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THU: Thursday Contributed Sessions

THU 13: Poster Session: Applications

THU 13.3: Poster

Thursday, September 11, 2025, 16:30–18:30, ZHG Foyer 1. OG

Stochastic Emulation of Quantum Algorithms — •Anagha Shriharsha and Daniel Braun — Institute for Theoretical Physics, Eberhard Karls University of Tübingen, Auf der Morgenstelle 14 D - 72076 Tübingen

We introduce a fully classical stochastic emulation of pure-state quantum circuits by treating higher-order partial derivatives of an N-particle position distribution as analogue quantum states and discretizing them into 2(n + 1) classical stochastic bits. Each single- and two-qubit unitary gate is realised as a convex stochastic map on these grabit bins, reproducing the exact realified evolution up to a global prefactor and enabling an automated translation of any pure-state quantum algorithm into a classical stochastic algorithm. We demonstrate the approach on the Deutsch Jozsa and Bernstein Vazirani algorithms, as well as on the Quantum Fourier Transform and the Quantum Approximate Optimization Algorithm, validating that gate-by-gate stochastic propagation faithfully tracks the intended quantum evolution. By analysing how the number of samples must grow with qubit count for fixed accuracy, we uncover how genuine many-particle interference emerges within classical probabilities and at what sampling cost.

Keywords: quantum algorithm; stochastic matrices; classical entanglement; quantum interference