Scoring-based Static Variable Ordering for Decision Diagram-based Quantum Circuit Simulation

TL;DR

This paper introduces a scoring-based heuristic for static variable ordering in decision diagram-based quantum circuit simulation, significantly improving speed and enabling the simulation of complex circuits like Shor's within practical timeframes.

Contribution

It proposes a novel static variable ordering method for DD-based quantum simulation, demonstrating substantial speedups over default orders.

Findings

Achieved up to 150x speedup in benchmark circuits.

Successfully simulated Shor's 1011 factorization in 5 hours.

Outperformed previous methods in simulation efficiency.

Abstract

Decision diagram (DD)-based quantum circuit simulators represent quantum states and gates using DDs, enabling memory-efficient and fast simulations for some quantum circuits like Shor. Although it is known that DD size and processing time vary depending on the variable order in classical circuits, there has not been much research on the variable order under quantum circuit simulation. One existing study pointed out that dynamic reordering worsens the simulation time and numerical accuracy, and there is no comprehensive research on static orders in the context of quantum circuit simulation. Therefore, this paper proposes a scoring-based heuristic method for determining a static variable order that enables efficient DD-based quantum circuit simulation. When applied to benchmark circuits, the default original variable orders resulted in slow simulations, whereas the proposed method achieved speedups of up to 150x. Furthermore, the proposed order completed the simulation of Shor's 1011 factorization in 5 hours on a single-core laptop, although it was not completed within two days previously.