Shallow Shadows: Expectation Estimation Using Low-Depth Random Clifford Circuits

Learn about practical schemes for quantum state property measurement through a conference talk presented at TQC 2023. Explore an innovative approach to expectation estimation using low-depth random Clifford circuits that bridges random Pauli and Clifford measurement techniques. Discover how this method achieves optimal sample complexity while maintaining experimental feasibility by scaling circuit depth logarithmically with system size. Examine the implementation of classical shadows, random quantum circuits, and tensor networks to estimate observable expectation values and compute depth-modulated shadow norm bounds. Follow along as the presentation covers the theoretical framework, requirements, classical post-processing steps, and experimental results, complete with visual demonstrations through plots. Originally presented at the 18th Conference on the Theory of Quantum Computation, Communication and Cryptography at the University of Aveiro, this talk provides valuable insights into advanced quantum state measurement techniques.