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QI: Fachverband Quanteninformation
QI 15: Quantum Computing Theory
QI 15.4: Vortrag
Mittwoch, 20. März 2024, 10:30–10:45, HFT-FT 101
Shot noise reduction by problem-tailored measurements — •Timo Eckstein1,2, Refik Mansuroglu1, Martin Kliesch3, and Michael J. Hartmann1,2 — 1FAU Erlangen-Nürnberg, Germany — 2MPI for the Science of Light, Germany — 3TU Hamburg, Germany
The preparation and measurements of low-energy eigenstates of strongly correlated many-body systems are considered an auspicious real-world use case of near-term quantum computers. Such quantum states feature nontrivial long-range entanglement, which cannot be efficiently described using classical methods but may still be prepared on quantum devices.
Here, we address the challenge of efficiently extracting information from the quantum device in such applications. Naive measurement schemes, like estimating eigenvalues of Pauli strings can require excessive amounts of measurements. These requirements are significantly reduced by our strategy.
In contrast to observable agnostic methods like shadow tomography, we focus on observable specific ones. Specifically, starting from tractable subsystems, we constructed measurements that are tailored for energy estimation of interacting quantum systems with local Hamiltonians. This construction leads to estimators with smaller variances compared to local Pauli bases. Indeed, in our numerical studies, we find linear variance improvements which translate to quadratic savings in the required number of measurements. We show this to hold analytically if constrained to positively correlated splitting or alternatively to Pauli-bipartitions.
Keywords: Energy estimation; Shot noise reduction; Near-term quantum computing