CASQUE Subcircuit Routing for Quantum Clouds

• CASQUE subcircuit routing is a dynamic mechanism that assigns dummy-padded quantum subcircuits to heterogeneous backends based on fidelity, leakage risk, and queue penalties.
• It leverages a multi-objective cost function within the NADGO stack to optimize scheduling by minimizing latency, power consumption, and adversarial leakage risks.
• The system integrates real-time telemetry, particle-filter scheduling, and cryptographic audit logs to enforce operational privacy and ensure scalable quantum workload dispatch.

CASQUE subcircuit routing is a dynamic resource allocation and scheduling mechanism used in quantum cloud service environments to assign subcircuit segments of a padded quantum workload to heterogeneous hardware backends. It operates within the NADGO (Noise-Adaptive Dummy-Gate Obfuscation) orchestration stack, integrating privacy-preserving techniques, multi-objective optimization, and real-time leakage monitoring to enforce operational privacy and minimize execution overheads across cryogenic-scale quantum control systems (Punch et al., 31 Aug 2025).

1. Functional Role in NADGO Scheduling Stack

CASQUE subcircuit routing is positioned as the decision engine responsible for backend assignment of segmented, dummy-padded quantum subcircuits (denoted as $C'_k$). After the initial quantum circuit is obfuscated with hardware-aware $t$-design dummy gates to create indistinguishable cover traffic, and subsequent timing randomization is performed by a particle-filter scheduler, CASQUE selects the optimal execution backend for each subcircuit according to live system telemetry.

Objectives fulfilled by CASQUE include:

• Prioritization of hardware with higher calibration fidelity for selected gates.
• Avoidance of execution channels with elevated leakage risk, as detected by a per-interval estimator $\hat\Delta_t$.
• Regulation of queue stress and latency, optimizing for cryogenic power and timing constraints.

CASQUE thus constitutes a privacy-aware and efficiency-optimized routing layer, explicitly tying backend selection to both operational and adversarial observables.

2. Mathematical Formulation of Multi-Objective Routing Cost

The routing decision is made by minimizing a cost function parameterized by three key metrics for each candidate backend $h$ (Punch et al., 31 Aug 2025). The cost is expressed as:

$$\text{Cost}(h) = \alpha (1 - \hat{F}_{id}(h)) + \omega_{\text{leak}} \cdot \text{LeakRisk}(h) + \gamma \cdot \text{QueuePenalty}(h)$$

• $\hat{F}_{id}(h)$: Proxy for hardware-calibrated fidelity; higher values are preferable.
• $\text{LeakRisk}(h)$: Risk metric returned by leakage estimator $\hat\Delta_t$; elevated risk increases cost.
• $\text{QueuePenalty}(h)$: Quantifies backlog and latency for each backend.
• $\alpha, \omega_{\text{leak}}, \gamma$: Fixed weights controlling trade-off.

Routing incorporates cost hysteresis: Switching is triggered when $\hat\Delta_t$ exceeds the leakage budget threshold ($\Delta_\text{budget}$ minus tolerance $\tau$) for $m$ consecutive intervals, or when a backend offers a relative cost drop of at least $\delta$.

3. Integration in Quantum Job Orchestration

CASQUE routing is invoked for each subcircuit segment within the NADGO pipeline, comprising the following sequence:

Step	Description	Output
Policy Alignment	Client and system negotiate privacy parameters	Contract
$t$-Design Padder	Adds structured dummy gates	Padded circuit
Particle-Filter Scheduler	Randomizes timing per segment	Segment dispatch plan
CASQUE Router	Assigns backend $h$ through cost function	Segment-to-backend map
Leakage Monitor/Kill-Switch	Enforces leakage threshold	Abort/Proceed signals
Audit Log	Logs decisions and runtime context	Hash-chained history

CASQUE’s backend selection ("$h_k \leftarrow$ SelectBackend($C'_k$)") is performed for each circuit chunk, logged in the cryptographically verifiable audit trail.

4. Privacy, Efficiency, and Security Implications

The principal contribution of CASQUE routing is the linkage of circuit execution topology to privacy constraints, hardware conditions, and system load:

Privacy:

• By distributing subcircuits across heterogeneous backends and integrating real-time leakage risk signals, CASQUE obfuscates execution metadata, limiting adversarial inference even when control-plane timing and scheduling logs are accessible.
• The use of leak-aware cost terms ensures routing actively adapts to threat conditions, maintaining leakage within preset budgets with abort rates below 1 percent in evaluated scenarios (Punch et al., 31 Aug 2025).

Efficiency:

• Queue penalty informs routing against latency-prone or overloaded hardware, directly reducing cumulative wait and cryogenic power.
• Selection favors fidelity-calibrated backends, improving execution success probability for quantum workloads.

Security:

• Auditability is preserved—every routing decision and associated cost rationale is entered into an append-only, hash-chained ledger.
• Routing policy is robust to shifting adversarial pressure, due to hard-coded weight parameters and cost hysteresis.

5. Comparison to Classical and Neural Routing Schemes

CASQUE subcircuit routing differs fundamentally from classical IC and neural FCN-based routing approaches as presented in "Training a Fully Convolutional Neural Network to Route Integrated Circuits" (Jain et al., 2017):

• Traditional IC routing methods (e.g., Dijkstra, Steiner tree, branch-leg heuristics) operate over explicit, rule-defined physical design spaces; neural approaches (via per-pixel binary segmentation) infer rules from annotated layout data and optimize global connectivity and resource assignments in one pass.
• CASQUE instead routes at a higher abstraction layer, optimizing backend assignment and leakage risk—embedding privacy and multi-tenancy directly into the routing objective rather than solely physical connectivity.

A plausible implication is that, while FCNs can potentially be adapted to subcircuit routing for resource allocation in quantum control, CASQUE is specifically tailored for privacy-aware, multi-objective environments with live telemetry and adversarial threat models.

6. System Impact, Scalability, and Limitations

CASQUE routing delivers quantifiable improvements in NADGO system benchmarks:

• Maintains leakage well within per-interval targets throughout both simulated and hardware emulation evaluations.
• Achieves lower latency and power consumption than static circuit padding strategies at matched leakage envelopes (Punch et al., 31 Aug 2025).
• Scales under increased workload and concurrency, given constant-tuned weights and uniform application of cost hysteresis.

This suggests minor overhead is incurred for privacy enforcement, with interval-abort rate below 1 percent and end-to-end costs competitive with naive methods.

Potential limitations include the need for accurate, live fidelity calibration and leakage estimation; miscalibration may skew routing choices. The cost function is dependent on hand-selected weights, which may require application-specific adaptation. Routing decisions do not optimize for physical circuit topology, focusing instead on backend choice and privacy compliance.

7. Concluding Summary

CASQUE subcircuit routing is a core privacy-enforcing component in quantum job orchestration, assigning padded subcircuit segments to execution backends via a rigorously defined, multi-objective cost function. The mechanism's integration with $t$-design dummy-gate padding and particle-filter timing randomization ensures that observable control-plane metadata remains decoupled from the actual computation, preserving both performance and auditable privacy in cryogenic-scale cloud quantum environments (Punch et al., 31 Aug 2025). The design enables low-latency, secure, and scalable quantum workload dispatch with transparent operational guarantees.