Quantum Compilation Toolkit for Rydberg Atom Arrays with Implications for Problem Hardness and Quantum Speedups

TL;DR

This paper introduces a comprehensive quantum compilation toolkit for Rydberg atom arrays to efficiently solve the maximum independent set problem, including graph reduction, compatibility checks, and embedding, with implications for problem hardness and quantum speedups.

Contribution

The authors develop an end-to-end pipeline for mapping MIS problems onto Rydberg hardware, incorporating novel reduction and embedding techniques to enhance problem solvability and analyze problem hardness.

Findings

Real-world networks can be reduced significantly in sub-second time.

Reduction techniques reveal an easy-hard-easy transition in Rydberg-native MIS instances.

The toolkit enables tackling a broader class of problems with near-term Rydberg quantum devices.

Abstract

We propose and implement a comprehensive quantum compilation toolkit for solving the maximum independent set (MIS) problem on quantum hardware based on Rydberg atom arrays. Our end-to-end pipeline involves three core components to efficiently map generic MIS instances onto Rydberg arrays with unit-disk connectivity, with modules for graph reduction, hardware compatibility checks, and graph embedding. The first module (reducer) provides hardware-agnostic and deterministic reduction logic that iteratively reduces the problem size via lazy clique removals. We find that real-world networks can typically be reduced by orders of magnitude on sub-second time scales, thus significantly cutting down the eventual load for quantum devices. Moreover, we show that reduction techniques may be an important tool in the ongoing search for potential quantum speedups, given their ability to identify hard problem instances. In particular, for Rydberg-native MIS instances, we observe signatures of an easy-hard-easy transition and quantify a critical degree indicating the onset of a hard problem regime. The second module (compatibility checker) implements a hardware compatibility checker that quickly determines whether or not a given input graph may be compatible with the restrictions imposed by Rydberg quantum hardware. The third module (embedder) describes hardware-efficient graph embedding routines to generate (approximate) encodings with controllable overhead and optimized ancilla placements. We exemplify our pipeline with experiments run on the QuEra Aquila device available on Amazon Braket. In aggregate, our work provides a set of tools that extends the class of problems that can be tackled with near-term Rydberg atom arrays.