Predicting features of complex, large-scale quantum systems is essential to the characterization and engineering of quantum architectures. We present an efficient approach for predicting a large number of linear features using classical shadows obtained from very few quantum measurements. This approach is guaranteed to accurately predict @math linear functions with bounded Hilbert-Schmidt norm from only @math measurement repetitions. This sampling rate is completely independent of the system size and saturates fundamental lower bounds from information theory. We support our theoretical findings with numerical experiments over a wide range of problem sizes (2 to 162 qubits). These highlight advantages compared to existing machine learning approaches.
Direct fidelity estimation is a procedure that allows for predicting a single pure target fidelity @math up to accuracy @math . The best-known technique is based on few Pauli measurements that are selected randomly using importance sampling @cite_49 . The required number of samples depends on the target: it can range from a dimension-independent order of @math (if @math is a stablizer state) to roughly @math in the worst case.
@cite_49
2090368878
We describe a simple method for certifying that an experimental device prepares a desired quantum state ρ. Our method is applicable to any pure state ρ, and it provides an estimate of the fidelity between ρ and the actual (arbitrary) state in the lab, up to a constant additive error. The method requires measuring only a constant number of Pauli expectation values, selected at random according to an importance-weighting rule. Our method is faster than full tomography by a factor of d, the dimension of the state space, and extends easily and naturally to quantum channels.