Predicting Many Properties of a Quantum System from Very Few Measurements
This provides an efficient method for quantum technology development by enabling broad property prediction from few measurements, though it builds on existing concepts with incremental improvements in efficiency.
The authors tackled the problem of predicting many properties of large-scale quantum systems with minimal measurements by introducing classical shadows, an approximate classical description requiring only order log M measurements to accurately predict M different functions of the state, independent of system size and saturating information-theoretic bounds.
Predicting properties of complex, large-scale quantum systems is essential for developing quantum technologies. We present an efficient method for constructing an approximate classical description of a quantum state using very few measurements of the state. This description, called a classical shadow, can be used to predict many different properties: order $\log M$ measurements suffice to accurately predict $M$ different functions of the state with high success probability. The number of measurements is independent of the system size, and saturates information-theoretic lower bounds. Moreover, target properties to predict can be selected after the measurements are completed. We support our theoretical findings with extensive numerical experiments. We apply classical shadows to predict quantum fidelities, entanglement entropies, two-point correlation functions, expectation values of local observables, and the energy variance of many-body local Hamiltonians. The numerical results highlight the advantages of classical shadows relative to previously known methods.