The promise of quantum computing for population genetics and molecular ecology

Andrew Davinack^*

• Wheaton College Massachusetts, Norton, United States

Despite the explosion of genomic data in recent decades, population geneticists still struggle to detect structure in certain systems. Early analyses using mitochondrial DNA and Sanger-sequenced loci offered coarse insights into divergence and connectivity (Avise 1987;Avise 1991;Zhang & Hewitt 2003), but many studies, particularly on high-dispersal taxa, returned "flat" results interpreted as panmixia. The rise of genome-wide approaches like RADseq and the integration of machine learning (ML) promised greater resolution by increasing marker density and computational power (Davey & Blaxter 2010;Lowry et al. 2016;Hodel et al. 2017;Li & Ralph 2019). Yet in many cases, even thousands of SNPs and advanced clustering algorithms fail to reveal meaningful patterns (Meirmans 2015;David 2018;Hohenlohe et al. 2021). This persistent opacity raises a key question: is the problem in the data, or in the tools we use to analyze it? Many conventional methods reduce high-dimensional genetic data into linear projections or simplified models, potentially discarding subtle, nonlinear signals of structure. While ML approaches such as random forests or neural networks have improved detection in some cases, they too rely on classical assumptions, feature engineering, and dimensionality reduction that may miss complex relationships.Quantum computing offers a fundamentally different paradigm-one that may open new doors for detecting structure in noisy, weakly differentiated, or cryptically admixed populations. In this article, I argue for integrating quantum machine learning (QML) into population genetics, outlining how quantum tools might expose hidden diversity where classical methods plateau. Even with genome-scale data, molecular ecologists continue to face challenges in inferring population structure, especially in taxa with high dispersal, low diversity, or recent divergence. Classical methods such as FST, PCA, STRUCTURE, and AMOVA often fail to resolve differentiation in these systems, producing ambiguous results even when ecological or biogeographic barriers suggest otherwise (Lowe & Allendorf 201;Kelly & Palumbi 2010;David & Loveday 2018). Genomic approaches like RAD-seq, and the use of thousands of SNPs, were expected to overcome these issues. Machine learning methods-support vector machines, random forests, deep learning-have pushed the field further, especially in identifying subtle structure and loci under selection (Schrider & Kern 2018;Sheehan & Song 2016). However, these approaches still rely on classical computation and statistical frameworks. They require extensive training data, are sensitive to noise and missing data, and often project information into lower-dimensional spaces for tractability. Critically, they may overlook nonlinear relationships among loci, or signals obscured by admixture, gene flow, or founder effects. In invasive species, for instance, repeated introductions and high admixture often create complex patterns that defy clean clustering (see Huang et al. 2024). Even in well-sampled, high-resolution datasets, structure may remain "hidden". not because it doesn't exist, but because our tools aren't built to find it.The core issue isn't always data quantity. It is representational capacity. When we compress complex genetic variation into classical spaces, we risk losing the very patterns we seek. A new computational paradigm may be required, one capable of handling highdimensional, nonlinear, and noisy biological data in fundamentally different ways. Quantum computing departs fundamentally from classical computation. Instead of binary bits (0 or 1), quantum computers use qubits, units that exist in superposition, capable of being 0 and 1 simultaneously. This allows quantum systems to explore multiple states at once, vastly expanding the space of possible solutions. Qubits can also become entangled, meaning the state of one qubit is intrinsically linked to another, regardless of distance. Together, superposition and entanglement enable quantum systems to operate in exponentially larger, high-dimensional spaces known as Hilbert spaces. This makes quantum algorithms particularly powerful for pattern recognition, optimization, and classification in complex datasets. Two concepts are especially relevant to population genetics. First, quantum feature mapping allows classical data, such as SNP genotypes or haplotype frequencies, to be embedded into quantum state space, potentially making weak or nonlinear patterns more separable. Second, quantum machine learning (QML) models, such as quantum support vector machines (QSVMs) and quantum k-means, can operate in these spaces to detect structure that classical models might miss. While still in early development, QML is increasingly being applied to real-world problems in fields like drug discovery, molecular design, and bioinformatics. These use cases suggest that quantum systems are not just faster-they may offer qualitatively different ways of understanding data. Many biological systems pose exactly the kinds of challenges quantum computing is suited to address: low-variation datasets, weak signals, and nonlinear interactions. In molecular ecology, these issues are common. Consider mitochondrial DNA from a species with global dispersal, or genome-wide SNPs from recently diverged populations. Classical analyses may detect no structure, but that doesn't mean none exists. Quantum computing could shift this paradigm. For example, quantum feature mapping may embed genetic data into a space where structure becomes linearly separable, even if it appears undifferentiated in PCA. Quantum classifiers, like QSVMs, could be used to assign individuals to weakly distinct populations, even in cases of high admixture or recent introduction events. In systems with reticulate evolution, cryptic speciation, or asymmetric gene flow, quantum models may better capture the underlying complexity.Beyond classification, quantum optimization algorithms could enhance model selection and parameter tuning. In seascape or landscape genetics, where researchers often model genetic differentiation as a function of multiple, correlated environmental variables, quantum optimization may more efficiently explore the solution space-avoiding overfitting and identifying the most explanatory variables. These tools are not just theoretical. Quantum algorithms have already been used in genome assembly, drug target prediction, and peptide design (Boev et al. 2021;Dhoriyani et al. 2025;Vakili et al. 2025). As population genetics grapples with ever-larger datasets and increasingly subtle patterns, the adoption of quantum tools is a logical extension. Quantum approaches will likely not replace classical methods outright, but they may provide complementary insight, especially in systems where traditional approaches return ambiguity. For population genetics, quantum computing offers not just more power, but a fundamentally new lens through which to view biological complexity.It should be noted that many quantum machine learning models are quantum analogs of classical AI methods, such as QSVMs derived from support vector machines, or quantum neural networks adapted from deep learning. As such, progress in quantum approaches is often informed by advances in classical AI, underscoring the need for cross-training in both fields. Developing robust hybrid models will require expertise in both quantum algorithms and traditional machine learning frameworks. To realize the potential of quantum computing in population genetics, a coherent pipeline is essential-one that bridges classical genetic data and quantum machine learning models. Figure 1 outlines a six-step conceptual framework designed to help researchers integrate quantum methods into population structure analysis: 1. Input Preparation This first step begins with standard classical processing: filtering SNPs, aligning sequences, removing low-quality data, and formatting inputs using tools such as PLINK, VCFtools, or BCFtools. Clean, structured data is essential for downstream encoding and modeling. Genotype or haplotype information must be converted into a quantum-readable format. Techniques like angle encoding (mapping genotypes to rotational angles on qubits) or amplitude encoding (embedding entire genotype vectors into quantum state amplitudes) translate biological data into a format compatible with quantum circuits. Encoded data is embedded into a high-dimensional Hilbert space using parameterized quantum circuits. This transformation allows weak or nonlinear patterns, such as subtle gene flow or cryptic structure, to become more separable, much like kernel methods in classical ML but with exponentially expanded feature space. With data now embedded, quantum machine learning algorithms (e.g., quantum support vector machines, quantum k-means, quantum neural networks) are applied to detect population differentiation, cluster individuals, or identify outliers. These models operate in the quantum feature space and may outperform classical approaches in noisy or weakly structured datasets. Quantum measurement collapses the qubit state into classical outcomes, typically as bitstrings or probability distributions. These outputs are interpreted as cluster memberships, structure probabilities, or other biologically relevant predictions. Finally, results are validated, visualized, and interpreted using traditional statistical and genetic tools (e.g., STRUCTURE, ADMIXTURE, AMOVA, or DAPC). This hybrid approach leverages the strengths of both quantum and classical systems. Together, these steps provide a flexible but actionable roadmap for bringing quantum computing into real-world population genetic research. The potentially enormous gains in data analysis of population-level genetic data are contingent on several hardware and algorithmic limitations. Current quantum devices (termed Noisy Intermediate-Scale Quantum or 'NISQ' systems), have relatively few qubits (often fewer than 100 usable ones) and are prone to error and decoherence (Lau et al. 2022;Chen et al. 2023). These constraints limit the size and depth of quantum circuits, which in turn restricts the scale of biological datasets that can be analyzed directly on hardware. Moreover, data encoding itself presents a bottleneck in the proposed pipeline. While angle encoding is conceptually straightforward and compatible with small-scale data (e.g. mtDNA haplotypes or select SNP panels), amplitude encoding -which enables exponentially efficient processing, requires complex normalization and may be impractical on current devices. Encoding hundreds or thousands of SNPs across many individuals is still computationally expensive, even on simulated backends.Given the early stage of development, many proposed quantum applications in biology remain speculative. Empirical benchmarking, especially using small, tractable datasets such as mtDNA haplotypes, SNP panels, or synthetic admixed population, is critical for validating the feasibility and value of QML in real-world scenarios. Such preliminary studies can generate essential performance metrics, guide algorithm refinement, and justify further investment in scaling up applications. Finally, one significant challenge is the fact that many quantum algorithms lack biological grounding, meaning that they were not designed with population genetics principles in mind, and few benchmarks exist to compare quantum outputs to traditional methods like DAPC or ADMIXTURE. As such, interpretability and validation will remain critical challenges, and early applications will likely depend on hybrid quantum-classical workflows that combine quantum pattern recognition with classical biological inference.In short, quantum tools may offer qualitatively different insights, especially in difficult datasets where classical tools struggle. But these gains must be evaluated against current limitations in scale, stability and interpretability -challenges that are likely to be overcome only through cross-disciplinary innovation and algorithm refinement CONCLUSION AND A CALL TO ACTION Quantum computing is not a distant future, it is already reshaping fields from chemistry to bioinformatics. For population genetics and molecular ecology, the moment is ripe to explore how quantum tools might uncover the hidden structure that classical methods miss. This transformation will not happen passively though. It will require intentional collaboration between quantum physicists, data scientists, and biologists. Pilot studies on small datasets for e.g., mitochondrial haplotypes, reduced SNP panels, or simulated admixed populations, can provide early proof-of-concept and establish benchmarks for quantum vs. classical performance. Data challenges, benchmarking competitions, and shared datasets can accelerate this process, especially when supported by institutions that span both fields. Equally important is education: graduate programs and workshops should begin introducing ecologists to quantum concepts, particularly in encoding, modeling, and quantum-enhanced optimization. National and international funding agencies are already prioritizing quantum innovation, including through interdisciplinary research initiatives. Molecular ecologists should seize this opportunity to lead, not follow, in applying quantum tools to biological questions. The tools are available. The theory is sound. What's needed now is action. By embracing quantum methods today, we can reimagine how we study population structure, biodiversity, and evolution tomorrow. The quantum future of molecular ecology has already begun, if we choose to step into it. 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