Compiling Quantum Circuits for Dynamically Field-Programmable Neutral Atoms Array Processors

Daniel Bochen Tan1, Dolev Bluvstein2, Mikhail D. Lukin2, and Jason Cong1

1Computer Science Department, University of California, Los Angeles, CA 90095
2Department of Physics, Harvard University, Cambridge, MA 02138

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Dynamically field-programmable qubit arrays (DPQA) have recently emerged as a promising platform for quantum information processing. In DPQA, atomic qubits are selectively loaded into arrays of optical traps that can be reconfigured during the computation itself. Leveraging qubit transport and parallel, entangling quantum operations, different pairs of qubits, even those initially far away, can be entangled at different stages of the quantum program execution. Such reconfigurability and non-local connectivity present new challenges for compilation, especially in the layout synthesis step which places and routes the qubits and schedules the gates. In this paper, we consider a DPQA architecture that contains multiple arrays and supports 2D array movements, representing cutting-edge experimental platforms. Within this architecture, we discretize the state space and formulate layout synthesis as a satisfiability modulo theories problem, which can be solved by existing solvers optimally in terms of circuit depth. For a set of benchmark circuits generated by random graphs with complex connectivities, our compiler OLSQ-DPQA reduces the number of two-qubit entangling gates on small problem instances by 1.7x compared to optimal compilation results on a fixed planar architecture. To further improve scalability and practicality of the method, we introduce a greedy heuristic inspired by the iterative peeling approach in classical integrated circuit routing. Using a hybrid approach that combined the greedy and optimal methods, we demonstrate that our DPQA-based compiled circuits feature reduced scaling overhead compared to a grid fixed architecture, resulting in 5.1X less two-qubit gates for 90 qubit quantum circuits. These methods enable programmable, complex quantum circuits with neutral atom quantum computers, as well as informing both future compilers and future hardware choices.

Neutral atom arrays are gaining popularity as a platform for quantum computing because of the large number of qubits, high-fidelity operations, and long coherence. A unique feature of these arrays is the ability to change the coupling between qubits by physically moving them around. To run quantum circuits to this reconfigurable architecture, our compiler places qubits to specific positions and routes their movements through various stages of operation. In this paper, we systematically present the design space and constraints in such compilation. We also provide an open-source compiler that not only tackles these challenges but can generate animations of how qubits move.

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[2] Ludwig Schmid, David F Locher, Manuel Rispler, Sebastian Blatt, Johannes Zeiher, Markus Müller, and Robert Wille, "Computational capabilities and compiler development for neutral atom quantum processors—connecting tool developers and hardware experts", Quantum Science and Technology 9 3, 033001 (2024).

[3] Dolev Bluvstein, Simon J. Evered, Alexandra A. Geim, Sophie H. Li, Hengyun Zhou, Tom Manovitz, Sepehr Ebadi, Madelyn Cain, Marcin Kalinowski, Dominik Hangleiter, J. Pablo Bonilla Ataides, Nishad Maskara, Iris Cong, Xun Gao, Pedro Sales Rodriguez, Thomas Karolyshyn, Giulia Semeghini, Michael J. Gullans, Markus Greiner, Vladan Vuletić, and Mikhail D. Lukin, "Logical quantum processor based on reconfigurable atom arrays", Nature 626 7997, 58 (2024).

[4] Daniel Bochen Tan, Wan-Hsuan Lin, and Jason Cong, "Compilation for Dynamically Field-Programmable Qubit Arrays with Efficient and Provably Near-Optimal Scheduling", arXiv:2405.15095, (2024).

[5] Daniel Bochen Tan, Shuohao Ping, and Jason Cong, "Depth-Optimal Addressing of 2D Qubit Array with 1D Controls Based on Exact Binary Matrix Factorization", arXiv:2401.13807, (2024).

[6] Korbinian Staudacher, Ludwig Schmid, Johannes Zeiher, Robert Wille, and Dieter Kranzlmüller, "Multi-controlled Phase Gate Synthesis with ZX-calculus applied to Neutral Atom Hardware", arXiv:2403.10864, (2024).

[7] Joshua Viszlai, Willers Yang, Sophia Fuhui Lin, Junyu Liu, Natalia Nottingham, Jonathan M. Baker, and Frederic T. Chong, "Matching Generalized-Bicycle Codes to Neutral Atoms for Low-Overhead Fault-Tolerance", arXiv:2311.16980, (2023).

[8] Hanrui Wang, Pengyu Liu, Daniel Bochen Tan, Yilian Liu, Jiaqi Gu, David Z. Pan, Jason Cong, Umut A. Acar, and Song Han, "Atomique: A Quantum Compiler for Reconfigurable Neutral Atom Arrays", arXiv:2311.15123, (2023).

[9] Ludwig Schmid, Sunghye Park, Seokhyeong Kang, and Robert Wille, "Hybrid Circuit Mapping: Leveraging the Full Spectrum of Computational Capabilities of Neutral Atom Quantum Computers", arXiv:2311.14164, (2023).

[10] Yannick Stade, Ludwig Schmid, Lukas Burgholzer, and Robert Wille, "An Abstract Model and Efficient Routing for Logical Entangling Gates on Zoned Neutral Atom Architectures", arXiv:2405.08068, (2024).

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