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QPU Micro-Kernels for Stencil Computation
KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology.ORCID iD: 0000-0003-0639-0639
KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology.ORCID iD: 0009-0009-4901-1716
KTH, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for High Performance Computing, PDC.ORCID iD: 0000-0002-9479-7393
KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology.ORCID iD: 0009-0000-2892-3235
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2026 (English)In: Proceedings of Supercomputing Asia and International Conference on High Performance Computing in Asia Pacific Region, SCA/HPCAsia 2026, Association for Computing Machinery (ACM) , 2026, p. 68-80Conference paper, Published paper (Refereed)
Abstract [en]

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.

Place, publisher, year, edition, pages
Association for Computing Machinery (ACM) , 2026. p. 68-80
Keywords [en]
Monte Carlo Methods for PDEs, Quantum Computing, Quantum Micro-Kernels, Stencil Computation
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-378753DOI: 10.1145/3773656.3773676Scopus ID: 2-s2.0-105031771273OAI: oai:DiVA.org:kth-378753DiVA, id: diva2:2049927
Conference
Supercomputing Asia and International Conference on High Performance Computing in Asia Pacific Region, SCA/HPCAsia 2026, Osaka, Japan, January 26-29, 2026
Note

Part of ISBN 9798400720673

QC 20260331

Available from: 2026-03-31 Created: 2026-03-31 Last updated: 2026-05-12Bibliographically approved
In thesis
1. Hardware-Centric Tightly-Coupled Quantum/Classical Computations: A hardware description language for quantum computing
Open this publication in new window or tab >>Hardware-Centric Tightly-Coupled Quantum/Classical Computations: A hardware description language for quantum computing
2026 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

By exploiting quantum mechanical behavior, quantum computers have the potential to carry out classically hard computations, such as the prime factorization of integers, with disruptive, exponentially better efficiency, yet they struggle with classically simple task like integer addition. Hybrid applications, combining both quantum and classical computations, attempt to take advantage of the strength of both approaches while avoiding their weaknesses. In such applications, the design of the interface between quantum and classical computers deserves attention as a potential performance bottleneck.

In this thesis, the design of a modular software stack for hybrid quantum/classical applications that is agnostic to the used quantum technology platform is developed both for high-level application-oriented as well as high-performance low-level use-cases. A hardware description language for quantum circuits derived from the industry standard VHDL language is proposed, and its usage in tightly-coupled hybrid applications, where quantum and classical computations overlap in time, is discussed. To enable low-latency coupling, the proposed hybrid architecture connects quantum computations to hardware implementations of timing critical classical computations and utilizes established hardware/software co-design patterns to interface higher-level classical computations.

Experimental evidence of noise effects on state-of-the-art quantum hardware is presented for the case of solving partial differential equations. This supports the conclusion that frequent interaction between short and shallow quantum and classical computations is necessary even for loosely-coupled hybrid applications under these circumstances, strengthening the case for a low-latency, high-bandwidth quantum-classical interface as proposed in this thesis.

Abstract [sv]

Genom att utnyttja kvantmekaniska effekter har kvantdatorer potentialen att lösa klassiskt svåra beräkningsproblem, som exempelvis primtalsfaktorisering av heltal, med exponentiellt bättre effektivitet, medan de har svårt att lösa klassiskt enkla uppgifter såsom summering av heltal. Hybrida applikationer, som kombinerar båda kvant- och klassiska beräkningar, försöker utnyttja styrkorna av båda tillvägagångssätten och undviker deras svagheter. Sådana applikationer behöver ta hänsyn till utformningen av gränssnittet mellan kvant- och klassiska datorer för att undvika flaskhalsar som begränsar prestandan.

I denna avhandling utvecklas en modulär mjukvarustack för hybrida kvant/klassiska applikationer som är agnostisk till den underliggande kvantteknologiska plattformen. Användningen i både högnivå, applikationsbaserade såväl som i lågnivå, högprestanda scenarierna diskuteras. Ett hårdvarubeskrivningsspråk för kretsbaserade kvantberäkningar baserat på industristandardspråket VHDL med fokus på tätt kopplade hybrida applikationer, där kvant- och klassiska beräkningar överlappar i tid, presenteras. För att minimera latensen vid informationsöverföringen mellan kvant- och klassiska beräkningar föreslås att tidskritiska klassiska delar realiseras i programmerbar hårdvara. Existerande lösningar från samordnad hård- och mjukvarudesign kan användas för att sammankoppla de klassiska lågnivåberäkningarna med högnivåmjukvaran.

En experimentell undersökning av effekten av brus i kontemporära kvantdatorer på beräkningsresultat för lösningen av partiella differentialekvationer presenteras. Den understryker vikten av sammankopplingen av talrika korta kvantberäkningar med hjälp av klassiska metoder även för löst kopplade användningar. Detta resultat bekräftar behovet av kvant/klassiska gränssnitt med låg latens och hög bandbredd.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2026. p. xv, 61
Series
TRITA-EECS-AVL ; 2026:54
Keywords
quantum computing, quantum control systems, hybrid quantum/classical applications, hardware description languages, register-transfer-level models, programmable logic, FPGAs, VHDL, kvantberäkningar, digitala styrsystem för kvantdatorer, hybrida kvant/klassiska användningar, hårdvarubeskrivningsspråk, register-transfer modeller, programmerbar logik, FPGA, VHDL
National Category
Computer Sciences
Research subject
Computer Science
Identifiers
urn:nbn:se:kth:diva-381105 (URN)978-91-8106-631-9 (ISBN)
Public defence
2026-06-10, https://kth-se.zoom.us/s/69771296581, D3, Lindstedtsvägen 5, Stockholm, 14:00 (English)
Opponent
Supervisors
Note

QC 20260513

Available from: 2026-05-13 Created: 2026-05-12 Last updated: 2026-05-19Bibliographically approved

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Markidis, StefanoPennati, LucaNetzer, GilbertPasquale, MarcoPeng, Ivy

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