# Using Quantum Computing to Infer Behaviors of Biological and Artificial Neural Networks

We recently published a pre-print research paper on arXiv that explores the use of quantum algorithms and computing to explore and ask questions ** about** the functional dynamics of neural networks. This is a component of the still-nascent topic of applying quantum computing to the modeling and simulations of biological and artificial neural networks. In this work, we showed how a carefully constructed set of conditions can use two foundational quantum algorithms, Grover and Deutsch-Josza, in such a way that the output measurements admit an interpretation that guarantees we can infer if a simple representation of a neural network (which applies to both biological and artificial networks) after some period of time has the potential to continue sustaining dynamic activity. Or whether the dynamics are guaranteed to stop either through ‘epileptic’ dynamics or quiescence.

Quantum computing may contribute to the study of neural networks in two key ways. The first is large-scale simulations of neural dynamics across scales of spatial and temporal organization. The second is carefully chosen and structured problems

aboutneural dynamics that make careful and clever use of quantum algorithms.

Quantum computing, at least theoretically at present, has the potential to revolutionize areas where classical computers show limitations, particularly in cryptography and the simulation of complex physical and chemical systems, including quantum mechanics itself. Notably, quantum algorithms like Shor’s for integer factorization could significantly disrupt traditional cryptographic techniques, presenting a mix of challenges

and opportunities in the realm of data security [1]. While research in quantum computing has historically focused on these well-established topics, the exploration of new problem classes that are particularly suitable for quantum computation is an active area of research, including the application of known quantum algorithms and the development of new ones. In fact, Google Quantum and X Prize just announced a new competition specifically to promote the development of practical, real-world quantum computing algorithms and applications.

However, a still-nascent topic is the application of quantum computing to the modeling and simulation of biological and artificial neural networks. In particular, a completely unexplored topic is the use of quantum algorithms and computing to explore and ask questions about the functional dynamics of neural networks. We have recently proposed that prioritizing research in these areas is important, as it can potentially significantly advance our understanding of the brain and mind and the increasingly rapid development of artificial intelligence.

To be sure, the intersection of quantum computing, neuroscience, and related topics has generated considerable interest already, leading to quite a few books, technical papers, and popular articles. Some of what has been written is speculative but scientifically thoughtful (see, for example, [2], [3], [4], [5], [6], [7]), and a lot is not. Probably most well-known are the arguments by Hammoroff, Penrose, and others suggesting that microtubules in neurons act as quantum computing elements in fundamental ways [8], [9]. While still controversial, recent experimental results suggest that neurons might indeed leverage properties of quantum effects in how they compute [10], a remarkable result.

Our focus in the paper we published, however, is different. We are interested in the practical application of quantum algorithms for probing and understanding neural dynamics rather than exploring the possibility of quantum computational mechanisms within the brain itself. Despite the growing interest in these topics, rigorous mathematical and quantitative arguments applying quantum algorithms for solving meaningful neuroscience and artificial neural network questions remain in their infancy.

There are two broad areas in which quantum computing may contribute to the scientific study of neural networks. The first is large-scale simulations of neural dynamics across scales of spatial and temporal organization, bounded and informed by the known physiology (in the case of the brain) and known models (for artificial intelligence and machine learning). The second is carefully chosen and structured problems ** about** neural dynamics that make careful and clever use of quantum algorithms.

Sufficiently large-scale simulations would allow observing, experimenting, and iterating numerical experiments under a wide range of parameter and model conditions. If, as neuroscientists suspect, complex emergent cognitive properties are partly due to sufficiently large interactions among foundational physiological and biological components and processes across temporal and spatial scales of organization, the need to carry out very large iterative simulations may be critical to understanding the dynamics that give rise to cognitive properties. Simulations of this kind would support understanding emergent effects that depend on the scale of the computational space, to the extent it can be computed.

However, open-ended large-scale simulations alone will not be sufficient for understanding how the brain, or artificial intelligence for that matter, works. In effect, open-ended large-scale simulations in isolation are what led to the significant challenges and missed targets faced by the highly publicized and hugely funded Blue Brain Project [11]. Arriving at such an understanding necessitates carefully chosen and defined problems about the neural network dynamics being simulated. This is critical. Observing neural dynamics in action — for example, the firing patterns of large numbers of neurons — in isolation and without context, by itself, cannot reveal the underlying algorithms that are operating on those dynamics or why they exist. It is no different than attempting to understand the brain from a systems perspective by studying a single participating protein or ion channel in isolation. Quantum computing potentially has a unique role to play in deciphering and understanding the contributions that scale has on functional network dynamics and behaviors.

In the work we describe in this new paper, we show how a carefully constructed problem can leverage two foundational quantum algorithms, Grover and Deutsch-Josza, in such a way that the output measurements from the quantum computations admit an interpretation that guarantees we can infer a particular behavior about the network dynamics. Specifically, we address the following question: Given a simple representation of a neural network (which applies to both biological and artificial networks) after some period of time of the evolution of its

dynamics, does the network have the potential to continue sustaining dynamic activity? Or are the dynamics guaranteed to stop in one of two ways: either through ’epileptic’ type saturated dynamics or quiescence

(i.e., all activity dying away)? We show that by structuring (asking) the problem in a particular way, the implementation of the Grover and Deutsch-Josza algorithms arrives at a solution much more efficiently than

would be possible by strictly classical methods. As we argue in the in the paper, when one considers the combinatorial size of the computational space of the real brain, for example, these types of questions become inaccessible to classical methods.

Our intent in this work was to explore an interesting proof of concept problem and to motivate the potential of quantum computation to neural networks as an important research direction. We introduce a number of novel results, including the technical structure of how the problem was set up, and, to our knowledge, one of the only few examples of a practical application of Deutsch-Jozsa. The first application of this kind to the study of neural network dynamics. We have intentionally chosen a tractable and applied problem that has real-world implications and consequences for neural networks, solved in the simplest and most intuitive possible way using two of the best-known foundational quantum algorithms. Given the bespoke nature of setting up, mathematically proving (when possible), and solving quantum computing problems, the results we discuss here are an exercise in thinking about how neural network dynamics questions need to be structured within a quantum computational framework by leveraging deep knowledge about the physiology and models of neural networks. While the problem as structured and the quantum computing approaches we discuss are simple, we have attempted to be mathematically rigorous.

Access to the full paper is available in the link below on arXiv.