Hybrid Quantum-Classical Pipeline for Identifying Higher Order Correlations in Neurons
By Caroline, Jennifer
Introduction
The proposed research aims to develop a hybrid quantum-classical pipeline to identify higher-order, or motif-level, correlations in neurons populations. We will analyze two-photon calcium imaging data collected from the mouse auditory cortex when mice are given auditory stimuli of different frequencies. Currently, we plan to use the data collected by Bowen et al. 2024. We will begin by pre-processing the data: identifying neuronal spikes, reducing dimensionality, and calculating correlation between neurons. The output will be a neuronal graph that is both directional and weighted: neurons are expressed as nodes, connections between neurons are expressed as edges, directionality indicates whether neuron A affected neuron B or vice versa, and the weights inform relatedness or possible motifs among neurons.
Intellectual Merit
The intellectual merit of this experiment is rooted in previously developed methods for analyzing calcium imaging data and constructing neuronal graphs. In the brain, neurons often form connected circuits where a firing event in one neuron can either activate or suppress firing in another neuron, or even a group of neurons (often called a functional subcircuit). An accepted method to represent these connections in this field is in the form of neuronal graphs. There are several approaches to creating these graphs classically, and the most recent papers follow the steps listed below:
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Data structure: Convert the calcium imaging data to a matrix where the rows represent neurons and the columns represent time points.
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Noise reduction: Denoise the calcium imaging data to separate the signal from complex physiological noise (there are a variety of methods for this, but we have yet to synthesize possible approaches).
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Similarity and correlation: Compare the similarity between neurons using a variety of metrics, such as Pearson correlation coefficients or transfer entropy values (accounts for temporality, and therefore enables the creation of directional graphs).
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Cluster analysis: Perform cluster analysis with k-means, Louvain community detection, or DBSCAN.
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Network analysis: If the data is represented as a network, statistics such as modularity, small-worldness, and calculated clustering coefficients can also be derived from the adjacency matrix of the neuronal graph.
However, motif identification within networks is an NP-hard algorithm and becomes slower with multiple constraints such as activation and suppression. We propose a neuroscience application of the QOMIC (quantum optimization for motif identification) algorithm developed by Ngo et al. 2025. Using QOMIC, we hope to outperform classical algorithms by identifying more motifs and reducing the computational expense. With the knowledge gained from the QOMIC implementation, we will develop our own quantum algorithm that aims to address QOMIC's weaknesses. Identifying more functional subcircuits and motifs in the brain can enable a better understanding of how different neurons interact with each other and respond to sound stimuli.
Broader Impact
Our research may indicate functional subcircuits in the brain. These dynamics are critical for understanding how groups of neurons collectively encode information and transition between neural states. Importantly, the patterns we identify may be extrapolated beyond the auditory system and reflect the general organizational motifs of the cerebral cortex. Many cortical regions share a similar layered architecture and exhibit comparable population-level computations, suggesting that higher-order coactivation patterns and network structures observed within the auditory cortex may also underlie processes in visual, somatosensory, and association cortices. Identifying recurring activation motifs and community structures in these areas could offer a deeper, systems-level understanding of how the brain encodes sensory information, supports memory, and produces complex cognitive functions such as decision-making and conscious perception. This approach thus provides a scalable and generalizable framework for exploring collective neural behavior across the brain.