Quantum 2025 – wissenschaftliches Programm

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MON: Monday Contributed Sessions

MON 18: Quantum Algorithms

MON 18.8: Vortrag

Montag, 8. September 2025, 18:15–18:30, ZHG007

Quantum Phase Estimation for Block-encodings — •Shawn Skelton — Leibniz Universität Hannover

We present an algorithm for quantum phase estimation (QPE) acting on a block-encoded Hamiltonian. Block-encodings have become one of the most common oracle assumptions in the circuit model; existing algorithms for QPE with block-encodings rely on sophisticated applications of quantum singular value transformation (QSVT) to extract a bit-by-bit estimate of the desired phase.

Our algorithm instead uses von Neumann's measurement procedure and implements time evolution using the quantum eigenvalue transformation (QET), which is closely related to QSVT. One arrives at an extremely simple algorithm for QPE that achieves nearly-optimal query complexity with respect to textbook QPE oracle assumptions, and is coherent without introducing additional qubits.

We then use recent bounds on the Clifford + T costs of block-encoding to show how our algorithm can efficiently prepare QPE beginning from a linear combination of Pauli strings. We arrive at a Clifford + T complexity bound for QPE with respect to model-relevant parameters of the Hamiltonian and the desired precision. In the process, we provide a very general error analysis for Clifford + T implementations of QSP/QSVT circuits.

Keywords: quantum adiabtic theorem; quantum computing; quantum signal processing