An Abstract Model and Efficient Routing for Logical Entangling Gates on Zoned Neutral Atom Architectures

TL;DR

This work tackles routing and scheduling of transversal entangling gates in zoned neutral-atom quantum architectures to enable scalable fault-tolerant computing. It introduces an abstract zoned-architecture model, and a graph-theoretic routing method (NALAC) that uses a maximal independent set and DSatur-based edge coloring to maximize parallelism while minimizing qubit shuttling overhead. The authors provide a concrete implementation within the Munich Quantum Toolkit and demonstrate substantial reductions in routing overhead and enhanced parallelism over naive methods, with polynomial compilation times and hardware-design insights. Overall, the approach supports automated design and hardware-software co-design for scalable FTQC using neutral atoms, and lays groundwork for extending to full error-correction cycles and magic-state techniques.

Abstract

Recent experimental achievements have demonstrated the potential of neutral atom architectures for fault-tolerant quantum computing. These architectures feature the dynamic rearrangement of atoms during computation, enabling nearly arbitrary two-dimensional rearrangements. Additionally, they employ a zoned layout with dedicated regions for entangling, storage, and readout. This architecture requires design automation software that efficiently compiles quantum circuits to this hardware and takes care that atoms are in the right place at the right time. In this paper, we initiate this line of work by providing, (1) an abstract model of the novel architecture and, (2) an efficient solution to the routing problem of entangling gates. By this, we aim to maximize the parallelism of entangling gates and minimize the overhead caused by the routing of atoms between zones. In addition to that, we keep the realm of fault-tolerant quantum computing in mind and consider logical qubit arrays, each of which encodes one logical qubit. We implemented the proposed idea as a tool called NALAC and demonstrated its effectiveness and efficiency by showing that it can significantly reduce the routing overhead of logical entangling gates compared to the naive approach. As part of the Munich Quantum Toolkit (MQT), NALAC is publicly available as open-source at https://github.com/cda-tum/mqt-qmap.

Figures (21)

• Figure 1: Zoned architecture considered within this work based on the experimental setup from bluvsteinLogicalQuantumProcessor2023.
• Figure 2: One execution cycle up to the execution of the CZ gate as described in \ref{['exp:one-execution-cycle']}.
• Figure 3: Illustration of the four constraints on shuttling operations.
• Figure 4: The physical architecture and the configuration (left), i. e.⁠, array size for the code, serve as the input. A logical architecture is derived from this and used to find a logical routing (middle). This logical routing is then translated into a logical array routing (right).
• Figure 5: Comparison of sequential entangling operations (left) with proposed parallel execution and efficient logical qubit movement (right).

Theorems & Definitions (14)

• Example 1: Logical Qubit Arrays
• Example 2: Transversal CZ gate
• Example 3: Native Gates
• Example 4: One Execution Cylce
• Example 5: Shuttling Constraints
• Example 6: Naive vs. Proposed Solution
• Example 7: Interaction Graph
• Example 8: Independent Set
• Example 9: Order Preservation of AOD Qubits
• Example 10: Coloring Constraint