Weighted Context-Free-Language Ordered Binary Decision Diagrams

TL;DR

This paper introduces Weighted Context-Free-Language Ordered BDDs (WCFLOBDDs), a new hierarchical decision diagram structure that outperforms existing methods in quantum circuit simulation by significantly increasing the number of qubits manageable within a time limit.

Contribution

The paper proposes WCFLOBDDs, a novel data structure that enhances decision diagram efficiency for representing complex functions, especially in quantum circuit simulation.

Findings

WCFLOBDDs are exponentially more succinct than WBDDs for some functions.

WCFLOBDDs handle 1-64 times more qubits than WBDDs within a 15-minute timeout.

WCFLOBDDs perform comparably to the best of WBDDs and CFLOBDDs in quantum simulation tasks.

Abstract

This paper presents a new data structure, called \emph{Weighted Context-Free-Language Ordered BDDs} (WCFLOBDDs), which are a hierarchically structured decision diagram, akin to Weighted BDDs (WBDDs) enhanced with a procedure-call mechanism. For some functions, WCFLOBDDs are exponentially more succinct than WBDDs. They are potentially beneficial for representing functions of type $\mathbb{B}^n \rightarrow D$, when a function's image $V \subseteq D$ has many different values. We apply WCFLOBDDs in quantum-circuit simulation, and find that they perform better than WBDDs on certain benchmarks. With a 15-minute timeout, the number of qubits that can be handled by WCFLOBDDs is 1-64$\times$ that of WBDDs (and 1-128$\times$ that of CFLOBDDs, which are an unweighted version of WCFLOBDDs). These results support the conclusion that for this application -- from the standpoint of problem size, measured as the number of qubits -- WCFLOBDDs provide the best of both worlds: performance roughly matches whichever of WBDDs and CFLOBDDs is better. (From the standpoint of running time, the results are more nuanced.)