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Design Automation for Quantum Circuits

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'''Design Automation for Quantum Circuits''' means using software to make quantum computing hardware and applications easier to develop. It turns high-level quantum algorithms into optimized circuits for specific quantum systems. Unlike classical circuit design, which has well-developed tools, quantum design automation is still new and challenging. This is because quantum bits (qubits) behave differently. They are sensitive to noise, have limited connections, and use reversible logic. These issues require special methods for breaking down gates, reducing errors, mapping circuits, and simulating them. As quantum processors grow and change, automated design is crucial to ensure they work well and correctly on different hardware.[1]

The automation process in quantum circuit design includes various stages such as algorithm specification, circuit synthesis, gate decomposition, qubit mapping, and noise-aware optimization. These stages help transform abstract quantum algorithms into physical instructions that can run on real quantum devices, often constrained by specific topologies and hardware characteristics.[2]

As the quantum computing ecosystem matures, numerous frameworks and toolchains have emerged to support this design process. Platforms like IBM’s Qiskit, Google’s Cirq, and the MQT Suite provide environments for simulating, optimizing, and compiling quantum circuits tailored to current quantum hardware. These tools play a critical role in making quantum computing more scalable, reproducible, and accessible to researchers and engineers.[3]

Quantum Circuits: An Overview

Quantum circuits are models that show how quantum computers work. They use quantum bits, or qubits, which are different from regular bits. Regular bits are either 0 or 1. Qubits can be both 0 and 1 at the same time because of a feature called superposition. Also, qubits can be entangled. This means the state of one qubit is connected to another, no matter how far apart they are.[4]

In quantum circuits, quantum gates are used to perform calculations. These gates change the qubits in a manner that can be reversed. We show these gates using special mathematical tools called unitary matrices. We used these gates to create the quantum algorithms. Some common gates are the Hadamard gate, which helps to create superposition, and the CNOT gate, which helps to create entanglement. These gates work in steps and do not waste energy, unlike regular gates. They follow the rules of quantum mechanics. [5]

In classical logic circuits, signals and logic states are predictable. However, in quantum circuits, we need to carefully control physical systems, such as trapped ions, superconducting circuits, or light-based parts. Quantum circuits are sensitive; therefore, they must be designed with limits on how long they can stay stable, how accurate the gates are, and how qubits connect. These factors greatly affect how accurately they work and their error rates.[6]

There are two types of quantum circuit model. The logical layer is related to the ideal operations required for computing. The physical layer deals with the real hardware limits and layout. It needs mapping and optimization to fit logical circuits to the available qubits and their interactions.[7]

Need for Design Automation

Design automation for quantum circuits’ means using software to make quantum computing hardware and applications easier to develop. It converts high-level quantum algorithms into optimized circuits for specific quantum systems. Unlike classical circuit design, which has well-developed tools, quantum design automation remains new and challenging. This is because the quantum bits (qubits) behave differently. They are sensitive to noise, have limited connections, and employ reversible logic. These issues require special methods to break down the gates, reduce errors, map circuits, and simulate them. As quantum processors grow and change, automated design is crucial to ensure they work well and correctly on different hardware.[8]

One major problem is the hardware connectivity. In many quantum systems, not all qubits are directly linked. This means that extra steps, such as SWAP gates, are required for the far-apart qubits to work together. This makes the circuits longer and more prone to errors. In addition, qubits can only maintain their quantum state for a short time, which is called the coherence time. Thus, longer circuits are more likely to fail owing to decoherence and noise.[9]

Another important issue is that the native gate sets are not the same everywhere. Quantum algorithms use standard gate libraries such as Clifford+T. However, they must be changed into operations that the hardware can handle. This change can lead to mistakes and requires a lot of time if performed by hand. It also differs among quantum devices.[10]

As the number of quantum devices increases, better ways to manage them are needed. Without automation, it is difficult to repeat results, keep track of circuit details, such as gate count and quality, and improve circuits over time. This need has led to the creation of quantum Electronic Design Automation (EDA) tools, which are similar to classical EDA but are made for quantum needs.[11]

Stages in the Design Automation Flow

Comparison between classical and quantum circuit design flows, illustrating differences in synthesis, mapping, and implementation stages.[12][13]

1. Algorithm Specification

The design process begins by creating a plan to solve a computer problem using quantum ideas. At this stage, the focus is on quantum operations and goals, rather than hardware. Some common quantum programming languages used are OpenQASM (for Qiskit), Quil (by Rigetti), and Cirq’s Python-based syntax. These languages help users to create circuits with basic and complex gates, conditional logic, and measurements. The aim is to create a logical circuit that works well and is efficient; however, it is not yet ready for hardware. [14][15]

2. Quantum Circuit Design

At this point, the main algorithm is turned into a quantum circuit using gates from a universal set, such as Clifford+T. The logical parts are broken down into single- and two-qubit operations. Quantum compilers use rules to simplify circuits by reducing the depth and number of gates while maintaining their functionality. This step aims to create a clear and correct circuit that is ready for mapping and adapting to the hardware.[16]

3. Compilation and Mapping

Quantum compilation involves adapting the logical circuit to accommodate the specific constraints of a given device, which include:·

  • Support for the native gate set
  • Qubit connectivity·
  • Physical error models

The mapping process assigns each logical bit to a physical qubit in the hardware. Owing to limitations in connectivity, SWAP gates can be introduced to facilitate interactions between non-adjacent qubits. Additionally, scheduling is employed to organize the execution of gates within coherence time windows.[17]

4. Error Mitigation and Correction

Quantum systems are very sensitive to noise and can lose their stability. Before running, the circuit can be adjusted to account for errors.

  • Error mitigation: Fixing errors after they happen or adjusting the circuit with methods like zero-noise extrapolation.
  • Error correction: Using quantum codes like surface codes to fix errors.

Most NISQ (Noisy Intermediate-Scale Quantum) devices use error mitigation instead of full error correction because they have a limited number of qubits. [18]

5. Execution on Hardware or Simulator

The quantum circuit is run on a real quantum computer or a simulator that acts like the hardware. Simulators can show all possible errors and are good for testing before actual use. Running the circuit means sending it to a system like IBM Quantum, Rigetti Aspen, or IonQ, and getting raw measurement data as the result.[19]

6. Post-Processing and Analysis

Following the execution, the measurement results undergo statistical analysis to derive the final outputs. For probabilistic algorithms, multiple iterations (shots) are aggregated to estimate the outcome distributions. This phase may also encompass result filtering, classical postprocessing, and plotting. In hybrid quantum-classical workflows, such as the Variational Quantum Eigensolver (VQE) and the Quantum Approximate Optimization Algorithm (QAOA), the results are subsequently passed to a classical optimizer.[20]

Commonly Used Tools and Frameworks

  1. ^ Cui, Rongyuan; Lyu, Zhuyang (2023-11-17). "Analysis of quantum gates in quantum circuits". Theoretical and Natural Science. 10 (1): 1–8. doi:10.54254/2753-8818/10/20230301. ISSN 2753-8818.
  2. ^ Kim, Dongmin; Heng, Sengthai; Han, Youngsun (2022-02-28). "A Parallelized Qubit Mapping Algorithm for Large-scale Quantum Circuits". IEIE Transactions on Smart Processing & Computing. 11 (1): 40–48. doi:10.5573/IEIESPC.2021.11.1.40. ISSN 2287-5255.
  3. ^ Mulherkar, Jaideep; Rajdeepak, Rishikant; Sunitha, V. (2022-10). "Implementation of quantum hitting times of cubelike graphs on IBM's Qiskit platform". International Journal of Quantum Information. 20 (07). doi:10.1142/S0219749922500204. ISSN 0219-7499. {{cite journal}}: Check date values in: |date= (help)
  4. ^ Jin, Ki-Sung; Cha, Gyu-Il (2023-07-01). "Multilayered logical qubits and synthesized quantum bits". Quantum Science and Technology. 8 (3): 035008. doi:10.1088/2058-9565/accec5. ISSN 2058-9565.
  5. ^ Flarend, Alice; Hilborn, Bob (2022-04-15), "Quantum Gates and Quantum Circuits", Quantum Computing: From Alice to Bob (1 ed.), Oxford University PressOxford, pp. 57–70, doi:10.1093/oso/9780192857972.003.0006, accessed 22 may 2025., isbn 978-0-19-285797-2, retrieved 2025-05-22 '"`UNIQ--templatestyles-0000001D-QINU`"'<cite class="citation cs2"></cite> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{[[Template:citation|citation]]}}</code>: </span><span class="cs1-visible-error citation-comment">Empty citation ([[Help:CS1 errors#empty_citation|help]])</span>[[Category:CS1 errors: empty citation]]: check |doi= value (help), ISBN 978-0-19-285797-2, retrieved 2025-05-23 {{citation}}: Check |doi= value (help); templatestyles stripmarker in |doi= at position 105 (help)
  6. ^ Xiang, Ze-Liang; Ashhab, Sahel; You, J. Q.; Nori, Franco (2013-04-09). "Hybrid quantum circuits: Superconducting circuits interacting with other quantum systems". Reviews of Modern Physics. 85 (2): 623–653. doi:10.1103/RevModPhys.85.623. ISSN 0034-6861.
  7. ^ Binti Adnan, Nurul Ain; Yamashita, Shigeru; Devitt, Simon J.; Nemoto, Kae (2014), Yamashita, Shigeru; Minato, Shin-ichi (eds.), "2D Qubit Layout Optimization for Topological Quantum Computation", Reversible Computation, vol. 8507, Cham: Springer International Publishing, pp. 176–188, doi:10.1007/978-3-319-08494-7_14, isbn 978-3-319-08493-0, retrieved 2025-05-23, ISBN 978-3-319-08493-0, retrieved 2025-05-23 {{citation}}: Check |doi= value (help)
  8. ^ Al‐Rabadi, Anas N. (2009-03-27). "Circuits for m ‐valued classical, reversible and quantum optical computing with application to regular logic design". International Journal of Intelligent Computing and Cybernetics. 2 (1): 52–101. doi:10.1108/17563780910939255. ISSN 1756-378X.
  9. ^ Zhang, Deng-Yu; Tang, Shi-Qing; Wang, Xin-Wen; Xie, Li-Jun; Gao, Feng (2011-04-01). "Feasible schemes for quantum swap gates of optical qubits via cavity QED". Chinese Physics B. 20 (4): 040308. doi:10.1088/1674-1056/20/4/040308. ISSN 1674-1056.
  10. ^ Abdessaied, Nabila; Amy, Matthew; Soeken, Mathias; Drechsler, Rolf (2016-05-18). "Technology Mapping of Reversible Circuits to Clifford+T Quantum Circuits". International Symposium on Multiple-Valued Logic. IEEE: 150–155. doi:10.1109/ISMVL.2016.33. ISBN 978-1-4673-9489-5.
  11. ^ Fourie, Coenrad J (2020-07-01). "Electronic Design Automation tools for superconducting circuits". Journal of Physics: Conference Series. 1590 (1): 012040. doi:10.1088/1742-6596/1590/1/012040. ISSN 1742-6588.
  12. ^ Wille, R., et al. (2024). "The MQT Handbook". arXiv preprint.
  13. ^ Cui, R., Lyu, Z. (17 November 2023). "Analysis of quantum gates in quantum circuits". Theoretical and Natural Science. 10 (1). Eliwise Academy: 1–8. doi:10.54254/2753-8818/10/20230301.
  14. ^ Cross, Andrew; Javadi-Abhari, Ali; Alexander, Thomas; De Beaudrap, Niel; Bishop, Lev S.; Heidel, Steven; Ryan, Colm A.; Sivarajah, Prasahnt; Smolin, John; Gambetta, Jay M.; Johnson, Blake R. (2022-09-30). "OpenQASM 3: A Broader and Deeper Quantum Assembly Language". ACM Transactions on Quantum Computing. 3 (3): 1–50. doi:10.1145/3505636. ISSN 2643-6809.
  15. ^ Jones, N. Cody; Van Meter, Rodney; Fowler, Austin G.; McMahon, Peter L.; Kim, Jungsang; Ladd, Thaddeus D.; Yamamoto, Yoshihisa (2012-07-31). "Layered Architecture for Quantum Computing". Physical Review X. 2 (3). doi:10.1103/PhysRevX.2.031007. ISSN 2160-3308.
  16. ^ Kissinger, Aleks; van de Wetering, John (2020-08-11). "Reducing the number of non-Clifford gates in quantum circuits". Physical Review A. 102 (2). doi:10.1103/PhysRevA.102.022406. ISSN 2469-9926.
  17. ^ Perez-Leija, Armando; Weimann, Steffen; Gräfe, Markus; Szameit, Alexander; Busch, Kurt (2017). "Photonic Two-Qubit SWAP Gates". Quantum Information and Measurement (QIM) 2017. Washington, D.C.: OSA: QT6A.36. doi:10.1364/qim.2017.qt6a.36.
  18. ^ Weaving, Tim; Ralli, Alexis; Kirby, William M.; Love, Peter J.; Succi, Sauro; Coveney, Peter V. (2023-10-17). "Benchmarking noisy intermediate scale quantum error mitigation strategies for ground state preparation of the HCl molecule". Physical Review Research. 5 (4). doi:10.1103/PhysRevResearch.5.043054. ISSN 2643-1564.
  19. ^ Zhou, Chen; Chan, Jay; Guan, Wen; Sun, Shaojun; Wang, Alex; Wu, Sau Lan; Livny, Miron; Carminati, Federico; Di Meglio, Alberto (2020-10-09). "Application of Quantum Machine Learning to High Energy Physics Analysis at LHC using IBM Quantum Computer Simulators and IBM Quantum Computer Hardware". Proceedings of European Physical Society Conference on High Energy Physics — PoS(EPS-HEP2019). Trieste, Italy: Sissa Medialab: 116. doi:10.22323/1.364.0116.{{cite journal}}: CS1 maint: unflagged free DOI (link)
  20. ^ Liu, Xiaoyuan; Angone, Anthony; Shaydulin, Ruslan; Safro, Ilya; Alexeev, Yuri; Cincio, Lukasz (2022). "Layer VQE: A Variational Approach for Combinatorial Optimization on Noisy Quantum Computers". IEEE Transactions on Quantum Engineering. 3: 1–20. doi:10.1109/TQE.2021.3140190. ISSN 2689-1808.
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