Efficient quantum circuit contraction using tensor decision diagrams

Simulating quantum circuits efficiently on classical computers is crucial given the limitations of current noisy intermediate-scale quantum devices. This paper adapts and extends two methods used to contract tensor networks within the fast tensor decision diagram (FTDD) framework. The methods, called iterative pairing and block contraction, exploit the advantages of tensor decision diagrams to reduce both the temporal and spatial cost of quantum circuit simulations. The iterative pairing method minimizes intermediate diagram sizes, while the block contraction algorithm efficiently handles circuits with repetitive structures, such as those found in quantum walks and Grover's algorithm. Experimental results demonstrate that, in some cases, these methods significantly outperform traditional contraction orders like sequential and cotengra in terms of both memory usage and execution time. Furthermore, simulation tools based on decision diagrams, such as FTDD, show superior performance to matrix-based simulation tools, such as Google tensor networks, enabling the simulation of larger circuits more efficiently. These findings show the potential of decision diagram-based approaches to improve the simulation of quantum circuits on classical platforms.