[Paper Review] Quantum Algorithm Implementations for Beginners

Patrick J. Coles, Stephan Eidenbenz+30 more|arXiv (Cornell University)|Apr 10, 2018

Quantum Computing Algorithms and Architecture98 references144 citations

TL;DR

This paper provides a beginner-friendly introduction to quantum algorithm implementation, explaining core principles through accessible algebra and demonstrating 20 quantum algorithms on IBM's real quantum hardware. It highlights key differences between simulator results and actual hardware performance, offering a practical blueprint for classical programmers transitioning to quantum computing.

ABSTRACT

As quantum computers become available to the general public, the need has arisen to train a cohort of quantum programmers, many of whom have been developing classical computer programs for most of their careers. While currently available quantum computers have less than 100 qubits, quantum computing hardware is widely expected to grow in terms of qubit count, quality, and connectivity. This review aims to explain the principles of quantum programming, which are quite different from classical programming, with straightforward algebra that makes understanding of the underlying fascinating quantum mechanical principles optional. We give an introduction to quantum computing algorithms and their implementation on real quantum hardware. We survey 20 different quantum algorithms, attempting to describe each in a succinct and self-contained fashion. We show how these algorithms can be implemented on IBM's quantum computer, and in each case, we discuss the results of the implementation with respect to differences between the simulator and the actual hardware runs. This article introduces computer scientists, physicists, and engineers to quantum algorithms and provides a blueprint for their implementations.

Motivation & Objective

• To bridge the gap between classical programming and quantum computing for non-quantum experts.
• To explain quantum programming principles using accessible algebra, minimizing reliance on deep quantum mechanics knowledge.
• To provide self-contained, succinct descriptions of 20 quantum algorithms for educational and implementation purposes.
• To demonstrate practical implementation of these algorithms on real IBM quantum hardware.
• To compare simulation results with actual hardware runs, identifying discrepancies due to noise and error rates.

Proposed method

• The paper uses elementary linear algebra to describe quantum states, gates, and circuits, avoiding advanced quantum mechanical formalism.
• Each algorithm is described in a self-contained manner, focusing on logical structure and quantum circuit design.
• Implementations are mapped to IBM's quantum computing platform, leveraging its circuit model and open-source tools like Qiskit.
• Simulations are run alongside real hardware executions to compare outcomes and assess noise effects.
• Results are analyzed by contrasting idealized simulation behavior with noisy, error-prone hardware outputs.
• The approach emphasizes reproducibility and practical learning for computer scientists, physicists, and engineers.

Experimental results

Research questions

• RQ1 How can quantum algorithms be explained and implemented in a way accessible to classical programmers?
• RQ2 What are the key differences between idealized quantum simulations and real hardware execution results?
• RQ3 Which quantum algorithms can be effectively demonstrated on current noisy intermediate-scale quantum (NISQ) devices?
• RQ4 How do hardware noise and decoherence affect the fidelity of quantum algorithm implementations?
• RQ5 What practical guidelines can be derived for implementing quantum algorithms on real quantum hardware?

Key findings

• The paper successfully demonstrates 20 quantum algorithms on IBM's real quantum hardware, providing a practical reference for beginners.
• Simulated results consistently outperform hardware runs due to noise and decoherence, especially in deeper circuits.
• Simple algorithms like Deutsch-Jozsa and Bernstein-Vazirani show high fidelity on hardware, indicating good performance on near-term devices.
• More complex algorithms exhibit significant error rates on hardware, highlighting the challenge of noise in current systems.
• The gap between simulation and hardware performance underscores the importance of error mitigation and hardware-aware algorithm design.
• The study provides a reproducible framework for implementing and testing quantum algorithms on real quantum processors.