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Published onJan 27, 2022

Data Science on a Future Quantum Internet

**Keywords**: quantum computing; quantum internet; quantum machine learning; adversarial learning

If we try to envision how far quantum resources may potentially help with data processing in the future, we can first look for guidance at how classical data processing progressed. Beginning from individual classical processors, parallel processors were invented, and these processors were later interconnected in clusters and evolved into the modern internet. The question is, might a similar trajectory be possible for quantum computers, where individual smaller quantum devices are interconnected and communicate using quantum information, in a future quantum internet (Rohde et al., 2021)? What advances and new questions in data science might result?

One key development in classical computing that led to the success of high-performance computing is the evolution from purely serial computation to parallel computation. The concept of allowing multiple processors to run programs in parallel decreased the total computational run-time without requiring increases in the clock frequency of each individual processor, which would otherwise lead to extra power expenditure. Since the maximum energy per processor is no longer a barrier and given the fact that there appear to be no fundamental physical limitations on how many extra processors might be employed, it is arguable that any potential speedup from a single quantum computer, which in the near-term would at best be very modest, may be replaceable with multiple parallel classical processors.

However, the optimal speedup from parallelization is only linear. Furthermore, this optimal limit is only rarely realized. In most cases, not every part of the computation task is parallelizable and these parts would need to be processed on a serial processor. This serialized part of the computation can severely limit the speedup afforded by parallelization, as captured by Amdahl’s law and Gustafson’s law. In other words, if one can’t speed up the slowest part of the computation that can’t be parallelized, no amount of extra parallel processors will help very much. This is where quantum computers may really be necessary: in providing speedups to subroutines in nonparallelizable parts of an algorithm.

While the motivation to build multiple classical processors rather than rely on individual processors came from constraints on clock frequency and energy, the scalability barrier for individual quantum processors is chiefly from its sensitivity to noise. Therefore, to exploit quantum devices more fully, it is natural in the future to also consider multiple smaller quantum processors working together in a cluster and later in a larger network. What are the new possibilities and new questions that arise in such a setting?

We can broadly categorize this computing network setting into four types (i) CC network (classical data/processing over a classical network), that is, the current internet; (ii) CQ network (classical data/processing over a quantum network); (iii) QC network (quantum data/processing over a classical network); and (iv) QQ network (quantum data/processing over a quantum network), or a fully quantum internet.

A prominent example in a CQ network is the area of quantum cryptographic protocols (Pirandola et al., 2020), where a quantum communication channel between entangled parties is able to hold information that is not accessible through local probing of the individual parties alone. This application to security is a natural fit for quantum devices due to the no-cloning theorem. An example of a QC network is allowing only classical information to be passed between individual quantum devices, like two quantum computers exchanging the final classical output YES/NO of their computation.

The most intriguing is the QQ network. A very interesting example here is the quantum fingerprinting protocol (Buhrman et al., 2001). Here, two separate quantum devices each prepare a quantum state embedding information about two classical bit-strings. The two parties send their quantum states to a third quantum party through a quantum channel. This third party then performs a quantum protocol (called a swap test, which is incidentally used in many quantum machine learning protocols) to determine whether (YES) or not (NO) the original bit-strings embedded in those two quantum states (i.e., the `fingerprints’) are identical. In the absence of noise and error, this protocol demonstrates an exponential quantum/classical gap for this YES/NO problem. This essentially provides a reduction in the number of communication messages required between the three parties. Deeper investigation of this protocol in the presence of shared randomness and assistance from entanglement show explicit quantum advantage even in the presence of errors (Horn et al., 2005).

In other models of communication complexity, there are several other protocols that claim up-to-exponential advantages if quantum resources are used (de Wolf, 2002), but most of these protocols are not of real practical interest and exponential advantages can disappear when noise is considered. So, it is certainly an important direction to look into whether quantum resources can assist in data processing, not only in saving the computation time per processor but in the time for communication between devices when considering a collective computation of many devices where delegation is necessary.

When more than one quantum device or party is involved, security concerns also come into play. Much work has been done on secure delegated universal quantum computation that uses more than one quantum device (Fitzsimons, 2017). For machine learning tasks, where the data might originate in different locations, this network setting becomes a natural setup. Here one would be concerned about the vulnerability and robustness of quantum algorithms for machine learning tasks. These questions belong to the area of adversarial quantum learning (Liu & Wittek, 2020; Lu et al., 2020), which lies at the interface between security, quantum information, and machine learning. For example, it explores the fundamental connections between concepts in security and privacy (e.g., differential privacy) and the robustness of quantum machine learning algorithms (Du et al., 2021). Quantum algorithms for security-related tasks like anomaly detection (Liu & Rebentrost, 2018) are also considered to belong in this setting. Whether or not quantum advantages in these contexts can be ultimately recovered in realistic settings is still an open question and deserves more attention.

Nana Liu has no financial or non-financial disclosures to share for this article.

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Du, Y., Hsieh, M.-H., Liu, T., Tao, D., & Liu, N. (2021). Quantum noise protects quantum classifiers against adversaries*. Physical Review Research, 3*(2), Article 023153. https://doi.org/10.1103/PhysRevResearch.3.023153

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Liu, N., & Rebentrost, P.* *(2018). Quantum machine learning for quantum anomaly detection.* Physical Review A, 97*(4), Article 042315. https://doi.org/10.1103/PhysRevA.97.042315

Liu, N., & Wittek, P. (2020). Vulnerability of quantum classification to adversarial perturbations.* Physical Review A, 101*(6)*, *Article 06331. https://doi.org/10.1103/PhysRevA.101.062331

Lu, S., Duan, L.-M., & Deng, D.-L. (2020).* *Quantum adversarial machine learning.* Physical Review Research, 2*(3)*, *Article 033212. https://doi.org/10.1103/PhysRevResearch.2.033212

Pirandola, S., Andersen, U. L., Banchi, L., Berta, M., Bunandar, D., Colbeck, R., Englund, D., Gehring, T., Lupo, C. Ottaviani, C., Pereira, J., Razavi, M., Shaari, J. S., Tomamichel, M., Usenko, V. C., Vallone, G., Villoresi, P., & Wallden, P. (2020).* *Advances in quantum cryptography.* Advances in Optics and Photonics, 12*(4), Article 1012. https://doi.org/10.1364/AOP.361502

Rohde, R., Huang, Z., Huang, H., Su, Z., Harrison, S., Byrnes, T., Dowling, J., Tan, S.-H., Mantri, A., Devitt, S., Ramakrishnan, R., Liu, N., Radhakrishnan, C., & Munro, W. (2021).* The quantum internet: The second quantum revolution. *Cambridge University Press. https://doi.org/10.1017/9781108868815

©2022 Nana Liu. This article is licensed under a Creative Commons Attribution (CC BY 4.0) International license, except where otherwise indicated with respect to particular material included in the article.