We present classical simulation techniques for measure once quantum branching programs. For bounded error syntactic quantum branching program of width $w$ that computes a function with error $delta$ we present a classical deterministic branching program of the same length and width at most $(1+2/(1-2delta))^{2w}$ that computes the same function. Second technique is a classical stochastic simulation technique for bounded error and unbounded error quantum branching programs. Our result is that it is possible stochastically-classically simulate quantum branching programs with the same length and almost the same width, but we lost bounded error acceptance property.
@InProceedings{ablayev:DagSemProc.07411.3, author = {Ablayev, Farid}, title = {{Classical Simulation Complexity of Quantum Branching Programs}}, booktitle = {Algebraic Methods in Computational Complexity}, pages = {1--10}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2008}, volume = {7411}, editor = {Manindra Agrawal and Harry Buhrman and Lance Fortnow and Thomas Thierauf}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07411.3}, URN = {urn:nbn:de:0030-drops-13107}, doi = {10.4230/DagSemProc.07411.3}, annote = {Keywords: Quantum algorithms, Branching Programs, Complexity} }
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