Efficient quantum circuit contraction using Tensor Decision Diagrams

Quantum computing holds the potential to solve complex problems currently beyond the capabilities of classical computers by exploiting the principles of quantum mechanics. However, due to the immaturity of such computers and the inability to know the state of the circuit during execution, efficient quantum simulators on classical computers are needed. This paper compares different methods for the contraction of quantum circuits represented as tensor networks. Tensor Decision Diagrams (TDD) are used to implement two contraction ordering methods that exploit the structure of the circuits to reduce temporal and spatial costs. Experimental results show that these methods improve other well established approaches and that they are faster that other well-known simulation tools based on other circuit representations. In addition, an analysis of different implementations of the same quantum algorithm highlights the impact of gate sets on contraction efficiency.