Shallow shadows: Expectation estimation using low-depth random Clifford circuits -Bertoni | TQC 2023

Christian Bertoni
Shallow shadows: Expectation estimation using low-depth random Clifford circuits

We provide practical and powerful schemes for learning properties of a quantum state using a small number of measurements. Specifically, we present a randomized measurement scheme modulated by the depth of a random quantum circuit in one spatial dimension. This scheme interpolates between two known classical shadows schemes based on random Pauli measurements and random Clifford measurements. We focus on the regime where depth scales logarithmically in the system size and provide evidence that this retains the desirable sample complexity properties of both extremal schemes while also being experimentally feasible. We present methods for two key tasks; estimating expectation values of certain observables from generated classical shadows and, computing upper bounds on the depth-modulated shadow norm, thus providing rigorous guarantees on the accuracy of the output estimates. We achieve our findings by bringing together tools of shadow estimation, random circuits, and tensor networks.

July 24, 2023
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TQC 2023 | 24-28 July 2023, University of Aveiro, Portugal

18th Conference on the Theory of Quantum Computation, Communication and Cryptography.

TQC is a leading annual international conference for students and researchers working in the theoretical aspects of quantum information science. The scientific objective is to bring together the theoretical quantum information science community to present and discuss the latest advances in the field.

Organisation:
Squids - Schools for Quantum Information Development
Universidade de Aveiro: Departamento de Matemática, CIDMA & Fábrica

Sponsors:
Phasecraft, UK
Google Quantum AI, USA
QuSoft, The Netherlands
Quantum for Life Centre, Denmark
Technology Innovation Institute, UAE
ML4Q, Germany
Dulwich Quantum