Quantum Circuit Simulation with Fast Tensor Decision Diagram

TL;DR

Quantum circuit simulation faces exponential complexity, especially for deep or random circuits. FTDD merges tensor networks with tensor decision diagrams, introducing a linear-time rank simplification (Tetris) and near-optimal contraction ordering, augmented by edge-centric TDDs and BDD-inspired optimizations. Empirical results show large speedups over state-of-the-art DD-based and some array-based simulators on redundancy-rich circuits, with robust performance for NISQ-relevant workloads. The framework, implemented in C++ and available as open-source, offers a practical, high-performance tool for quantum software development and benchmarking.

Abstract

Quantum circuit simulation is a challenging computational problem crucial for quantum computing research and development. The predominant approaches in this area center on tensor networks, prized for their better concurrency and less computation than methods using full quantum vectors and matrices. However, even with the advantages, array-based tensors can have significant redundancy. We present a novel open-source framework that harnesses tensor decision diagrams to eliminate overheads and achieve significant speedups over prior approaches. On average, it delivers a speedup of 37$\times$ over Google's TensorNetwork library on redundancy-rich circuits, and 25$\times$ and 144$\times$ over quantum multi-valued decision diagram and prior tensor decision diagram implementation, respectively, on Google random quantum circuits. To achieve this, we introduce a new linear-complexity rank simplification algorithm, Tetris, and edge-centric data structures for recursive tensor decision diagram operations. Additionally, we explore the efficacy of tensor network contraction ordering and optimizations from binary decision diagrams.

Figures (9)

• Figure 1: Overview of the presented FTDD framework.
• Figure 2: Qubit and quantum gates represented in matrices and tensor symbols: (a) single-qubit; (b) $H$ gate; (c) $CZ$ gate; (d) $CZ$ using hyper-edges.
• Figure 3: The example quantum circuit represented as a tensor network before and after contracting the tensors highlighted in green. $R_{X}$, $R_{Y}$ and $T$ are common single-qubit rotation gates.
• Figure 4: (a) The tensor $H \otimes H$ and its array; (b) Its TDD before and after normalization and reduction. A red (blue) edge indicates an index of 0 (1).
• Figure 5: Applying our Tetris algorithm to the example circuit of Fig. \ref{['fig2']}. Panels (a) to (d) depict the transition from the original circuit to the simplified version as we proceed through a layer-by-layer process, commencing from layer 2.