Hybrid quantum gap estimation algorithm using a filtered time series

Understand

Quantum simulation advantage over classical memory limitations would allow compact quantum circuits to yield insight into intractable quantum many-body problems, but the interrelated obstacles of large circuit depth in quantum time evolution and noise seem to rule out unbiased quantum simulation in the near term.

• We prove that classical post-processing, i.e., long-time filtering of an offline time series, exponentially improves the circuit depth needed for quantum time evolution.
• We apply the filtering method to the construction of a hybrid quantum-classical algorithm to estimate energy gap, an important observable not governed by the variational theorem.
• We demonstrate, within an operating range of filtering, the success of the algorithm in proof-of-concept simulation for finite-size scaling of a minimal spin model.