Simon's Algorithm in the NISQ Cloud

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.