Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2607.11217 · Digital Discovery

Quantum Multiscale Modeling: A Hierarchy of Algorithms for Complex Chemical Systems

Seenivasan Hariharan, Kareljan Schoutens, Sachin Kinge, Lucas Visscher

On Aqora:Seenivasan HariharanSeenivasan Hariharan
quant-phphysics.chem-phSubmitted Jul 13, 2026• Announced Jul 14, 2026• 0 citations
v1 · Jul 13, 2026v2 · Sep 29, 2026
arXivHTMLPDF

Abstract

Multiscale modeling of complex chemical systems requires algorithms that operate coherently across electronic, atomistic, mesoscopic, and continuum scales. While quantum algorithms have been proposed for each regime, no systematic framework exists to compose them across scale boundaries. Here, we identify the conditions under which fault-tolerant quantum algorithms might preserve scale-specific quantum advantages. We map quantum phase estimation, Hamiltonian simulation with Gibbs state preparation, quantum random walks, and quantum partial differential equation solvers onto electronic structure, molecular dynamics, mesoscopic kinetics, and continuum reactor physics, respectively. Crucially, these correspondences do not imply unconditional end-to-end quantum advantage; speedups depend heavily on state preparation, memory architectures, matrix conditioning, and classical readout costs. Six unresolved questions define this composition problem, illustrated via a quantum hierarchy for \ce{CO} oxidation over \ce{Pt(111)}. We propose viewing inter-scale transfer as a quantum channel composition problem at the interface of algorithm design and non-equilibrium statistical mechanics, and ask whether information loss at scale boundaries is intrinsic to multiscale modeling or merely a consequence of lossy classical transduction between algorithmic layers. The resulting roadmap suggests that multiscale quantum advantage is governed primarily by the structure of information transfer between algorithmic layers, rather than by performance at individual scales alone.

Comments
30 pages, 1 figure

Related papers

Exploring the use of quantum computing for facilitating spatially and temporally resolved models of a biological cell

Muralikrishnan Gopalakrishnan Meena, Dileep Kishore, Jerry M. Parks +5 more

Whole-cell simulation, modeling all of a cell's functional systems over its life cycle, is an outstanding challenge in computational biology. Even the simplest living cell contains thousands of interacting proteins and metabolites (on the order of trillions of atoms) whose full functional dynamics spans roughly five orders of magnitude in space (nm to $μ$m) and nearly nineteen in time (fs to hours). Further, many of the governing physical and chemical properties remain incompletely characterized. Simulating such complex systems at fully atomistic resolution over a full cell cycle is computationally intractable on classical architectures, raising a central question: Can quantum computing offer a viable path to whole-cell simulations that integrate molecular- and systems-level complexity? This Perspective examines the potential of quantum computing across three hierarchical scales: atomistic-molecular modeling, metabolic and regulatory networks, and whole-cell spatial modeling. We present a complexity analysis comparing classical and quantum algorithms for representative biological problems, identifying regimes of substantial theoretical speedup under specified algorithmic assumptions. We highlight algorithmic developments designed to leverage both near-term exploratory and fault-tolerant quantum architectures, and discuss practical bottlenecks: data encoding overhead, system conditioning, measurement constraints, and hybrid quantum-HPC integration. Together, these results outline a roadmap for quantum-accelerated whole-cell modeling and the biological insights such multiscale frameworks may eventually enable.

quant-pharXiv:2607.27571•Jul 31, 2026•0 citations

Quantum Algorithms for Multiscale Partial Differential Equations

Junpeng Hu, Shi Jin, Lei Zhang

Abstract. Partial differential equation (PDE) models with multiple temporal/spatial scales are prevalent in several disciplines such as physics, engineering, and many others. These models are of great practical importance but notoriously difficult to solve due to prohibitively small mesh and time step sizes limited by the scaling parameter and CFL condition. Another challenge in scientific computing could come from curse-of-dimensionality. In this paper, we aim to provide a quantum algorithm, based on either direct approximations of the original PDEs or their homogenized models, for prototypical multiscale problems inPDEs, including elliptic, parabolic, and hyperbolic PDEs. To achieve this, we will lift these problems to higher dimensions and leverage the recently developed Schrödingerization based quantum simulation algorithms to efficiently reduce the computational cost of the resulting high-dimensional and multiscale problems. We will examine the error contributions arising from discretization, homogenization, and relaxation, and analyze and compare the complexities of these algorithms in order to identify the best algorithms in terms of complexities for different equations in different regimes.

arXiv:2304.06902•Multiscale Modeling and Simulation•Jul 30, 2024•6 citations

Quantum Algorithm for Subcellular Multiscale Reaction-Diffusion Systems

Lockwood, Margot, Nathan Wiebe, Connah Johnson +5 more

Computational modeling of cellular systems, where reactants are governed by biochemical equations and physical representations, requires extensive classical computing resources. These limitations significantly constrain the system size and spatiotemporal scales of simulations. A key challenge lies in the "curse of dimensionality", where the number of possible reaction terms grows exponentially with the number of species, and the computation of reaction rates involving many-body interactions becomes intractable in polynomial time on classical computers. In this work, we introduce a quantum algorithmic framework designed to overcome these challenges, leveraging the architecture of quantum computing to simultaneously compute reaction rates and track the spatiotemporal dynamical evolutions of subcellular systems. We generalize the reaction-diffusion equation (RDE) for multiscale systems with arbitrary species count, encompassing higher-order interactions. Our approach achieves two principal quantum advantages: (i) an exponential quantum speedup in reaction-rate computation, contingent on the efficient preparation of polynomially accurate ground states on a quantum computer, and (ii)) a quadratic scaling in spatial grid points and polynomial scaling in the number of species for solving nonlinear RDEs, contrasting sharply with classical methods that scale exponentially with the system's degrees of freedom. To our knowledge, this represents the first efficient quantum algorithm for solving multiscale reaction-diffusion systems. This framework opens the door to simulations of biologically relevant subcellular processes across previously inaccessible spatial and temporal scales, with profound implications for computational biology, soft matter physics, and biophysical modeling.

arXiv:2509.20668•Sep 25, 2025•0 citations

Hierarchical Quantum-Classical Decomposition: Theoretical Principles for Multi-Scale Problem Solving

Poojitha Appaneni

This work establishes theoretical foundations for hierarchical quantum-classical algorithm design, where complex problems are decomposed across multiple spatial, temporal, or organizational scales with quantum and classical computation assigned to appropriate levels. We develop a mathematical framework that characterizes optimal problem decomposition strategies based on subproblem structure, inter-scale coupling strength, and available quantum resources. The theory proves that multi-scale decomposition can reduce quantum circuit depth requirements while maintaining solution quality, establishing bounds on the communication overhead between hierarchical levels. We derive conditions under which bottom-up quantum processing of finescale subproblems followed by classical integration produces provably near-optimal solutions for the full problem. Our analysis incorporates adaptive refinement strategies where computational resources are dynamically allocated based on intermediate results, proving convergence theorems for iterative hierarchical algorithms. The framework applies to diverse problem classes including molecular simulation across electronic and nuclear scales, network optimization from local to global levels, and scheduling problems with nested temporal structures. We establish fundamental trade-offs between decomposition granularity, quantum advantage preservation, and solution accuracy, identifying problem characteristics that favor hierarchical quantum-classical approaches. This theoretical foundation provides principles for designing scalable quantum algorithms that leverage multi-scale problem structure to overcome quantum hardware limitations while achieving computational advantages in complex real-world applications.

•Nov 26, 2025•0 citations

Scalable Simulation of Quantum Dynamics on Topological Quantum Hardware

Kritanjan Polley, Mark E. Tuckerman

Quantum computers offer a significant advantage in simulating quantum systems compared to classical computers for certain problems, although most current applications are limited to calculating static molecular properties using hybrid quantum-classical hardware. In this work, we establish a framework for the representation of quantum dynamics in molecular and condensed matter systems, designed for execution on topological quantum hardware. By leveraging the non-Abelian braiding statistics of Fibonacci and Ising anyons, we utilize the Solovay-Kitaev algorithm to approximate unitary propagators for a range of systems. We demonstrate the efficacy of these algorithms across a hierarchy of complexity, from two-level systems and one dimensional double-well potentials to condensed phase spin-boson models, simple molecules, and molecular reaction kinetics. These algorithms provide a scalable and robust pathway for simulating many-body condensed phase chemical physics on fault-tolerant quantum devices.

quant-pharXiv:2609.19484•Sep 18, 2026•0 citations

Quantum Computing in Corrosion Modeling: Bridging Research and Industry

Juan Manuel Aguiar Hualde, Kowalik, Marek, Lian Remme +7 more

Corrosion presents a major challenge to the longevity and reliability of products across various industries, particularly in the aerospace sector. Corrosion arises from chemical processes occurring on an atomistic scale, which lead to macroscopic degradation. Addressing this issue requires multi-scale modeling approaches, which rely on microscopic parameters that are challenging to measure experimentally or model with conventional quantum chemistry techniques. In this work, we develop and demonstrate a hybrid quantum-classical workflow tailored for atomistic simulations of corrosion processes, with a specific focus on the initial step of the oxygen reduction reaction -- a critical trigger for the corrosion of aluminum alloys widely used in modern aircraft. Using a combination of classical quantum chemistry methods and quantum computing frameworks, we identify reaction geometries characterized by multi-configurational electronic structures that are ideal for exploring with quantum algorithms. For the first time in this context, we explore both noisy intermediate-scale quantum and fault-tolerant quantum algorithms for these multi-configurational system, integrating them within a workflow designed to bridge atomistic simulations with macroscopic modeling approaches, such as finite element methods. Furthermore, we conduct a detailed quantum resource estimation to assess when and how quantum computers may play a meaningful role in tackling these problems. Our results demonstrate that significant advancements in quantum hardware but also in algorithms and error correction techniques are needed to make quantum computation practically viable for this class of problems. Nevertheless, this work establishes a critical foundation for applying quantum computation to corrosion modeling and highlights its potential to address complex, business-relevant challenges in materials science.

arXiv:2412.07933•Dec 10, 2024•2 citations
Multiscale modeling of complex chemical systems requires algorithms that operate coherently across electronic, atomistic, mesoscopic, and continuum scales. While quantum algorithms have been proposed for each regime, no systematic framework exists to compose them across scale boundaries. Here, we identify the conditions under which fault-tolerant quantum algorithms might preserve scale-specific quantum advantages. We map quantum phase estimation, Hamiltonian simulation with Gibbs state preparation, quantum random walks, and quantum partial differential equation solvers onto electronic structure, molecular dynamics, mesoscopic kinetics, and continuum reactor physics, respectively. Crucially, these correspondences do not imply unconditional end-to-end quantum advantage; speedups depend heavily on state preparation, memory architectures, matrix conditioning, and classical readout costs. Six unresolved questions define this composition problem, illustrated via a quantum hierarchy for \ce{CO} oxidation over \ce{Pt(111)}. We propose viewing inter-scale transfer as a quantum channel composition problem at the interface of algorithm design and non-equilibrium statistical mechanics, and ask whether information loss at scale boundaries is intrinsic to multiscale modeling or merely a consequence of lossy classical transduction between algorithmic layers. The resulting roadmap suggests that multiscale quantum advantage is governed primarily by the structure of information transfer between algorithmic layers, rather than by performance at individual scales alone.
Whole-cell simulation, modeling all of a cell's functional systems over its life cycle, is an outstanding challenge in computational biology. Even the simplest living cell contains thousands of interacting proteins and metabolites (on the order of trillions of atoms) whose full functional dynamics spans roughly five orders of magnitude in space (nm to μμμm) and nearly nineteen in time (fs to hours). Further, many of the governing physical and chemical properties remain incompletely characterized. Simulating such complex systems at fully atomistic resolution over a full cell cycle is computationally intractable on classical architectures, raising a central question: Can quantum computing offer a viable path to whole-cell simulations that integrate molecular- and systems-level complexity? This Perspective examines the potential of quantum computing across three hierarchical scales: atomistic-molecular modeling, metabolic and regulatory networks, and whole-cell spatial modeling. We present a complexity analysis comparing classical and quantum algorithms for representative biological problems, identifying regimes of substantial theoretical speedup under specified algorithmic assumptions. We highlight algorithmic developments designed to leverage both near-term exploratory and fault-tolerant quantum architectures, and discuss practical bottlenecks: data encoding overhead, system conditioning, measurement constraints, and hybrid quantum-HPC integration. Together, these results outline a roadmap for quantum-accelerated whole-cell modeling and the biological insights such multiscale frameworks may eventually enable.
Abstract. Partial differential equation (PDE) models with multiple temporal/spatial scales are prevalent in several disciplines such as physics, engineering, and many others. These models are of great practical importance but notoriously difficult to solve due to prohibitively small mesh and time step sizes limited by the scaling parameter and CFL condition. Another challenge in scientific computing could come from curse-of-dimensionality. In this paper, we aim to provide a quantum algorithm, based on either direct approximations of the original PDEs or their homogenized models, for prototypical multiscale problems inPDEs, including elliptic, parabolic, and hyperbolic PDEs. To achieve this, we will lift these problems to higher dimensions and leverage the recently developed Schrödingerization based quantum simulation algorithms to efficiently reduce the computational cost of the resulting high-dimensional and multiscale problems. We will examine the error contributions arising from discretization, homogenization, and relaxation, and analyze and compare the complexities of these algorithms in order to identify the best algorithms in terms of complexities for different equations in different regimes.
Computational modeling of cellular systems, where reactants are governed by biochemical equations and physical representations, requires extensive classical computing resources. These limitations significantly constrain the system size and spatiotemporal scales of simulations. A key challenge lies in the "curse of dimensionality", where the number of possible reaction terms grows exponentially with the number of species, and the computation of reaction rates involving many-body interactions becomes intractable in polynomial time on classical computers. In this work, we introduce a quantum algorithmic framework designed to overcome these challenges, leveraging the architecture of quantum computing to simultaneously compute reaction rates and track the spatiotemporal dynamical evolutions of subcellular systems. We generalize the reaction-diffusion equation (RDE) for multiscale systems with arbitrary species count, encompassing higher-order interactions. Our approach achieves two principal quantum advantages: (i) an exponential quantum speedup in reaction-rate computation, contingent on the efficient preparation of polynomially accurate ground states on a quantum computer, and (ii)) a quadratic scaling in spatial grid points and polynomial scaling in the number of species for solving nonlinear RDEs, contrasting sharply with classical methods that scale exponentially with the system's degrees of freedom. To our knowledge, this represents the first efficient quantum algorithm for solving multiscale reaction-diffusion systems. This framework opens the door to simulations of biologically relevant subcellular processes across previously inaccessible spatial and temporal scales, with profound implications for computational biology, soft matter physics, and biophysical modeling.
This work establishes theoretical foundations for hierarchical quantum-classical algorithm design, where complex problems are decomposed across multiple spatial, temporal, or organizational scales with quantum and classical computation assigned to appropriate levels. We develop a mathematical framework that characterizes optimal problem decomposition strategies based on subproblem structure, inter-scale coupling strength, and available quantum resources. The theory proves that multi-scale decomposition can reduce quantum circuit depth requirements while maintaining solution quality, establishing bounds on the communication overhead between hierarchical levels. We derive conditions under which bottom-up quantum processing of finescale subproblems followed by classical integration produces provably near-optimal solutions for the full problem. Our analysis incorporates adaptive refinement strategies where computational resources are dynamically allocated based on intermediate results, proving convergence theorems for iterative hierarchical algorithms. The framework applies to diverse problem classes including molecular simulation across electronic and nuclear scales, network optimization from local to global levels, and scheduling problems with nested temporal structures. We establish fundamental trade-offs between decomposition granularity, quantum advantage preservation, and solution accuracy, identifying problem characteristics that favor hierarchical quantum-classical approaches. This theoretical foundation provides principles for designing scalable quantum algorithms that leverage multi-scale problem structure to overcome quantum hardware limitations while achieving computational advantages in complex real-world applications.
Quantum computers offer a significant advantage in simulating quantum systems compared to classical computers for certain problems, although most current applications are limited to calculating static molecular properties using hybrid quantum-classical hardware. In this work, we establish a framework for the representation of quantum dynamics in molecular and condensed matter systems, designed for execution on topological quantum hardware. By leveraging the non-Abelian braiding statistics of Fibonacci and Ising anyons, we utilize the Solovay-Kitaev algorithm to approximate unitary propagators for a range of systems. We demonstrate the efficacy of these algorithms across a hierarchy of complexity, from two-level systems and one dimensional double-well potentials to condensed phase spin-boson models, simple molecules, and molecular reaction kinetics. These algorithms provide a scalable and robust pathway for simulating many-body condensed phase chemical physics on fault-tolerant quantum devices.
Corrosion presents a major challenge to the longevity and reliability of products across various industries, particularly in the aerospace sector. Corrosion arises from chemical processes occurring on an atomistic scale, which lead to macroscopic degradation. Addressing this issue requires multi-scale modeling approaches, which rely on microscopic parameters that are challenging to measure experimentally or model with conventional quantum chemistry techniques. In this work, we develop and demonstrate a hybrid quantum-classical workflow tailored for atomistic simulations of corrosion processes, with a specific focus on the initial step of the oxygen reduction reaction -- a critical trigger for the corrosion of aluminum alloys widely used in modern aircraft. Using a combination of classical quantum chemistry methods and quantum computing frameworks, we identify reaction geometries characterized by multi-configurational electronic structures that are ideal for exploring with quantum algorithms. For the first time in this context, we explore both noisy intermediate-scale quantum and fault-tolerant quantum algorithms for these multi-configurational system, integrating them within a workflow designed to bridge atomistic simulations with macroscopic modeling approaches, such as finite element methods. Furthermore, we conduct a detailed quantum resource estimation to assess when and how quantum computers may play a meaningful role in tackling these problems. Our results demonstrate that significant advancements in quantum hardware but also in algorithms and error correction techniques are needed to make quantum computation practically viable for this class of problems. Nevertheless, this work establishes a critical foundation for applying quantum computation to corrosion modeling and highlights its potential to address complex, business-relevant challenges in materials science.