Speaker
Description
Precisely estimating eigenstate properties of quantum many-body systems is a task of fundamental importance that is naturally demanding when approached using classical computation alone. While the incorporation of quantum computation provides promising alternative paths, their practical utility in near-term and early fault-tolerant quantum devices requires offloading as much computational burden to classical computation as possible. In this work, we propose a hybrid quantum-classical algorithm that extracts properties of a target eigenstate, which requires only a single quantum register with one ancilla qubit from the quantum device, and achieves an exponential suppression of erroneous contributions via classical post-processing. Combining insights from virtual distillation and random time evolution, the algorithm can target both ground and excited state properties. Moreover, it admits a flexible choice of techniques in both the quantum and classical algorithmic components. We prove rigorous performance guarantees and present optimized quantum circuit constructions. Through an extensive set of numerical simulations, we also demonstrate the applicability and scalability of our framework in both near-term and early fault-tolerant settings. Furthermore, we showcase its potential when combined with state-of-the-art classical simulation techniques using tensor networks.
