Quantum Machine Learning Algorithms and Their Ecosystem

In recent decades, many quantum computing scientists have leaned towards researching and generating quantum algorithms and their practical realization (Cerezo et al., 2021; Montanaro, 2016). As discussed in the previous chapter, quantum computers differ from classical computers mainly in the form of computation they employ. They can solve problems that are intractable for classical systems (Arute et al., 2019). In a quantum computer, instead of classical bits, qubits are the fundamental unit of information. The implementation of quantum algorithms is based fundamentally on the physical qualities of these qubits compared to classical bits. Still, the physical realization of quantum computers has not yet reached the level of maturity attained by their classical counterparts, where millions of transistors can be placed in a limited space without compromising their accuracy or functioning.

Noise and error control are crucial for...

Technical requirements

To be able to follow this chapter, you will require the following technical skills:

• A basic level of Python
• Familiarity with Visual Studio Code or any Integrated Development Environment (IDE) that supports Jupyter Notebooks

Foundational quantum algorithms

A review of foundational quantum algorithms is necessary to understand the state-of-the-art progress in QC and its potential to overcome problems intractable for classical computation. Starting from the basic concepts, an algorithm is a series of computer-executable steps to conduct a computation or solve a problem (Montanaro, 2016). Consequently, an algorithm is considered quantum when it successfully performs on a quantum machine. Generally speaking, all classical algorithms could theoretically perform on such a system. Nevertheless, in a strict sense, quantum algorithms refer to those with at least one step involving quantum mechanical properties, such as superposition or entanglement. One of the main attributes of quantum computers is quantum parallelism, which allows for many existing quantum algorithms (Álvarez et al., 2008).

A quantum circuit often characterizes a quantum algorithm. A quantum circuit is a structure where the problem-solving...

QML algorithms

This discipline combines classical machine learning with quantum capabilities to produce better solutions. Enhancing ML algorithms and/or classical training with quantum resources broadens the scope of pure ML, as happens with some classical devices such as GPUs or TPUs.

It has been extensively reported that using quantum approaches in learning algorithms could have several advantages (reviewed by Schuld et al., 2018). However, most of the earliest research in this framework chased a decrease in computational complexity in conjunction with a speedup. Current investigations also study methods for quantum techniques to provide unconventional learning representations that could even outperform standard ML in the future.

In recent years, the theories and techniques of QC have evolved rapidly, and the potential benefits for real-world applications have become increasingly evident (Deb et al., 2021; Egger et al., 2021). How QC may affect ML is a key topic of research...

Quantum programming

In the last decade, the development of QC has accelerated. A significant example is the development of tools to offer solutions using high-level coding languages (Chong et al., 2017; Ganguly et al., 2021). Quantum programming languages are the basis for translating concepts into instructions for quantum computers. Nature Reviews (Heim et al., 2020) states that quantum programming languages are used for the following purposes:

• Examining the QC fundamentals (qubits, superposition, entanglement), then testing and validating quantum algorithms and their implementations
• Managing existing physical quantum hardware
• Forecasting the costs of quantum program execution on probable hardware

Current quantum programming languages primarily aim to optimize quantum gate-based low-level circuits. Quantum circuits are constructed from quantum gates and used for universal quantum computers. A list of the main quantum gates is provided as follows:

...

Quantum clouds

Along with programming languages, widespread research and commercial use of quantum programs requires the fundamental element of cloud access (Gong et al., 2021). These cloud solutions are directly linked to quantum circuits and chips for the final testing and experiments with quantum algorithms.

Cloud access has allowed institutions and individuals to advance their QC exploration. Businesses and universities can now experiment with QC on the cloud regardless of how technology evolves and becomes popular. This began back in 2016, when IBM linked a quantum computer to the cloud and enabled the development and execution of basic cloud-based quantum apps (Castelvecchi, 2017). By 2022, at least 13 well-known companies were offering online access to quantum computers:

• Amazon Braket (AWS)
• Leap (D-Wave)
• IBM Q Experience (IBM)
• Google Quantum AI (Google)
• Xanadu Quantum Cloud (Xanadu)
• Azure Quantum (Microsoft)
• Forest (Rigetti)
• Quantum Inspire...

Summary

• The foundational quantum computing algorithms have already demonstrated the potential benefits of this new computational paradigm, provided that a specific set of hardware capable of harnessing the advantages of the physical approach is available.
• There is an interesting variety of options regarding quantum and hybrid quantum-classical algorithms for solving problems related to machine learning, optimization, and simulation. Most have documentation and open source code available to reduce the learning curve for new adopters.
• Quantum computers are a reality since anyone who needs to can access them and start the process of research and discovery toward a potential solution. Also, if there is commercial interest, multiple cloud services provide access to several quantum technologies that can be explored in parallel with high computational power to run quantum simulators.

References

• Abbas, A., Sutter, D., Zoufal, C., Lucchi, A., Figalli, A., & Woerner, S. (2021). The power of quantum neural networks. Nature Computational Science 2021 1:6, 1(6), 403–409. doi: 10.1038/s43588-021-00084-1
• Ablayev, F., Ablayev, M., Huang, J. Z., Khadiev, K., Salikhova, N., & Wu, D. (2020). On quantum methods for machine learning problems part I: Quantum tools. Big Data Mining and Analytics, 3(1), 41–55. doi: 10.26599/BDMA.2019.9020016
• Albash, T., & Lidar, D. A. (2018). Adiabatic quantum computation. Reviews of Modern Physics, 90(1), 015002. doi: 10.1103/REVMODPHYS.90.015002/FIGURES/11/MEDIUM
• Álvarez, G. A., Danieli, E. P., Levstein, P. R., & Pastawski, H. M. (2008). Quantum parallelism as a tool for ensemble spin dynamics calculations. Physical Review Letters, 101(12), 120503. doi: 10.1103/PHYSREVLETT.101.120503/FIGURES/3/MEDIUM
• Arute, F., Arya, K., Babbush, R., Bacon, D., Bardin, J. C., Barends, R., Biswas, R., Boixo...