Quantum circuit transpilation facilitates the decomposition of complex operations into simpler hardware-compatible gates. This results in significant changes to the input circuit, and consequently, it becomes imperative to verify the correctness of the transpilation process. Quantum circuit equivalence checking is used to verify the operational equivalence of large quantum circuits to ensure the correctness of computation. Although small quantum circuits can be simulated easily on a classical computer without transpilation, this approach is unscalable for larger, more complex quantum circuits. Furthermore, a scalable quantum equivalence checking algorithm exhibiting subpar performance when applied to larger quantum circuits lacks reliability. Therefore, an equivalence-checking algorithm with scalability and acceptable performance is necessary to verify large quantum circuits. In this paper, we propose QuaSi, a simulation-based verification methodology designed to generate distinct test cases to achieve a scalable and reliable quantum circuit equivalence-checking. Our proposed approach surpasses existing state-of-the-art simulation-based methodologies by boosting the success rate of verification, in addition to reducing the verification latency. When evaluating using large benchmarks with up to 130 qubits, QuaSi furnished significantly improved performance compared to existing approaches in all types of scenarios. Furthermore, we proposed an algorithm to locate the erroneous gates to facilitate debugging the transpilation process.
Quantum circuit transpilation facilitates the decomposition of complex operations into simpler hardware-compatible gates. This results in significant changes to the input circuit, and consequently, it becomes imperative to verify the correctness of the transpilation process. Quantum circuit equivalence checking is used to verify the operational equivalence of large quantum circuits to ensure the correctness of computation. Although small quantum circuits can be simulated easily on a classical computer without transpilation, this approach is unscalable for larger, more complex quantum circuits. Furthermore, a scalable quantum equivalence checking algorithm exhibiting subpar performance when applied to larger quantum circuits lacks reliability. Therefore, an equivalence-checking algorithm with scalability and acceptable performance is necessary to verify large quantum circuits. In this paper, we propose QuaSi, a simulation-based verification methodology designed to generate distinct test cases to achieve a scalable and reliable quantum circuit equivalence-checking. Our proposed approach surpasses existing state-of-the-art simulation-based methodologies by boosting the success rate of verification, in addition to reducing the verification latency. When evaluating using large benchmarks with up to 130 qubits, QuaSi furnished significantly improved performance compared to existing approaches in all types of scenarios. Furthermore, we proposed an algorithm to locate the erroneous gates to facilitate debugging the transpilation process.
Quantum computing has proven to be capable of accelerating many algorithms by performing tasks that classical computers cannot. As quantum algorithms and implementations grow more complex, the need for rigorous circuit verification becomes critical, ensuring correct compilation and enhancing circuit fidelity through error correction and assertions. In this paper, we propose QuBEC, a Decision Diagram-based quantum equivalence checking approach, that requires less latency compared to existing techniques, while accounting for circuits with quantum error correction redundancy. QuBEC reduces verification time on benchmark circuits by up to 443×, while the number of Decision Diagram nodes required is reduced by up to 798.31×, compared to state-of-the-art strategies. The proposed QuBEC framework can contribute to the advancement of quantum computing by enabling faster and more efficient verification of quantum circuits, paving the way for the development of larger and more complex quantum algorithms.
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/.
This research paper provides an in-depth examination of verification and testing approaches for quantum circuits, focusing on methodologies essential for ensuring the correctness, reliability and operational efficiency of quantum computing systems. Since quantum circuits function on the fundamental principles of superposition and entanglement, they present verification challenges that cannot be effectively addressed using conventional classical testing techniques. As a result, the development of specialized quantum-specific verification strategies has become critically important. The study highlights simulation-based verification as a foundational technique, wherein the outcomes of quantum circuit simulations are systematically compared with results obtained from physical quantum hardware. This process enables the identification of functional inconsistencies and supports iterative refinement of circuit designs. In addition, randomized benchmarking is examined as a key evaluation method for estimating circuit fidelity and quantifying error rates through the application of random gate sequences and performance comparisons against established benchmarks. To further improve system robustness, the research investigates fault-tolerant mechanisms, particularly quantum error correction codes, which play a vital role in minimizing the effects of noise, decoherence and hardware imperfections. The integration of advanced quantum metrology and characterization techniques is also explored, enabling precise measurement and detailed analysis of quantum system behavior. These techniques provide deeper insights into circuit performance and contribute significantly to validation processes. By combining simulation-based verification, randomized benchmarking, fault-tolerant protocols and quantum metrology, this study proposes a comprehensive and reliable framework for quantum circuit verification and testing. The findings contribute to the advancement of dependable quantum technologies and support their growing applications in areas such as cryptography, materials science and other emerging domains.
In this research paper, I have thoroughly described about the topic “study on Verification and Testing Strategies for Quantum Circuits.” The research on quantum circuit verification and testing methodologies examines how to ensure the dependability and functioning of quantum computing systems, which are crucial to their transformational potential. Quantum circuits use superposition and entanglement, which need verification and testing methods. Innovative quantum circuit-specific methodologies are needed since conventional computing methods fail in quantum computing. A major research area is simulation-based verification, which compares simulated quantum circuit outputs to genuine hardware implementations. Developers may identify circuit design or implementation problems by comparing simulated and predicted results, enabling incremental improvement. Randomized benchmarking procedures may also evaluate quantum circuit integrity and error rates. These protocols quantify operational features of circuits by submitting them to randomized operations and evaluating their performance against preset benchmarks, leading attempts to enhance reliability and performance. Fault-tolerant methods, such as error correction codes, reduce quantum hardware noise and mistakes, improving quantum circuit reliability. The incorporation of error correcting techniques makes quantum circuits more resilient to environmental perturbations, making them more practical. Advanced quantum metrology and characterization methods provide accurate measurement and characterization of quantum systems, making quantum circuit testing and validation easier. These approaches help identify circuit performance improvements by correctly characterizing quantum features and behavior. This research integrates simulation-based verification, randomized benchmarking procedures, fault-tolerant approaches, and quantum metrology to ensure quantum circuit functioning and dependability. This research advances quantum technologies and realizes their transformative potential in cryptography, materials science, and other fields by explaining verification and testing strategies tailored to quantum computing systems
The rapid rate of progress in the physical realization of quantum computers sparked the development of elaborate design flows for quantum computations on such devices. Each stage of these flows comes with its own representation of the intended functionality. Ensuring that each design step preserves this intended functionality is of utmost importance. However, existing solutions for equivalence checking of quantum computations heavily struggle with the complexity of the underlying problem and, thus, no conclusions on the equivalence may be reached with reasonable efforts in many cases. In this work, we uncover the power of simulation for equivalence checking in quantum computing. We show that, in contrast to classical computing, it is in general not necessary to compare the complete representation of the respective computations. Even small errors frequently affect the entire representation and, thus, can be detected within a couple of simulations. The resulting equivalence checking flow substantially improves upon the state of the art by drastically accelerating the detection of errors or providing a highly probable estimate of the operations' equivalence.
Verifying whether two quantum circuits are equivalent is a central challenge in the compilation and optimization of quantum programs. We introduce \textsc{Manjushri}, a new automated framework for scalable quantum-circuit equivalence checking. \textsc{Manjushri} uses local projections as discriminative circuit fingerprints, implemented with weighted binary decision diagrams (WBDDs), yielding a compact and efficient symbolic representation of quantum behavior. We present an extensive experimental evaluation that, for random 1D Clifford+T circuits, explores the trade-off between \textsc{Manjushri} and \textsc{ECMC}, a tool for equivalence checking based on a much different approach. \textsc{Manjushri} is much faster up to depth 30 (with the crossover point varying from 39--49, depending on the number of qubits and whether the input circuits are equivalent or inequivalent): when inputs are equivalent, \textsc{Manjushri} is about 10× faster (or more); when inputs are inequivalent, \textsc{Manjushri} is about 8× faster (or more). For both kinds of equivalence-checking outcomes, \textsc{ECMC}'s success rate out to depth 50 is impressive on 32- and 64-qubit circuits: on such circuits, \textsc{ECMC} is almost uniformly successful. However, \textsc{ECMC} struggled on 128-qubit circuits for some depths. \textsc{Manjushri} is almost uniformly successful out to about depth 38, before tailing off to about 75\% at depth 50 (falling to 0\% at depth 48 for 128-qubit circuits that are equivalent). These results establish that \textsc{Manjushri} is a practical and scalable solution for large-scale quantum-circuit verification, and would be the preferred choice unless clients need to check equivalence of circuits of depth $>$38.