Efficient Implementation of LIMDDs for Quantum Circuit Simulation

Realizing the promised advantage of quantum computers over classical computers requires both physical devices and corresponding methods for the design, verification and analysis of quantum circuits. In this regard, decision diagrams have proven themselves to be an indispensable tool due to their capability to represent both quantum states and unitaries (circuits) compactly. Nonetheless, recent results show that decision diagrams can grow to exponential size even for the ubiquitous stabilizer states, which are generated by Clifford circuits. Since Clifford circuits can be efficiently simulated classically, this is surprising. Moreover, since Clifford circuits play a crucial role in many quantum computing applications, from networking, to error correction, this limitation forms a major obstacle for using decision diagrams for the design, verification and analysis of quantum circuits. The recently proposed Local Invertible Map Decision Diagram (LIMDD) solves this problem by combining the strengths of decision diagrams and the stabilizer formalism that enables efficient simulation of Clifford circuits. However, LIMDDs have only been introduced on paper thus far and have not been implemented yet—preventing an investigation of their practical capabilities through experiments. In this work, we present the first implementation of LIMDDs for quantum circuit simulation. A case study confirms the improved performance in both worlds for the Quantum Fourier Transform applied to a stabilizer state. The resulting package is available under a free license at https://github.com/cda-tum/ddsim/tree/limdd.