- The paper presents an experimental execution of Shor's algorithm on the IBM Q system for factoring small numbers (N=15, 21, 35), adapting the algorithm to suit current hardware constraints.
- The study utilized a semi-classical Quantum Fourier Transform and bypassed the standard continued fraction method, achieving good accuracy for N=15 and 21, but observing significant limitations for N=35 with only 14% successful runs.
- This work highlights the critical need for optimizing quantum circuits, mitigating hardware noise, and developing hybrid classical-quantum approaches to advance the practical implementation of complex quantum algorithms.
An Experimental Study of Shor's Factoring Algorithm on IBM Q
The research paper presents an experimental exploration of Shor's factoring algorithm executed on the IBM Q system, focusing on the compact yet challenging case of factoring the integers N=15, $21$, and $35$. This work is significant as it addresses the complexities and limitations inherent in current quantum computing technologies, like the IBM Q's superconducting qubits, while simultaneously demonstrating the potential of quantum algorithms to surpass classical methods for specific computational tasks.
The experiment leverages a compiled version of Shor's algorithm, which is notorious for its ability to factor large integers theoretically faster than the best classical algorithms. The implementation on the IBM Q's superconducting qubits presented several challenges, notably due to the necessity of minimizing qubit and gate usage to reduce noise and error rates. The paper employed a semi-classical quantum Fourier transform (sc-QFT) that enables the efficient usage of a limited number of qubits, a critical adaptation given the constraints of the IBM Q hardware.
This paper discusses the optimization strategies for qubit utilization, including reducing the quantum circuit depth and mitigating noise impact—key considerations when deploying Shor's algorithm on contemporary quantum devices. The authors also explore a unique method to bypass the continued fraction algorithm typically needed for period finding in Shor's process by analyzing the distribution of estimated phases and directly assigning periods using a calculated overlap coefficient.
Key numerical results indicate that the implementation for N=15 and N=21 achieves theoretical conformance in experimental data with minimal discrepancies, as measured by quantitative tools like the square of statistical overlap (SSO). For N=35, a significant drop in experimental accuracy was observed, pinpointing the limitations of the current hardware when gate errors accumulate—successful runs were noted merely 14% of the time.
From a practical standpoint, this work highlights the importance of optimizing classical-quantum hybrid approaches to tackle hardware limitations. Theoretically, this contributes to the literature by reinforcing the functionalities and potential caveats of executing quantum algorithms on superconductor-based quantum computers. Moreover, the experimental approach that eschews reliance on hardware features not yet widely available—like in-sequence measurements and qubit resets—offers a roadmap for further scalability and applicability in the nascent phase of quantum computing.
In conclusion, the implications of this work stress the significance of ongoing research in quantum gate efficiency, error rates, and feedback mechanisms that will eventually propel practical quantum computing. As quantum hardware evolves, these experiments pave the way for more robust execution of complex quantum algorithms, potentially enabling broader factorization tasks and beyond. Additionally, this paper serves as a stepping stone towards understanding the practical challenges and solutions in implementing quantum algorithms within current quantum architectures, offering a glimpse into the incremental advancements necessary before these techniques can broadly outperform classical hardware at scale.
