QPU Micro-Kernels: Circuit & OS Paradigms

• QPU micro-kernels are specialized quantum circuit abstractions and OS components that enable low-latency, fault-tolerant job scheduling and scalable quantum execution.
• Circuit-level micro-kernels implement shallow, parametrized circuits for localized updates using Monte Carlo estimators, ensuring fixed resource usage and parallelization.
• OS-level micro-kernels utilize minimal, message-driven scheduling techniques with real-time queues and interrupt handlers to manage quantum resources efficiently.

QPU micro-kernels are specialized, minimal quantum circuits or operating system modules that serve as the foundational execution and control units for quantum processing units (QPUs). They bifurcate along two axes: (1) as shallow, parametrized quantum circuits for fine-grained computational tasks such as stencil node updates in scientific computing, and (2) as micro-kernel operating system abstractions facilitating low-latency, deterministic, and fault-isolated scheduling and orchestration of quantum jobs. The micro-kernel paradigm, both at the circuit and OS level, enables scalable, parallel execution, robust resource management, and modular integration into hybrid quantum-classical workflows (Markidis et al., 16 Nov 2025, Ramsauer et al., 25 Jul 2025, Paler, 17 Oct 2024).

1. QPU Micro-Kernels: Quantum Circuit Abstraction

In the computational context, a QPU micro-kernel is a parametrized shallow quantum circuit $U(x;\theta)$ acting on a fixed, small set of qubits ($q$), where $x$ encodes local input data (e.g., neighboring solution values and stencil weights for PDE discretizations), and $\theta$ is derived from this data. Preparation and measurement of $U(x;\theta)$ serve as a Monte Carlo estimator of local updates, with each invocation providing one unbiased sample for the targeted computation (Markidis et al., 16 Nov 2025). The resource requirements—qubit count and circuit depth—remain constant regardless of the global problem size, in contrast to deep circuits encoding entire computational domains. This fixed resource footprint makes QPU micro-kernels amenable to parallelization across grid points and time steps, a model reminiscent of classical GPU kernels.

For example, in time-stepping schemes for PDEs (e.g., the 1D Heat equation), the deterministic stencil update

$u_i^{n+1} = \sum_j w_j u_{i+j}^{n}$

is replaced by quantum Monte Carlo sampling. Two circuit realizations are prominent:

• Bernoulli Micro-Kernel: Encodes each neighbor’s value as a single-qubit amplitude and allocates measurement shots proportionally to the stencil weights. The estimator is the weighted average of outcomes, with a resource requirement of $q=1$ and depth $d=1$ in the minimal case.
• Branching Micro-Kernel: Employs selector qubits to map the categorical stencil weights into a superposition and applies controlled rotations to a readout qubit, yielding the update in expectation. Resource requirements are $q=3$ and $d\approx 12$ (expanding to $d\approx 118$ after transpilation) (Markidis et al., 16 Nov 2025).

2. Micro-Kernel OS Architecture for QPUs

At the system level, QPU micro-kernels manifest as minimal, message-driven operating system kernels managing quantum resource scheduling, real-time job dispatch, and robust state isolation. The Quantum Abstraction Layer (QAL) micro-kernel operates as the intermediary between user-space quantum applications and device-specific hardware drivers, implementing essential services through modular components (Ramsauer et al., 25 Jul 2025):

• Interrupt Handlers: Edge-triggered mechanisms for job completion and error notification, with soft-IRQ routines for policy-deferred scheduling.
• Hybrid Scheduler: Real-time and best-effort job queues (EDF and weighted round-robin), supporting deadlines, preemptive context-switching, and hybrid workloads.
• Resource Manager: Allocation and tracking for qubits, pulse and timing channels, as well as memory and DMA pools.
• Device Driver Interface: Message-based façade supporting IOCTL, doorbell registers, and shared buffer mapping.
• Inter-Process Communication: Well-typed message queues for submit, cancel, checkpoint, and completion control flows.

The QAL micro-kernel enforces a minimal trusted computing base, isolating complexity (compilation, optimization, error decoding) outside the core kernel and utilizing capability-based shared memory.

3. Design Principles and Fault Tolerance

The micro-kernel approach—employed in both circuit micro-kernels and OS micro-kernels—prioritizes minimality, formal verifiability, modularity, and explicit message-passing over shared state (Paler, 17 Oct 2024). In the context of quantum operating systems (QCOS), only dispatch and priority scheduling reside in-kernel, with all advanced functionality provided by peer components via non-blocking, buffered message queues (commonly implemented over high-performance networks such as MPI on supercomputers).

Fault tolerance is achieved via:

• Formal Verification: Ensuring kernel logic conforms precisely to specification, reducing the risk of latent bugs.
• Interrupt-Driven Preemption: High-priority hardware or decoding faults preempt regular processing, maintaining responsiveness.
• Surface Code Fault-Tolerance: Logical error rates per round are bounded by

$$p_L \leq \alpha \left(\frac{p}{p_\mathrm{th}}\right)^{(d+1)/2}$$

with system availability $A$ designed to exceed $0.9998$ via node replication and failover scheduling (Paler, 17 Oct 2024).

• Fault Handlers: Dedicated interrupt routines for hardware errors, with queue-based deferred error processing.

4. Resource Analysis and Performance Metrics

Both the circuit-level and kernel-level micro-kernel paradigms are characterized by predictable, bounded resource usage and performance metrics.

QPU Micro-Kernels (Circuit Level):

Kernel Type	Qubit Count ($q$)	Circuit Depth ($d$)	$L_2$ Error ($M=4000$ shots)	Execution Time (IBM Brisbane, $M=4000$)
Bernoulli	1 or 3	1 (transpiled: 3)	$\approx1\%$ (Heat eqn)	$\sim3.5$ s (per node)
Branching	3	12 (transpiled: 118)	$\approx16\%$ (Heat eqn)	$\sim3.5$–$11.4$ s (per node)

The micro-kernel paradigm allows batching and in-circuit fusion. Batched submission amortizes job launch overhead over $k$ parallel circuits, while in-circuit fusion packs $k$ micro-kernel invocations into a single larger circuit, reducing per-node launch overhead at the expense of higher circuit depth (Markidis et al., 16 Nov 2025).

QPU Micro-Kernels (OS Level):

• Dispatch Latency: x86_64: $3.2\,\mu$s; ARM64: $4.1\,\mu$s; RISC-V64: $4.8\,\mu$s (user IOCTL to pulse start)
• Interrupt Turnaround: x86_64: $1.1\,\mu$s; ARM64: $1.4\,\mu$s; RISC-V64: $1.6\,\mu$s (pulse end to user wakeup)
• End-to-End Throughput: x86_64: $85\,\mathrm{k}$ jobs/sec; ARM64: $70\,\mathrm{k}$ jobs/sec; RISC-V64: $60\,\mathrm{k}$ jobs/sec (1000-gate, 1024-shot circuits) (Ramsauer et al., 25 Jul 2025).

5. Scheduling, Parallelization, and Orchestration

Micro-kernel schedulers orchestrate both real-time and batch quantum jobs. The QAL uses a two-level design: a Real-Time Queue for deadline-based dispatch (EDF), and a Best-Effort Queue with weighted round-robin for throughput:

$$\text{quantum}(j) = \alpha\,\left(\frac{1}{w_j}\right), \quad w_j=\text{priority}(j)$$

Each job consumes up to $\text{quantum}(j)$ before pre-emption; context-switching routines maintain device invariants (Ramsauer et al., 25 Jul 2025).

Circuit-level micro-kernels enable explicit parallelization: each grid node and time step independently dispatches a micro-kernel with only local data dependencies, mirroring modern GPU paradigms. This stands in contrast to global quantum solvers requiring deep, non-local circuits. Batching and fusion are critical for managing scheduling overheads and maximizing QPU utilization (Markidis et al., 16 Nov 2025).

6. Extensions: Hybrid Computation, Error Correction, and Virtualization

The micro-kernel framework extends to fault-tolerant, error-corrected, and hybrid quantum-classical computations. QAL micro-kernels support:

• Distributed Decoding Loops: Pinning real-time threads to IRQ cores for syndrome extraction and passing results to decoders running in user space or on-card controllers.
• Dynamic Mid-Circuit Measurement: Scheduler and driver IPC calls can checkpoint quantum state and branch classically on measurement outcomes, supporting feedback loops critical for error correction and hybrid algorithms.
• Qubit-Pool Virtualization: SR-IOV-like mechanisms allow division of error-corrected arrays into isolated virtual functions with individual sub-schedulers and resource quotas, enabling secure multi-tenant access in HPC clusters.
• Latency-Bounded Quantum-Classical Feedback: Shared memory channels between the QAL kernel and general-purpose CPU cores allow for sub-$10\,\mu$s round-trip classical feedback in hybrid algorithms such as VQE (Ramsauer et al., 25 Jul 2025).

7. Limitations, Scalability, and Outlook

On current NISQ hardware, deep and multi-qubit micro-kernels (e.g., branching type) are impractical due to excessive noise, while ultra-shallow (Bernoulli) kernels remain viable, subject to $O(1/\sqrt{M})$ Monte Carlo statistical convergence. While techniques such as quantum amplitude estimation could theoretically improve convergence to $O(1/M)$, this incurs circuit depths that defeat NISQ constraints. Micro-kernel abstractions—at both the OS and circuit level—remain promising for large-scale, heterogeneous quantum-classical integration, underpinning system architectures designed for robustness, modularity, and scalability (Markidis et al., 16 Nov 2025, Ramsauer et al., 25 Jul 2025, Paler, 17 Oct 2024).