Towards real-world implementations of quantum machine learning

This is a Perspective on "Quantum Deep Hedging" by El Amine Cherrat, Snehal Raj, Iordanis Kerenidis, Abhishek Shekhar, Ben Wood, Jon Dee, Shouvanik Chakrabarti, Richard Chen, Dylan Herman, Shaohan Hu, Pierre Minssen, Ruslan Shaydulin, Yue Sun, Romina Yalovetzky, and Marco Pistoia, published in Quantum 7, 1191 (2023).

By Junyu Liu (Pritzker School of Molecular Engineering, The University of Chicago, Chicago, IL 60637, USA, Department of Computer Science, The University of Chicago, Chicago, IL 60637, USA, Kadanoff Center for Theoretical Physics, The University of Chicago, Chicago, IL 60637, USA, qBraid Co., Chicago, IL 60615, USA, and SeQure, Chicago, IL 60615, USA).

Quantum machine learning, which involves algorithms akin to machine learning operating on quantum devices, is anticipated to be a flagship application for quantum technologies. In the short term, some experiments and benchmarks have been demonstrated [1,2,3,4,5,6,7,8,9,10], indicating that quantum algorithms related to machine learning may offer solutions to specific challenges across a range of fields, including quantum physics [11], quantum chemistry [1], optimization [2,12], deep learning [13,14,15], sensing [16,17], and many other directions. In the long term, theoretical frameworks for various quantum machine learning algorithms suggest potential speedups over their classical counterparts [18,19,20], contingent on certain conditions related to quantum hardware. These conditions include the likely integration of quantum error correction and the development of efficient interfaces between classical and quantum processors [21].

It is a well-founded notion that quantum computers are capable of addressing problems that are inherently quantum in nature, a concept stemming from Richard Feynman’s original proposition on the quantum simulation of chemical processes [22]. This leads to the intriguing question of whether quantum algorithms could also be beneficial for other types of tasks. Quantum machine-learning algorithms serve as prime examples of this potential, with the ability to relate to numerous real-world issues, including those in finance. Notably, there is significant progress, as highlighted in a recent paper [23], which discusses the advancement of quantum-enhanced hedging and the application of reinforcement-learning algorithms to actual financial markets.

It can be difficult to establish, using computational complexity theory, whether a quantum algorithm truly holds a quantum advantage over all classical alternatives [24]. Similarly, many classical machine-learning algorithms that are practically used lack provable guarantees. For example, the theoretical underpinnings of the emergent capabilities of advanced classical large language models, such as GPT-3 and its successors, remain an unresolved question [25], despite their considerable practical success. Consequently, some argue that rather than solely focusing on demonstrating computational superiority, it might be equally valuable to prioritize the development of end-to-end applications [26]. This approach involves hands-on experimentation with machine-learning models, either on actual machines or through simulations, to ascertain any practical benefits or enhancements that quantum methods may offer. This philosophy aligns with the practical methodologies employed by our classical counterparts.

The paper [23] follows a similar spirit toward practical, real-world implementations of quantum machine learning. The corresponding quantum neural-network architecture is similar to that in a series of previous works, which include end-to-end data uploading and training [27,28,29]. It is argued that, first, the architecture itself is computationally efficient. With some locality designs, the architecture could avoid the so-called barren-plateau problem, as the gradient will only vanish polynomially [4,9]. Secondly, the architecture has a clear classical counterpart, akin to orthogonal classical neural networks. Finally, the quantum architecture appears to have comparable performance to its classical counterpart with an equal or smaller number of training parameters when the number of qubits increases. This experimental observation might be due to the nature of high-dimensional Hilbert spaces.

The authors have also developed a novel quantum-native reinforcement-learning method [30] for hedging using these architectures. There are classical reasons to believe that, despite its complexity, distributed reinforcement learning can yield superior models compared to standard methods. In their work, they attempt to transform classical pipelines into quantum-native ones. They argue that quantum computing may be inherently suitable for their tasks: quantum circuits provide mappings for exponentially large distributions, while measurements reveal only a subset of this information. They find this to be advantageous for the hedging task, where net jumps in stochastic trajectories could be naturally interpreted as the Hamming weights of the encoding. Finally, their findings with end-to-end implementations are verified in the Quantinuum processors with 16 qubits.

The paper [23] sets an excellent example of a real-world, end-to-end implementation of quantum machine-learning experiments. Their research opens up many future directions in the field. First, further experiments are necessary to compare and benchmark against state-of-the-art classical machine-learning models, revealing possible quantum speedups for specific tasks. Optimization of multiple subroutines, particularly concerning data encoding and transfer between classical and quantum processors, could be crucial. Second, exploring the impact of noise in these quantum experiments [31], and determining to what extent we should suppress, mitigate, or correct noise in near-term and future quantum technologies, could be an interesting direction. Lastly, it would be valuable to theorize why quantum models could offer benefits over classical ones, such as reducing the number of training parameters. In sum, coupled with the development of fault-tolerant, large-scale quantum hardware, high-quality quantum machine learning experiments, alongside robust theoretical research and informed conjectures, could advance the field of quantum machine learning and might contribute real-world applications using quantum devices.


JL would like to thank various people discussing with him about quantum technologies connecting to machine learning, especially Yuri Alexeev, Frederic Chong, Jens Eisert, Xu Han, Hsin-Yuan Huang, Hansheng Jiang, Liang Jiang, Risi Kondor, Jin-Peng Liu, Zi-Wen Liu, Antonio Mezzapaco, John Preskill, Max Zuo-Jun Shen, David Simmons-Duffin, Changchun Zhong and Quntao Zhuang. JL is supported in part by International Business Machines (IBM) Quantum through the Chicago Quantum Exchange, and the Pritzker School of Molecular Engineering at the University of Chicago through AFOSR MURI (FA9550-21-1-0209).

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