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Benchmarking the Lights Out Problem on Real Quantum Hardware

Maksims Dimitrijevs, Maria Palchiha, Abuzer Yakaryilmaz

TL;DR

The Lights Out problem is implemented on a 2D grid and on Mobius ladder graphs and the performance of Grover's search on real quantum hardware is evaluated, finding that IQM Garnet performs more reliably than other tested IQM devices.

Abstract

We implement the Lights Out problem on a 2D grid and on Mobius ladder graphs and evaluate the performance of Grover's search on real quantum hardware. We use two instances using 9 and 16 qubits, and implement them on publicly available quantum hardware by IBM and IQM. Our experiments show improvements in IBM hardware between the Heron r1 and Heron r2 generations, highlighting progress in IBM hardware during the 2023-2024 period. The Lights Out circuits produced output distributions close to uniform on IQM devices. To diagnose device limitations, we additionally ran a small Grover SAT baseline, finding that IQM Garnet performs more reliably than other tested IQM devices. We also observed that QPUs of the same manufacturing revision can differ significantly in performance (a newer device is not guaranteed to be better), and that calibration has a significant impact on the performance of quantum devices, so the choice of device strongly depends on calibration quality.

Benchmarking the Lights Out Problem on Real Quantum Hardware

TL;DR

The Lights Out problem is implemented on a 2D grid and on Mobius ladder graphs and the performance of Grover's search on real quantum hardware is evaluated, finding that IQM Garnet performs more reliably than other tested IQM devices.

Abstract

We implement the Lights Out problem on a 2D grid and on Mobius ladder graphs and evaluate the performance of Grover's search on real quantum hardware. We use two instances using 9 and 16 qubits, and implement them on publicly available quantum hardware by IBM and IQM. Our experiments show improvements in IBM hardware between the Heron r1 and Heron r2 generations, highlighting progress in IBM hardware during the 2023-2024 period. The Lights Out circuits produced output distributions close to uniform on IQM devices. To diagnose device limitations, we additionally ran a small Grover SAT baseline, finding that IQM Garnet performs more reliably than other tested IQM devices. We also observed that QPUs of the same manufacturing revision can differ significantly in performance (a newer device is not guaranteed to be better), and that calibration has a significant impact on the performance of quantum devices, so the choice of device strongly depends on calibration quality.
Paper Structure (16 sections, 6 figures, 11 tables)

This paper contains 16 sections, 6 figures, 11 tables.

Table of Contents

  1. Introduction
  2. Grover's Search and Lights Out
  3. Grover's Search
  4. Lights Out
  5. Implementation of Problem instances
  6. Lights Out instance for $2 \times 2$ grid
  7. Lights Out instance for Möbius ladder with 6 lamps
  8. Supplementary baseline circuits (SAT and two-qubit sanity check)
  9. Methods for running circuits on quantum hardware
  10. Setup for experiments
  11. Results
  12. Lights Out on $2 \times 2$ grid
  13. Lights Out on Möbius ladder with 6 lamps
  14. Supplementary baseline circuits (SAT and two-qubit sanity check)
  15. Result analysis and discussion
  16. ...and 1 more sections

Figures (6)

  • Figure 1: Graphs and basis states for the implementation of Lights Out instances.
  • Figure 2: Implementation of Grover's Search for Lights Out problem on $2 \times 2$ grid of lamps.
  • Figure 3: Implementation of Grover's Search for Lights Out problem on Möbius ladder with 6 lamps.
  • Figure 4: Implementation of Grover's Search for a small SAT problem.
  • Figure 5: Implementation of a small imitation of Grover's Search.
  • ...and 1 more figures