C. Bertoni (FUB): Shallow shadows: expectation estimation using low-depth random Clifford circuits
Channel: Centrum Fizyki Teoretycznej PAN
Date: 2023-04-23

Christian Bertoni (Dahlem Center for Complex Quantum Systems, Freie Universitat Berlin, Germany).
Shallow shadows: expectation estimation using low-depth random Clifford circuits. 
Classical shadows have recently emerged as an efficient method to extract expectation values of observables using randomized measurements. In particular, two schemes have been proven to be able to efficiently perform this task for certain classes of observables: random single-qubit Clifford measurements, and random global Clifford measurements. In this talk, I will present a new scheme in which measurements in the computational basis are performed after the application of a brickwork circuit of random two-qubit gates of an arbitrary depth. This interpolates between the two known cases, which correspond to either 0 or linear depth. At a depth scaling logarithmically in the number of qubits and for an average state, this scheme has the same sample efficiency as the global Clifford measurements scheme, while retaining some of the favorable characteristics of the single-qubit Clifford measurements scheme. This provides strong evidence that logarithmically deep Clifford circuits, which are experimentally feasible to implement, can be used in place of global Clifford gates for classical shadows.
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