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. One of them is based on the ZX-calculus, a graphical rewriting system for quantum computing. However, the power and capability of this equivalence checking method has barely been explored. The aim of this work is to evaluate the ZX-calculus as a tool for equivalence checking of quantum circuits. To this end, it is demonstrated how the ZX-calculus based approach for equivalence checking can be expanded in order to verify the results of compilation flows and optimizations on quantum circuits. It is also shown that the ZX-calculus based method is not complete—especially for quantum circuits with ancillary qubits. In order to properly evaluate the proposed method, we conduct a detailed case study by comparing it to two other state-of-the-art methods for equivalence checking: one based on path-sums and another based on decision diagrams. The proposed methods have been integrated into the publicly available QCEC tool (https://github.com/cda-tum/qcec) which is part of the Munich Quantum Toolkit (MQT).
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. One of them is based on the ZX-calculus, a graphical rewriting system for quantum computing. However, the power and capability of this equivalence checking method has barely been explored. The aim of this work is to evaluate the ZX-calculus as a tool for equivalence checking of quantum circuits. To this end, it is demonstrated how the ZX-calculus based approach for equivalence checking can be expanded in order to verify the results of compilation flows and optimizations on quantum circuits. It is also shown that the ZX-calculus based method is not complete—especially for quantum circuits with ancillary qubits. In order to properly evaluate the proposed method, we conduct a detailed case study by comparing it to two other state-of-the-art methods for equivalence checking: one based on path-sums and another based on decision diagrams. The proposed methods have been integrated into the publicly available QCEC tool (https://github.com/cda-tum/qcec) which is part of the Munich Quantum Toolkit (MQT).
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.
Realizing a conceptual quantum algorithm on an actual physical device necessitates the algorithm's quantum circuit description to undergo certain transformations in order to adhere to all constraints imposed by the hardware. In this regard, the individual high-level circuit components are first synthesized to the supported low-level gate-set of the quantum computer, before being mapped to the target's architecture-utilizing several optimizations in order to improve the compilation result. Specialized tools for this complex task exist, e.g., IBM's Qiskit, Google's Cirq, Microsoft's QDK, or Rigetti's Forest. However, to date, the circuits resulting from these tools are hardly verified, which is mainly due to the immense complexity of checking if two quantum circuits indeed realize the same functionality. In this paper, we propose an efficient scheme for quantum circuit equivalence checking-specialized for verifying results of the IBM Qiskit quantum circuit compilation flow. To this end, we combine characteristics unique to quantum computing, e.g., its inherent reversibility, and certain knowledge about the compilation flow into a dedicated equivalence checking strategy. Experimental evaluations confirm that the proposed scheme allows to verify even large circuit instances with tens of thousands of operations within seconds or even less, whereas state-of-the-art techniques frequently time-out or require substantially more runtime. A corresponding open source implementation of the proposed method is publicly available at https://github.com/iic-jku/qcec.
Quantum computing is gaining serious momentum in these days. With increasing capabilities of corresponding devices also comes the need for efficient and automated tools to design them. Verification, i.e., ensuring that the originally intended functionality of a quantum algorithm/circuit is preserved throughout all layers of abstraction during the design process, is a vital part of the quantum software stack. In this work, we present QCEC , a tool for quantum circuit equivalence checking which is part of the JKQ toolset for quantum computing. By exploiting characteristics unique to quantum computing, the tool allows users to efficiently verify the equivalence of two quantum circuits using a variety of methods and strategies.
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.
In the not-so-distant future, quantum computing will change the way we tackle certain problems. It promises to dramatically speed-up many chemical, financial, cryptographical, and machine-learning applications. However, in order to capitalize on those promises, complex design flows composed of steps, such as compilation, decomposition, mapping, or transpilation need to be employed before being able to execute a conceptual quantum algorithm on an actual device. This results in many descriptions at various levels of abstraction which may significantly differ from each other. The complexity of the underlying design problems makes it ever more important to not only provide efficient solutions for the single steps but also to verify that the originally intended functionality is preserved throughout all levels of abstraction. This motivates methods for equivalence checking of quantum circuits. However, most existing methods for this are inspired by equivalence checking in the classical realm and have merely been extended to support quantum circuits (i.e., circuits which do not only rely on 0's and 1's but also employ superposition and entanglement). In this work, we propose an advanced methodology that takes the different paradigms of quantum circuits not only as a burden but as an opportunity. In fact, the proposed methodology explicitly utilizes characteristics unique to quantum computing in order to overcome the shortcomings of existing approaches. We show that by exploiting the reversibility of quantum circuits, complexity can be kept feasible in many cases. Moreover, we show that, in contrast to the classical realm, simulation is very powerful in verifying quantum circuits. Experimental evaluations confirm that the resulting methodology allows one to conduct equivalence checking dramatically faster than ever before-in many cases just a single simulation run is sufficient. An implementation of the proposed equivalence checking flow is publicly available at https://iic.jku.at/eda/research/quantum_verification/.
Quantum computing is an emerging computational paradigm with the potential to outperform classical computers in solving a variety of problems. To achieve this, quantum programs are typically represented as quantum circuits, which must be optimized and adapted for target hardware through quantum circuit compilation. We introduce ZX-DB, a data-driven system that performs quantum circuit simplification and rewriting inside a graph database using ZX-calculus, a complete graphical formalism for quantum mechanics. ZX-DB encodes ZX-calculus rewrite rules as standard openCypher queries and executes them on an example graph database engine, Memgraph, enabling efficient, database-native transformations of large-scale quantum circuits. ZX-DB integrates correctness validation via tensor and graph equivalence checks and is evaluated against the state-of-the-art PyZX framework. Experimental results show that ZX-DB achieves up to an order-of-magnitude speedup for independent rewrites, while exposing pattern-matching bottlenecks in current graph database engines. By uniting quantum compilation and graph data management, ZX-DB opens a new systems direction toward scalable, database-supported quantum computing pipelines.