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 × over Google’s TensorNetwork library on redundancy-rich circuits, and 25 × and 144 × 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.
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 × over Google’s TensorNetwork library on redundancy-rich circuits, and 25 × and 144 × 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.
Simulating quantum circuits on classical computers is a notoriously hard, yet increasingly important task for the development and testing of quantum algorithms. In order to alleviate this inherent complexity, efficient data structures and methods, such as tensor networks and decision diagrams, have been proposed. However, their efficiency heavily depends on the order in which the individual computations are performed. For tensor networks, the order is defined by so-called contraction plans and a plethora of methods has been developed to determine suitable plans. On the other hand, simulation based on decision diagrams is mostly conducted in a straight-forward, i.e., sequential, fashion thus far. In this work, we study the importance of the path that is chosen when simulating quantum circuits using decision diagrams and show, conceptually and experimentally, that choosing the right simulation path can make a vast difference in the efficiency of classical simulations using decision diagrams. We propose an open-source framework (available at github.com/cda-tum/ddsim) that not only allows to investigate of dedicated simulation paths but also to reuse of existing findings, e.g., obtained from determining contraction plans for tensor networks. Experimental evaluations show that translating strategies from the domain of tensor networks may yield speedups of several factors compared to the state of the art. Furthermore, we design a dedicated simulation path heuristic that allows to improve the performance even further—frequently yielding speedups of several orders of magnitude. Finally, we provide an extensive discussion on what can be learned from tensor networks and what cannot.
Tensor networks have been successfully applied in simulation of quantum physical systems for decades. Recently, they have also been employed in classical simulation of quantum computing, in particular, random quantum circuits. This article proposes a decision diagram style data structure, called Tensor Decision Diagram (TDD), for more principled and convenient applications of tensor networks. This new data structure provides a compact and canonical representation for quantum circuits. By exploiting circuit partition, the TDD of a quantum circuit can be computed efficiently. Furthermore, we show that the operations of tensor networks essential in their applications (e.g., addition and contraction) can also be implemented efficiently in TDDs. A proof-of-concept implementation of TDDs is presented and its efficiency is evaluated on a set of benchmark quantum circuits. It is expected that TDDs will play an important role in various design automation tasks related to quantum circuits, including but not limited to equivalence checking, error detection, synthesis, simulation, and verification.
Abstract Quantum computing holds the potential to solve complex problems currently beyond the capabilities of classical computers by exploiting the principles of quantum mechanics. However, due to the immaturity of such computers and the inability to know the state of the circuit during execution, efficient quantum simulators on classical computers are needed. This paper compares different methods for the contraction of quantum circuits represented as tensor networks. Tensor Decision Diagrams (TDD) are used to implement two contraction ordering methods that exploit the structure of the circuits to reduce temporal and spatial costs. Experimental results show that these methods improve other well established approaches and that they are faster that other well-known simulation tools based on other circuit representations. In addition, an analysis of different implementations of the same quantum algorithm highlights the impact of gate sets on contraction efficiency.
The classical simulation of quantum circuits is essential in the development and testing of quantum algorithms. Methods based on tensor networks or decision diagrams have proven to alleviate the inevitable exponential growth of the underlying complexity in many cases. But the complexity of these methods is very sensitive to so-called contraction plans or simulation paths, respectively, which define the order in which respective operations are applied. While, for tensor networks, a plethora of strategies has been developed, simulation based on decision diagrams is mostly conducted in a straight-forward fashion thus far. In this work, we envision a flow that allows to translate strategies from the domain of tensor networks to decision diagrams. Preliminary results indicate that a substantial advantage may be gained by employing suitable simulation paths-motivating a thorough consideration.
Classical simulation remains essential for the development of quantum algorithms; however, traditional matrix-based methods struggle with scalability. While the Fast Tensor Decision Diagram (FTDD) framework offers a hybrid approach by combining the strengths of Tensor Networks and Decision Diagrams (DDs) for memory-efficient simulation, its core operations are often bottlenecked by memory management structures. Our primary motivation is to address the high computational and spatial cost associated with the hash tables, as well as to simplify the complexity of the simulation workflow. This work introduces systematic, low-level optimizations to the framework. Our main contribution is the enhancement of the memory management layer for the internal tables. We implemented a node reuse mechanism and designed a controlled strategy for hash table growth. These improvements minimize the memory footprint and reduce the costly hashing overhead inherent in DD-based simulators. We performed a thorough experimental analysis using a diverse set of quantum circuits, which were characterized by well-established metrics. Experimental results demonstrate that our enhancements improve the tool's performance and scalability. Notably, these advancements enable the simulation of complex circuits, such as Quantum Fourier Transform, with hundreds of qubits, on a standard server with 2-Tb of memory.
One of the key problems in tensor network based quantum circuit simulation is the construction of a contraction tree which minimizes the cost of the simulation, where the cost can be expressed in the number of operations as a proxy for the simulation running time. This same problem arises in a variety of application areas, such as combinatorial scientific computing, marginalization in probabilistic graphical models, and solving constraint satisfaction problems. In this paper, we reduce the computationally hard portion of this problem to one of graph linear ordering, and demonstrate how existing approaches in this area can be utilized to achieve results up to several orders of magnitude better than existing state of the art methods for the same running time. To do so, we introduce a novel polynomial time algorithm for constructing an optimal contraction tree from a given order. Furthermore, we introduce a fast and high quality linear ordering solver, and demonstrate its applicability as a heuristic for providing orderings for contraction trees. Finally, we compare our solver with competing methods for constructing contraction trees in quantum circuit simulation on a collection of randomly generated Quantum Approximate Optimization Algorithm Max Cut circuits and show that our method achieves superior results on a majority of tested quantum circuits. Reproducibility: Our source code and data are available at https://github.com/cameton/HPEC2022_ContractionTrees.