Accelerating Decision Diagram-based Multi-node Quantum Simulation with Ring Communication and Automatic SWAP Insertion

An N-bit quantum state requires a vector of length $2^N$, leading to an exponential increase in the required memory with N in conventional statevector-based quantum simulators. A proposed solution to this issue is the decision diagram-based quantum simulator, which can significantly decrease the necessary memory and is expected to operate faster for specific quantum circuits. However, decision diagram-based quantum simulators are not easily parallelizable because data must be manipulated dynamically, and most implementations run on one thread. This paper introduces ring communication-based optimal parallelization and automatic swap insertion techniques for multi-node implementation of decision diagram-based quantum simulators. The ring communication approach is designed so that each node communicates with its neighboring nodes, which can facilitate faster and more parallel communication than broadcasting where one node needs to communicate with all nodes simultaneously. The automatic swap insertion method, an approach to minimize inter-node communication, has been employed in existing multi-node state vector-based simulators, but this paper proposes two methods specifically designed for decision diagram-based quantum simulators. These techniques were implemented and evaluated using the Shor algorithm and random circuits with up to 38 qubits using a maximum of 256 nodes. The experimental results have revealed that multi-node implementation can reduce run-time by up to 26 times. For example, Shor circuits that need 38 qubits can finish simulation in 147 seconds. Additionally, it was shown that ring communication has a higher speed-up effect than broadcast communication, and the importance of selecting the appropriate automatic swap insertion method was revealed.