Efficient algorithm for full-state quantum circuit simulation with DD compression while maintaining accuracy

Abstract

With the development of noisy intermediate-scale quantum machines, quantum processors show their supremacy in specific applications. To better understand the quantum behavior and verify larger quantum bit (qubit) algorithms, simulation on classical computers becomes crucial. However, as the simulated number of qubits increases, the full-state simulation suffers exponential memory increment for state vector storing. In order to compress the state vector, some existing works reduce the memory by data encoding compressors. Nevertheless, the memory requirement remains massive. Meanwhile, others utilize compact decision diagrams (DD) to represent the state vector, which only demands linear memory size. However, the existing DD-based simulation algorithm possesses many redundant calculations that require further exploration. Besides, the traditional normalization-based nodes merging method of DD amplifies the side influences of approximate error. Therefore, to tackle the above challenges, in this paper, we first fully explore the redundancies in the recursive-based DD simulation (RecurSim) algorithm. Inspired by the regularities of the quantum circuit model, a scale-based simulation (ScaleSim) algorithm is proposed, which removes plenty of unnecessary computations. Furthermore, to eliminate the influences of approximate error, we propose a new pre-check DD building method, namely PCB, which maintains the accuracy of DD representation and produces more memory saving. Comprehensive experiments show that our method achieves up to 24124.2$\times$ acceleration and 3.2 $\times \,10^7\times$ memory reduction than traditional DD-based methods on quantum algorithms while maintaining the representation accuracy.