Quantum Algorithm Implementations for Beginners

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.

arXiv commentACM Transactions on Quantum Computing

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• Can Error Mitigation Improve Trainability of Noisy Variational Quantum Algorithms?
• A Comprehensive Review of Quantum Circuit Optimization: Current Trends and Future Directions
• Large-Scale Simulation of Shor's Quantum Factoring Algorithm
• Preparing Valence-Bond-Solid states on noisy intermediate-scale quantum computers
• The Cost of Improving the Precision of the Variational Quantum Eigensolver for Quantum Chemistry
• Adaptive Quantum State Tomography with Active Learning
• Quantum algorithms for scientific computing
• A quantum annealing-sequential quadratic programming assisted finite element simulation for non-linear and history-dependent mechanical problems
• A Bayesian Approach for Characterizing and Mitigating Gate and Measurement Errors
• Evaluating the Performance of Some Local Optimizers for Variational Quantum Classifiers
• Real-time simulation of light-driven spin chains on quantum computers
• A quantum computing concept for 1-D elastic wave simulation with exponential speedup
• Simulating of X-states and the two-qubit XYZ Heisenberg system on IBM quantum computer
• Quantum computing for genomics: conceptual challenges and practical perspectives
• Hierarchical Multigrid Ansatz for Variational Quantum Algorithms
• Experimental benchmarking of quantum state overlap estimation strategies with photonic systems
• Quantum Computing Approach for Energy Optimization in a Prosumer Community
• Quantum clustering and jet reconstruction at the LHC
• Expressiveness of Commutative Quantum Circuits: A Probabilistic Approach
• Approximate quantum gates compiling with self-navigation algorithm
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• Masking Countermeasures Against Side-Channel Attacks on Quantum Computers