Quantum Framework for Simulating Linear Partial Differential Equations without Queries

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Abstract
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Partial differential equations (PDEs) underpin a vast range of scientific and engineering applications, yet simulating high-dimensional and time-dependent PDEs remains challenging for both classical and quantum computation. To address this challenge, we introduce an explicitly constructed, oracle-free quantum framework. Specifically, all quantum circuits are built directly from fundamental gate operations, such as C-NOT gates and one-qubit rotations—basic units of quantum computing analogous to NOT, OR, and AND gates in classical computing. This explicitness enables clear resource estimation, avoids hidden complexities associated with oracle-based methods, and facilitates future hardware implementation. In addition, the framework addresses a broad class of linear PDEs, including those with time-dependent coefficients, inhomogeneous terms, and general Robin boundary conditions—encompassing special cases such as Dirichlet and Neumann boundaries.


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About the Speaker
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Nikita Guseynov is a PhD candidate in Electronic Science and Technology at the University of Michigan-Shanghai Jiao Tong University Joint Institute. He holds a B.Sc. and a M.Sc. in Physics from Lomonosov Moscow State University. He currently serves as a Researcher at Unitary Lab and a Principal Investigator for the National Natural Science Foundation of China. His primary research interests encompass solving partial differential equations using quantum algorithms, quantum chemistry, continuous-variable bosonic systems, and the compiling of quantum circuits.