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Compilation for Dynamically Field-Programmable Qubit Arrays with Efficient and Provably Near-Optimal Scheduling

Daniel Bochen Tan, Wan-Hsuan Lin, Jason Cong

TL;DR

This study breaks down the compilation forynamically field-programmable qubit arrays based on neutral atoms into three tasks: scheduling, placement, and routing, and presents efficient solutions to them.

Abstract

Dynamically field-programmable qubit arrays based on neutral atoms feature high fidelity and highly parallel gates for quantum computing. However, it is challenging for compilers to fully leverage the novel flexibility offered by such hardware while respecting its various constraints. In this study, we break down the compilation for this architecture into three tasks: scheduling, placement, and routing. We formulate these three problems and present efficient solutions to them. Notably, our scheduling based on graph edge-coloring is provably near-optimal in terms of the number of two-qubit gate stages (at most one more than the optimum). As a result, our compiler, Enola, reduces this number of stages by 3.7x and improves the fidelity by 5.9x compared to OLSQ-DPQA, the current state of the art. Additionally, Enola is highly scalable, e.g., within 30 minutes, it can compile circuits with 10,000 qubits, a scale sufficient for the current era of quantum computing. Enola is open source at https://github.com/UCLA-VAST/Enola

Compilation for Dynamically Field-Programmable Qubit Arrays with Efficient and Provably Near-Optimal Scheduling

TL;DR

This study breaks down the compilation forynamically field-programmable qubit arrays based on neutral atoms into three tasks: scheduling, placement, and routing, and presents efficient solutions to them.

Abstract

Dynamically field-programmable qubit arrays based on neutral atoms feature high fidelity and highly parallel gates for quantum computing. However, it is challenging for compilers to fully leverage the novel flexibility offered by such hardware while respecting its various constraints. In this study, we break down the compilation for this architecture into three tasks: scheduling, placement, and routing. We formulate these three problems and present efficient solutions to them. Notably, our scheduling based on graph edge-coloring is provably near-optimal in terms of the number of two-qubit gate stages (at most one more than the optimum). As a result, our compiler, Enola, reduces this number of stages by 3.7x and improves the fidelity by 5.9x compared to OLSQ-DPQA, the current state of the art. Additionally, Enola is highly scalable, e.g., within 30 minutes, it can compile circuits with 10,000 qubits, a scale sufficient for the current era of quantum computing. Enola is open source at https://github.com/UCLA-VAST/Enola
Paper Structure (12 sections, 1 theorem, 2 equations, 9 figures)

This paper contains 12 sections, 1 theorem, 2 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Motivation: Fidelity Analysis
  3. Scheduling: Edge Coloring
  4. Placement: Simulated Annealing
  5. Routing: Independent Set
  6. Evaluation
  7. Impact of Different Settings in Enola
  8. Quality Comparison with Previous Works
  9. Runtime Scaling of Enola
  10. Potential Impact of Multiple AODs
  11. Related Work
  12. Conclusion and Future Direction

Key Result

Theorem 1

For a group of commutable two-qubit gates on $n$ qubits, suppose the optimal number of Rydberg stages to schedule these gates on DPQA is $S_\mathrm{opt}$, there is an algorithm with time complexity $O(n^3)$ that assigns these gates to at most $S_\mathrm{opt}+1$ Rydberg stages.

Figures (9)

  • Figure 1: Dynamically field-programmable qubit arrays (DPQA). a) Qubits (blue dots) can transfer between SLM traps (circles) and AOD traps (intersections of red lines). AOD rows and columns can move while preserving their relative order. b) A global Rydberg laser excites all qubits. A two-qubit gate is applied if two qubits are within the Rydberg range.
  • Figure 2: Error breakdown of the OLSQ-DPQA and Enola results. The benchmarks are 3-regular MaxCut QAOA circuits used in Ref. tan2023compiling. For the 90-qubit circuits, Enola reduces two-qubit gate stages by 3.7x and improves the overall fidelity by 5.9x.
  • Figure 3: Scheduling in Enola. a) Scheduling a commutation group of two-qubit gates with edge coloring. b) Generic circuits can be divided to dependency subcircuits and commutation groups. Dependency subcircuits are scheduled ASAP.
  • Figure 4: Placement in Enola. a) Trivial placement from left to right, from top to bottom. b) Placement with gate distance optimized by simulated annealing. c) Dynamic placement: after a Rydberg stage (red) is executed (left), run simulated annealing on moved qubits for a new placement (right).
  • Figure 5: Routing in Enola. a) Definition of a move as a 4-tuple. b) Conflicts between two moves. c) Compatible moves are independent sets (IS) in the conflict graph (filled vertices). After finding an IS, delete the moves and their duals from the graph. The process continues until no moves are left.
  • ...and 4 more figures

Theorems & Definitions (1)

  • Theorem 1