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Simon's Algorithm in the NISQ Cloud.

Reece Robertson1,2,3, Emery Doucet1,2, Ernest Spicer4

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This study benchmarks quantum cloud devices using Simon's algorithm, revealing critical error rates and architectural insights for superconducting chips. Understanding quantum hardware is key for future quantum advantage.

Keywords:
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Area of Science:

  • Quantum Computing
  • Quantum Information Science
  • Computational Complexity Theory

Background:

  • Simon's algorithm offers a theoretical quantum advantage but requires fault-tolerant qubits.
  • Current quantum cloud platforms provide access to noisy, intermediate-scale quantum (NISQ) devices.
  • Benchmarking these NISQ devices is crucial for assessing their practical capabilities.

Purpose of the Study:

  • To benchmark the error rates of commercially available quantum computing devices via the quantum cloud.
  • To compare the performance of different physical quantum computing platforms, specifically IBM and IonQ.
  • To investigate the impact of device architecture and topology on quantum algorithm execution.

Main Methods:

  • Implementation of Simon's algorithm on quantum cloud platforms.
  • Analysis of algorithm output to quantify qubit error rates.
  • Comparative study of IBM's superconducting and IonQ's trapped-ion quantum processors.
  • Examination of transpilation strategies and their effect on performance.

Main Results:

  • Objective comparison of error rates across IBM and IonQ quantum hardware.
  • Demonstration that two-qubit operations on spatially separated qubits in superconducting architectures are detrimental.
  • Identification of platform-specific challenges and advantages for running quantum algorithms.
  • Quantification of performance variations based on qubit connectivity and topology.

Conclusions:

  • Simon's algorithm serves as an effective tool for benchmarking current quantum hardware.
  • Device architecture and qubit connectivity significantly influence quantum algorithm performance.
  • Careful consideration of hardware topology is essential for efficient transpilation and achieving quantum advantage on NISQ devices.
  • The study provides valuable data for selecting appropriate quantum hardware for specific algorithmic tasks.