Improved BDD Algorithms for the Simulation of Quantum Circuits

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Abstract

In this paper we develop novel algorithms for the simulation of quantum circuits on classical computers. The most efficient techniques previously studied, represent both quantum state vectors and quantum operator matrices as Multi-Terminal Binary Decision Diagrams (MTBDDS). This paper shows how to avoid representing quantum operators as matrices. Instead, we introduce a class of quantum operators that can be represented more compactly using a symbolic, BDD-based representation. We propose algorithms that apply operators on quantum states, using the symbolic representation. Our algorithms are shown to have superior performance over previous techniques, both asymptotically and experimentally.