Importance sampling of randomized measurements for probing entanglement

Abstract

We show that combining randomized measurement protocols with importance sampling allows for characterizing entanglement in significantly larger quantum systems and in a more efficient way than in previous work. A drastic reduction of statistical errors is obtained using classical techniques of machine-learning and tensor networks using partial information on the quantum state. In present experimental settings of engineered many-body quantum systems this effectively doubles the (sub-)system sizes for which entanglement can be measured. In particular, we show an exponential reduction of the required number of measurements to estimate the purity of product states and GHZ states.

Symmetry-resolved entanglement detection using partial transpose moments

“…In this context the quantum de Finetti theorem seems highly relevant. In future work, we will also investigate how importance sampling [62,63] and/or derandomization [28,64] can further improve moment estimation based on classical shadows. Finally, another promising direction of research would be to try to detect and characterize phase transitions in quantum mechanical Hamiltonians at finite (non-zero) temperature.…”

Efficient estimation of Pauli observables by derandomization

“…Randomized measurements have also been used to estimate entanglement entropy [6,21,41,46], topological invariants [9,14], benchmark physical devices [8,12,21,29], and predict outcomes of physical experiments [22]. Derandomization provides a principled approach for adapting randomized measurement pro- cedures to fine-grained structure and is closely related to an algorithmic technique -multiplicative weight update [2] -commonly used in machine learning and game theory.…”

Cross-Platform Comparison of Arbitrary Quantum Computations

“…The parameters M U and M S can be optimized through minimizing the statistical error with grid search 8,10 or using the perform importance sampling with partial information on the quantum state 26 . Both approaches require prior knowledge or simulation of the target state.…”