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Researchers have established a method to recover quantum Hamiltonians from a single measurement by leveraging a measurable gap in the commutator between time-evolved operators and local observables. This advance overcomes previous limitations requiring multiple observations, enabling efficient system identification even at extended time scales. The result provides a robust framework for characterizing quantum dynamics and understanding thermalization with reduced experimental overhead.

Sources coveringQuantum Zeitgeist, Quantum Frontiers

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Researchers Recover Hamiltonians from Time Evolution with High Probability

Quantum ZeitgeistJune 11, 20266 min read

Any normalized local observable evolving under an unknown Hamiltonian maintains a measurable gap, ensuring its properties can be determined even with prolonged evolution. This establishes a method for recovering Hamiltonians, up to a scaling factor, from a single measurement, unlike previous techniques needing multiple observations. The finding demonstrates that any such observable satisfies ∥[U(t), A]∥²F ≥ 1/poly(n), opening new avenues for quantum system identification.

Constantin Cedillo Vayson de Pradenne and colleagues at Harvard University, in collaboration with Caltech, have found that a unique approximate conserved observable exists and can be efficiently recovered for many local Hamiltonians. The findings show that any normalised, local observable orthogonal to the Hamiltonian exhibits a minimal commutator with the time-evolved operator, guaranteeing its identifiability. This provides a pathway to learning Hamiltonians even at extended time scales and offers a new understanding of thermalisation in quantum systems. Physicists have demonstrated a significant improvement in the lower bound of the commutator between a time-evolved operator, U(t) = exp(-iHt), and any normalised local observable, A, orthogonal to the…

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