Quantum computers promise to efficiently solve important problems classical computers never will. However, in order to capitalize on these prospects, a fully automated quantum software stack needs to be developed. This involves a multitude of complex tasks from the classical simulation of quantum circuits, over their compilation to specific devices, to the verification of the circuits to be executed as well as the obtained results. All of these tasks are highly non-trivial and necessitate efficient data structures to tackle the inherent complexity. Starting from rather straight-forward arrays over decision diagrams (inspired by the design automation community) to tensor networks and the ZX-calculus, various complementary approaches have been proposed. This work provides a look "under the hood" of today's tools and showcases how these means are utilized in them, e.g., for simulation, compilation, and verification of quantum circuits.
Quantum computers promise to efficiently solve important problems classical computers never will. However, in order to capitalize on these prospects, a fully automated quantum software stack needs to be developed. This involves a multitude of complex tasks from the classical simulation of quantum circuits, over their compilation to specific devices, to the verification of the circuits to be executed as well as the obtained results. All of these tasks are highly non-trivial and necessitate efficient data structures to tackle the inherent complexity. Starting from rather straight-forward arrays over decision diagrams (inspired by the design automation community) to tensor networks and the ZX-calculus, various complementary approaches have been proposed. This work provides a look "under the hood" of today's tools and showcases how these means are utilized in them, e.g., for simulation, compilation, and verification of quantum circuits.
With quantum computers promising advantages even in the near-term NISQ era, there is a lively community that develops software and toolkits for the design of corresponding quantum circuits. Although the underlying problems are different, expertise from the design automation community, which developed sophisticated design solutions for the conventional realm in the past decades, can help here. In this respect, decision diagrams provide a promising foundation for tackling many design tasks such as simulation, synthesis, and verification of quantum circuits. However, users of the corresponding tools often do not have a proper background or an intuition about how these methods based on decision diagrams work and what their strengths and limits are. In this work, we first review the concepts of how decision diagrams can be employed, e.g., for the simulation and verification of quantum circuits. Afterwards, in an effort to make decision diagrams for quantum computing more accessible, we then present a visualization tool for quantum decision diagrams, which allows users to explore the behavior of decision diagrams in the design tasks mentioned above. Finally, we present decision diagram-based tools for simulation and verification of quantum circuits using the methods discussed above as part of the open-source Munich Quantum Toolkit (MQT)—a set of tools for quantum computing developed at the Technical University of Munich and the Johannes Kepler University Linz and released under the MIT license. More information about the corresponding tools is available at https://github.com/cda-tum/ddsim . By this, we provide an introduction of the concepts and tools for potential users who would like to work with them as well as potential developers aiming to extend them.
As state-of-the-art quantum computers are capable of running increasingly complex algorithms, the need for automated methods to design and test potential applications rises. Equivalence checking of quantum circuits is an important, yet hardly automated, task in the development of the quantum software stack. Recently, new methods have been proposed that tackle this problem from widely different perspectives. However, there is no established baseline on which to judge current and future progress in equivalence checking of quantum circuits. In order to close this gap, we conduct a detailed case study of two of the most promising equivalence checking methodologies---one based on decision diagrams and one based on the ZX-calculus---and compare their strengths and weaknesses.
Quantum computers are becoming a reality and numerous quantum computing applications with a near-term perspective (e.g., for finance, chemistry, machine learning, and optimization) and with a long-term perspective (e.g., for cryptography or unstructured search) are currently being investigated. However, designing and realizing potential applications for these devices in a scalable fashion requires automated, efficient, and user-friendly software tools that cater to the needs of end users, engineers, and physicists at every level of the entire quantum software stack. Many of the problems to be tackled in that regard are similar to design problems from the classical realm for which sophisticated design automation tools have been developed in the previous decades.The Munich Quantum Toolkit (MQT) is a collection of software tools for quantum computing developed by the Chair for Design Automation at the Technical University of Munich which explicitly utilizes this design automation expertise. Our overarching objective is to provide solutions for design tasks across the entire quantum software stack. This entails high-level support for end users in realizing their applications, efficient methods for the classical simulation, compilation, and verification of quantum circuits, tools for quantum error correction, support for physical design, and more. These methods are supported by corresponding data structures (such as decision diagrams or the ZX-calculus) and core methods (such as SAT encodings/solvers). All of the developed tools are available as open-source implementations and are hosted on github.com/cda-tum.Note: A live version of this document is available at mqt.readthedocs.io.
Design, simulation, analysis and verification methodologies are crucial for developing electronic circuits and systems at large. Whereas long-standing EDA software is used in the semiconductor technology, there is no counterpart for quantum computing systems yet. Although the quantum computing community started utilizing and adapting some of the already existing EDA tools, for instance, to design quantum processors and control electronics for driving the qubits, or even to solve some quantum computing design tasks, they do not fully use the expertise gained over the last decades in the field of design automation. Current intermediate-scale quantum computers have been designed in an ‘adhoc’ manner with heterogeneous methods and tools. As we are entering the large-scale era, it is timely and key to further adopt EDA methodologies and software for quantum computing. In this paper, we provide an overview on how full-stack quantum computing systems are being implemented nowadays and discuss which the main challenges are for transitioning from this current scenario to a comprehensive framework encompassing full automated system-wide architecting, design, simulation, verification, and test.
Quantum computing is a revolutionary approach to computation that leverages the principles of quantum mechanics, enabling computers to process information in fundamentally different ways than classical computers. Unlike traditional bits, which represent data as either 0s or 1s, quantum bits, or qubits, can exist in multiple states simultaneously due to superposition. Additionally, qubits can be entangled, allowing them to be interconnected in ways that enhance computational power and efficiency. This unique behavior has the potential to run certain types of computation tasks much faster than classical computers can, marking a significant leap forward in technology. When building actual quantum computers to run practical quantum algorithms, one needs efficient ways to map the algorithms to the hardware components, similar to compiling classical algorithms onto CPU/GPU hardware. This thesis aims to tackle some of the important problems in the mapping process. First, can we address hardware errors and algorithm errors at the same time? Second, can we build a better circuit complexity metric to inspire better quantum architecture design, and can we design better quantum algorithms and compilation techniques using this improved metric? Lastly, can we use physics-level simulation results to inspire better circuit-level optimization techniques? We hope to provide positive answers to all three questions above through three separate architectural innovations.
With the emergence of more and more applications for quantum computing, also the development of corresponding methods for design automation is receiving increasing interest. In this respect, decision diagrams provide a promising basis for many design tasks such as simulation, synthesis, verification, and more. However, users of the corresponding tools often do not have a proper background or an intuition about how these methods based on decision diagrams work and what their strengths and limits are. In an effort to make decision diagrams for quantum computing more accessible, we present a visualization tool which visualizes quantum decision diagrams and allows to explore their behavior when used in the design tasks mentioned above. The installation-free web-tool allows users to interactively learn how decision diagrams can be used in quantum computing, e.g., to (1) compactly represent quantum states and the functionality of quantum circuits, (2) to efficiently simulate quantum circuits, and (3) to verify the equivalence of two circuits. The tool is available at https://iic.jku.at/eda/research/quantum_dd/tool