QPU Micro-Kernels for Stencil Computation
Year: 2026
Type: conference-paper
Abstract: We introduce QPU micro-kernels: shallow quantum circuits that perform a stencil node update and return a Monte Carlo estimate from repeated measurements. We show how to use them to solve Partial Differential Equations (PDEs) explicitly discretized on a computational stencil. From this point of view, the QPU serves as a sampling accelerator. Each micro-kernel consumes only stencil inputs (neighbor values and coefficients), runs a shallow parameterized circuit, and reports the sample mean of a readout rule. The resource footprint in qubits and depth is fixed and independent of the global grid. This makes micro–kernels easy to orchestrate from a classical host and to parallelize across grid points. We present two realizations. The Bernoulli micro-kernel targets convex-sum stencils by encoding values as single-qubit probabilities with shot allocation proportional to stencil weights. The branching micro–kernel prepares a selector over stencil branches and applies addressed rotations to a single readout qubit. In contrast to monolithic quantum PDE solvers that encode the full space-time problem in one deep circuit, our approach keeps the classical time loop and offloads only local updates. Batching and in-circuit fusion amortize submission and readout overheads. We test and validate the QPU micro-kernel method on two PDEs commonly arising in scientific computing: the Heat and viscous Burgers’ equations. On noiseless quantum circuit simulators, accuracy improves as the number of samples increases. On the IBM Brisbane quantum computer, single-step diffusion tests show lower errors for the Bernoulli realization than for branching at equal shot budgets, with QPU micro-kernel execution dominating the wall time.
Institution: KTH Royal Institute of Technology
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W7119504689