Title: Efficiently Probing Quantum Systems with Compressive Measurements
Abstract:
In the foreseeable future, the advent of large-scale error-corrected quantum computers will open new frontiers in both fundamental quantum science and practical applications. Yet the inherent complexity of these systems also poses challenges in precise control and accurate characterization of these systems. In this talk, we will present our recent work in understanding both the statistical and computational aspects of estimating (or learning) properties of quantum systems. While the sample complexity and runtime for estimating general quantum states scale exponentially with system size (i.e., the number of qubits), we will show how these requirements can be reduced to polynomial scaling for structured families of states, including matrix product states/operators and projected entangled-pair states/operators. We will also discuss how the design of measurement schemes impacts sample complexity and opportunities for more efficient estimation of large-scale quantum systems.
