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Quantum Computing at the Frontiers of Biological Sciences

Prashant S. Emani, Jonathan Warrell, Alan Anticevic, Stefan Bekiranov, Michael Gandal, Michael J. McConnell, Guillermo Sapiro, Alán Aspuru-Guzik, Justin Baker, Matteo Bastiani, Patrick McClure, John Murray, Stamatios N Sotiropoulos, Jacob Taylor, Geetha Senthil, Thomas Lehner, Mark B. Gerstein, Aram W. Harrow

arXiv:1911.07127v1quant-phq-bio.GNq-bio.NCq-bio.QM

TL;DR

Biological research faces complex, high-dimensional challenges in linking genetic variation to behavior and relating neuroimaging to molecular and cellular diversity. This paper examines quantum-computing approaches to biological problems, identifying some difficult optimization and inference tasks as potential candidates while noting that large-scale GWAS and QTL analyses are problematic for near-term quantum approaches.

Abstract

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The search for meaningful structure in biological data has relied on cutting-edge advances in computational technology and data science methods. However, challenges arise as we push the limits of scale and complexity in biological problems. Innovation in massively parallel, classical computing hardware and algorithms continues to address many of these challenges, but there is a need to simultaneously consider new paradigms to circumvent current barriers to processing speed. Accordingly, we articulate a view towards quantum computation and quantum information science, where algorithms have demonstrated potential polynomial and exponential computational speedups in certain applications, such as machine learning. The maturation of the field of quantum computing, in hardware and algorithm development, also coincides with the growth of several collaborative efforts to address questions across length and time scales, and scientific disciplines. We use this coincidence to explore the potential for quantum computing to aid in one such endeavor: the merging of insights from genetics, genomics, neuroimaging and behavioral phenotyping. By examining joint opportunities for computational innovation across fields, we highlight the need for a common language between biological data analysis and quantum computing. Ultimately, we consider current and future prospects for the employment of quantum computing algorithms in the biological sciences.

Classical versus Quantum Circuits: State of the Art and Opportunities for the Future

Quantum computers offer provable speedups for selected problems, but the performance of many quantum heuristics remains uncertain. The section also outlines technical limitations and biological applications that could motivate targeted quantum algorithms.

Exponential speedup

  • Quantum computers can offer exponential speedups for molecular simulation and random-circuit sampling, though the latter relies on a plausible conjecture about classical simulation [6, 13].Molecular simulation may be advantageous when simple classical approximations do not adequately capture a molecule’s properties, including in molecules with many active electrons such as organometallic compounds [13].Source: Classical versus Quantum Circuits:… · p. 5

Polynomial speedup

  • Grover search reduces brute-force search over N possibilities to O(√N) evaluations, but function minimization requires evaluating the function in superposition, limiting classical offloading and overall speedup.Quantum tree searches can also quadratically improve on classical searches [15]; if evaluating the objective function is memory- and time-intensive, the quantum computer must perform that evaluation, reducing the overall speedup.Source: Classical versus Quantum Circuits:… · pp. 5–6

Heuristic speedups

  • Quantum heuristics such as adiabatic optimization and QAOA have unknown speedups, potentially ranging from exponential improvement to none, and share the caveat about evaluating functions in superposition.Their performance is expected to become better understood as quantum computers are built, partly through empirical evidence.Source: Classical versus Quantum Circuits:… · p. 6

The source of quantum speedup

  • Quantum interference can enable asymptotic speedups, but some tasks, such as computing parity, have no quantum speedup, and determining when speedups exist remains an open problem.Quantum amplitudes can interfere constructively or destructively; Grover’s algorithm and the quantum Fourier transform illustrate how interference can help [18]. Parity takes O(N) time on either classical or quantum computers [19].Source: Classical versus Quantum Circuits:… · pp. 6–7

Opportunities for the future

  • Biological applications could motivate specific, mathematically well-posed tasks and targeted quantum algorithm development.The article develops this goal in the context of studying the human brain.Source: Classical versus Quantum Circuits:… · p. 7

Machine learning and big data

  • Current quantum computers cannot access large classical datasets in superposition, so filtering, data reduction, or small-data problems may be more suitable than large-data applications.A speculative qRAM could enable coherent queries to large datasets, but scalable error-corrected qRAM has no proposal and may not be easier to build than a large quantum computer [12, 20, 21].Source: Classical versus Quantum Circuits:… · p. 7

Simulation of classical and quantum systems

  • Quantum algorithms for linear systems and PDEs scale well with problem size but are restricted by parameters such as condition number and nonlinearity; VQE’s success depends on ansatz quality [22, 23, 24].VQE estimates ground-state energies of small molecules using parameterized trial-state circuits, with parameters varied to minimize energy.Source: Classical versus Quantum Circuits:… · p. 7

Biological applications

  • Biological quantum-computing studies include peptide-folding search with quantum annealing [26] and DNA-motif classification, where annealing slightly improved on classical methods, with similar ranking performance [27].Quantum simulation may also model chemical reactions and biological energy or electron transport, where quantum effects could affect accuracy [28–32, 33, 34].Source: Classical versus Quantum Circuits:… · pp. 7–8

Potential applications for Quantum Computing in Neuroscience

The section surveys computationally intensive neuroscience problems across genetics, genomics, neuroimaging, and behavioral phenotyping, and considers how quantum algorithms might address them. It emphasizes the multiscale integration challenge and the implications of qRAM requirements for near-term implementation.

Potential applications for Quantum Computing in Neuroscience

  • Linking molecular-genetic understanding to brain cells, regions, networks, and behavior requires combining methods across complex datasets and scales.The cross-level mapping is a many-to-many probabilistic problem with an enormous search space.Source: Potential applications for Quantum… · p. 8, Figure 2 · p. 9
  • The section traces representative challenges from genetics and genomics through neuroimaging to behavioral phenotyping, focusing on processing-intensive tasks recently addressed with machine learning.The chosen domains are a minimal sample intended to illustrate the computational problem, not an exhaustive account of neuroscientific methods or levels of inquiry.Source: Potential applications for Quantum… · p. 8
  • It juxtaposes classical solutions with plausible quantum algorithms for neuroscientific problems, distinguishing conventional approaches from qRAM-dependent methods because their requirements affect near-term implementation.The comparison is intended to frame open questions for developing new computational paradigms.Source: Potential applications for Quantum… · p. 8, Figure 2 · p. 9

Genetics and sequence analysis

The section surveys potential quantum-computing approaches to sequence matching, genetic-tree reconstruction, phenotype-linked analyses, and somatic-variant classification, while noting memory, data-access, and scale constraints.

Genetics and sequence analysis

  • Sequence matching and read mapping are ubiquitous but memory- and time-intensive; dynamic programming (Needleman–Wunsch [37], Smith–Waterman [38]) offers optimal alignment, while faster BLAST [39] is approximate.The large search space makes memory for the reference and mapping information, as well as processing speed, central challenges.Source: Genetics and sequence analysis · p. 9
  • Grover-based search [42] could accelerate suffix-array read mapping, but genome-scale reference storage without qRAM may limit gains; HQMMs [47–50] and hybrid HMM optimization offer other routes.Further mapping speed gains were reported under the assumption that a query string has unique membership in the reference database [43].Source: Genetics and sequence analysis · pp. 9–10
  • Tree reconstruction spans ancestral recombination graphs [51–53], pathogen evolutionary trees, and tumor mosaicism; exponentially larger ARG search spaces make quantum annealing [55–58] a possible small-input target.ARGs assign a coalescent tree to every sequence base, and the passage identifies this as a potential quantum-speedup opportunity without qRAM.Source: Genetics and sequence analysis · p. 10
  • Large GWAS/QTL datasets and matrix-heavy REML/GRM computations challenge near-term quantum methods; qRAM-enabled Quantum Least Squares [63,64] may offer up to exponential speedups, but qRAM costs remain uncertain.If the regression dimensionality can be reduced, conventional quantum annealers may also tackle these tasks.Source: Genetics and sequence analysis · p. 11
  • The Schizophrenia Genetics and Brain Mosaicism project [65] proposes case/control classifiers for psychiatric-disorder-associated variants; quantum machine learning [66] may help search their large parameter spaces.Single-cell studies indicate that every neuron may contain private somatic variants, with large structural variants in as many as 30% of neurons.Source: Genetics and sequence analysis · p. 11

Functional Genomics

Functional genomics is framed as a probabilistic, dynamic mapping from genetic variation through molecular and cellular intermediates to complex traits, with quantum methods proposed for difficult joint modeling and optimization. In the brain, gene pathways and cell-type proportions offer additional intermediate phenotypes for capturing biological complexity.

Functional Genomics

  • Genetic variation’s effects on higher-level behaviors involve developmental and gene-environment processes, creating a probabilistic, dynamic many-to-many mapping that varies across people67–69; imputed intermediate molecular phenotypes can predict high-level traits70.Source: Functional Genomics · p. 11
  • Bayesian-network structure learning, Boltzmann-machine inference, and VAE training are intractable, motivating exact small-input quantum searches and approximate quantum optimization [71–74].Quantum annealing may use tunneling between low-energy states to improve optimization; prior molecular-interaction knowledge can help guide causal interpretation.Source: Functional Genomics · p. 12
  • WGCNA derives pathway-enriched co-expression modules [75], while marker-gene NMF estimates cell-type fractions [71]; quantum annealing has been proposed for NMF [76,77].The brain’s neuronal diversity and gene-regulatory interactions yield intra- and inter-regional variation; exact hierarchical clustering may be a small-scale quantum-solution candidate, while NMF is non-convex.Source: Functional Genomics · p. 12

Mapping Neuro-Behavioral Variation in Humans via Neuroimaging and Deep Phenotyping

Human neuroimaging and deep behavioral phenotyping generate high-dimensional data that demand scalable methods for linking brain states, cellular and molecular variation, and behavior. Quantum methods may help with parts of this computational challenge, but several applications remain proposals or are supported only by small-scale or toy-model evidence.

Mapping Neuro-Behavioral Variation in Humans via Neuroimaging and Deep Phenotyping

  • Scalable, neurobiologically grounded methods are needed to link population-level genetic trends and individual behavioral variation across levels, support clinical phenotypes, and address neuroimaging’s computational bottlenecks.The passage also identifies rapid dimension reduction, parallelization of massively serial tasks, and modeling brain dynamics and structural change across scales as priorities for more precise disease-related patient segmentation.Source: Mapping Neuro-Behavioral Variation in… · p. 13
  • Quantum annealing could aid brain-surface and volume registration if its energy-minimization Hamiltonian can be mapped to an Ising-type model.The described FreeSurfer procedure first aligns cortical surfaces, then optimizes a volumetric transformation through elastic-model initialization and intensity matching.Source: Mapping Neuro-Behavioral Variation in… · p. 13
  • Association studies link genetic variants with imaging phenotypes, including UK Biobank GWAS [82]; fMRI connectome features predict psychotic symptoms in unseen individuals with schizophrenia or bipolar illness [83], while combined static and dynamic features predict a range of phenotypes [84].Source: Mapping Neuro-Behavioral Variation in… · p. 13
  • Quantum Boltzmann machines and quantum VAEs may model complex brain-network distributions and help study genetic or structural effects on connectivity or impute unobserved molecular data [73,74].Quantum linear-system solvers may also improve fitting of differential-equation models of global brain dynamics by making parameter testing more efficient and increasing resolution [63,64].Source: Mapping Neuro-Behavioral Variation in… · p. 14
  • General-purpose quantum solvers for nonlinear differential equations might enable more accurate out-of-steady-state neural-dynamics fitting, but currently seem unlikely to outperform classical methods [23].Such solvers could avoid linear approximations, including when modeling transitions between resting-state and task-based fMRI.Source: Mapping Neuro-Behavioral Variation in… · p. 14
  • Continuous digital phenotyping creates computational and privacy challenges, from rapid data reduction and subtle multi-sensor anomaly detection to protecting identifiable high-resolution video and audio.These data could support timely clinical decisions and just-in-time interventions, but require linking nonlinear brain-state dynamics with time-dependent behavior across individual and population signals; quantum computing may aid privacy-preserving metric generation and file encryption or decryption.Source: Mapping Neuro-Behavioral Variation in… · pp. 14–15
  • Quantum neural models and hidden quantum Markov models may uncover structure in brain-behavior data, with HQMMs potentially using reduced state spaces, though evidence is limited to small-scale simulations and toy models [47,49,50].Interpretable recurrent networks have also modeled fMRI and behavioral data jointly [93], while hidden-state methods could be applied to switching between resting and task-based brain states [94].Source: Mapping Neuro-Behavioral Variation in… · p. 15

Integration across disciplines

Integrating biological insights across behavioral, circuit-dynamics, and molecular/cellular scales remains challenging. The section proposes quantum machine learning as a potential aid for modeling their interdependencies and combining genomics, neuroimaging, and behavior.

Integration across disciplines

  • Quantum machine learning could help model nonlinear interdependencies across biological scales that are classically intractable, linking molecular phenotypes, neuroimaging measures, and behavioral targets.Proposed architectures include either a hierarchy from molecular to system-level phenotypes to behavior, or parallel molecular and neural factors influencing behavior.Source: Integration across disciplines · p. 15
  • Quantum neural networks96 and quantum variational classifiers97 could aid multiscale analysis on non-qRAM, gate-based quantum computers.Quantum variational classifiers have classified states designed to be hard to simulate classically, suggesting greater circuit generality than classical counterparts.Source: Integration across disciplines · p. 15
  • Interpretable, mechanism-agnostic deep neural networks could connect gene regulatory networks with structural and functional neuroimaging parameters.The proposed integration aims to combine genomic and neural system-level mechanisms with human behavior; physical, mechanistic models may also inform it.Source: Integration across disciplines · p. 15

Epilogue

Quantum computing could help address biological problems with large search spaces, but important hardware and algorithmic challenges remain. Near-term quantum methods and future hardware advances may expand its biological applications, though the timing and scale of progress are uncertain.

Epilogue

  • Quantum computers still need more qubits and connectivity, lower error rates, and broader algorithms; building a machine for 1024-bit RSA factoring requires five orders of magnitude more scale and two orders better error rates than existing machines.The epilogue notes that hardware goals can conflict: systems must be isolated from environmental noise yet permit fast, precise control and measurement.Source: Epilogue · p. 16
  • Because qRAM lacks a practical implementation, the epilogue favors intrinsically quantum approaches, including near-term kernel methods for genomics, optimization and machine learning for neuroscience, and algorithms for protein folding and quantum biology.It remains unclear whether quantum biology processes are relevant to higher-level brain function; brain algorithms at Marr’s algorithmic/representational level may be classical, although quantum machine learning makes this less necessary for artificial agents.Source: Epilogue · p. 16
  • Sufficiently powerful universal quantum computers may still be years away under cautious projections, but unforeseen breakthroughs in resolution or noise reduction could enable quantum computing to address pressing biological challenges.The passage describes the outlook as cautious but optimistic, while noting that the pace of future improvements is difficult to predict.Source: Epilogue · pp. 16–17
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