni, J. Haferkamp, M. Hinsche, M. Ioannou, J. Eisert, and H. Pashayan, arXiv:2209.12924 (2022).
[4] M. Arienzo, M. Heinrich, I. Roth, and M. Kliesch, Quantum Inf. Comput 23, 961 (2023).
[5] M. Ippoliti, Y. Li, T. Rakovszky, and V. Khemani, Phys. Rev. Lett. 130, 230403 (2023).
| Abstract category | Quantum Simulations |
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