SemQBench: Benchmarking Decomposition-Aware Runtime Policies for Quantum-HPC Search

1 Introduction

• A runtime can retain a valid assignment for one component even when another fails, then combine valid assignments found in different executions.The whole-form interface instead exposes only whether a full circuit execution solved the formula.Source: §1 · p. 2
• SemQBench compares seven policies, including two round-zero controls, by changing one runtime choice at a time while holding the source predicate fixed.Semantic audits verify that the two interfaces accept the same complete solutions.Source: §1 · pp. 2–3
• For the same bundled circuit, collecting valid component results across a batch cannot do worse than requiring every component to succeed in one execution.Useful amplification rounds also depend on each component’s valid-assignment fraction.Source: §1 · p. 3
• Across three IQM Garnet jobs with 106 distinct circuits, visible-component bundled fixed aggregation reduces point-estimate execution count by 2.20–4.00× relative to exact round-zero aggregation.It is no worse than the other amplified policies on the three reported resources, and the overhead sweep selects it in 99 of 108 settings.Source: §1 · p. 3
• Whole-form amplification shows no clear gain over exact random sampling and uses 6.7–104× more active device time than its measured controls.The evaluation covers four workload–mapping conditions, three IQM Garnet jobs, and 106 distinct circuits.Source: §1 · p. 3

2.1 Quantum-HPC workflow systems

• A runtime given only a whole-form circuit cannot validate or retain partial component progress.Quantum-HPC systems manage submission, backend selection, task execution, and checkpointing.Source: §2.1 · p. 3

2.2 Decomposition, circuit cutting, and search structure

• SemQBench uses established SAT connected-component decomposition, unlike circuit cutting, which partitions a constructed circuit and reconstructs its output distribution.A complete component-based solution requires a valid assignment from every component, without reconstructing a cut circuit.Source: §2.2 · p. 4

2.3 Quantum benchmarks and round-zero controls

• Round-zero controls use uniform sampling and known exact valid-assignment fractions to distinguish sampling success from success attributable to amplification.U-W controls whole-form execution, while U-C controls component-visible aggregation.Source: §2.3 · p. 4

2.4 Co-location and policy selection

• SemQBench bundles components of one formula, not unrelated programs; its measurements also keep executions, device time, and provider jobs distinct.The cost model is applied only after those resource coordinates are reported separately.Source: §2.4 · pp. 4–5, Figure 1 · p. 5

3 Application Boundary and Policies

• Figure 1 presents the workflow boundary and seven evaluation policies: two round-zero controls and five amplified policies.The comparisons address amplification, aggregation, packaging, and retention.Source: §3 · p. 5, Table 1 · p. 6

3.1 Application descriptor and run state

• The immutable descriptor freezes the formula, components, validators, legal policies, candidate rounds, and build settings before hardware outcomes are inspected.A separate run manifest records circuit identifiers, mappings, counts, calibration and job identifiers, checkpoints, and timings; a semantic audit checks equivalent complete-solution acceptance.Source: §3.1 · p. 5

3.2 Workloads

• The workloads are small and exhaustively checkable so resource differences can be attributed to the runtime policies being compared.They include a six-qubit exact-match search tested on two mappings, an unequal-width 2 + 3 workload with component satisfying-assignment counts 1 and 2, and a three-component 2 + 2 + 2 workload with counts 1, 3, and 2.Source: §3.2 · pp. 5–6

3.3 Policy definitions

• The seven policies are U-W and W for unamplified and amplified whole forms, U-C for unamplified component aggregation, and J, F, S, and A for amplified component execution.J uses bundled joint-shot validation; F bundled fixed aggregation; S static separated execution; A separated execution with adaptive retention.Source: §3.3 · p. 6
• Pairwise comparisons isolate amplification (U-W/W and U-C/F), aggregation (J/F), packaging (F/S), and retention (S/A).A replays measured component outcomes for retention and checkpointing rather than using live adaptive resubmission.Source: §3.3 · pp. 6–7

4.1 Round-zero controls

• Round-zero controls use uniform sampling: the whole-form one-shot success probability comes from the valid-assignment count, while the component-visible analytic distribution is calibrated independently of hardware.The measured U-C control instead uses the hardware histogram over validator subsets.Source: §4.1 · p. 7

4.2 Fixed aggregation

• For component-visible policies, fixed aggregation completes when every component has appeared in an accepting subset, and the reported count is the smallest k reaching 95% completion probability.For two- and three-component cases, unit tests matched the inclusion–exclusion calculation to direct sequence enumeration and verified monotonicity in k.Source: §4.2 · p. 7

4.3 Resource coordinates

• The resource vector is (N95, Dactive, H): the 0.95-quantile physical-circuit count, scheduled circuit duration summed across executions, and separately submitted provider-job count.It excludes reset delay and assigns no monetary cost to jobs.Source: §4.3 · p. 8
• The overhead sweep uses Qρ,σ with execution and job weights, but this modeled quantity is not provider billing, queue delay, usage, or measured wall-clock time.The sweep varies ρ across six values and σ across nine values after unit conversion.Source: §4.3 · p. 8

4.4 Measurement sources and uncertainty

• Completion counts and resource summaries are modeled from measured or analytic inputs; reported probability intervals use Bonferroni correction over 26 measured events, and do not establish differences among the four Table 4 reduction factors.For the two CNF workloads, candidate selection uses one shot half and reported probabilities use a disjoint held-out half.Source: §4.4 · p. 8

5 Hardware Setup

• Heralding and dynamical decoupling were disabled, so measurements describe the plain compiled circuits; every job used transpiler seed 42.Heralding flags some state-preparation errors, while dynamical decoupling inserts pulses during idle periods.Source: §5 · p. 9
• All hardware circuits ran on IQM Garnet, a 20-qubit square-lattice superconducting processor, across three provider jobs covering 106 distinct circuits.The three provider timelines were 9.33, 9.13, and 2.68 QPU-seconds; these include all shots, unlike the later per-execution microsecond durations.Source: §5 · pp. 8–9
• For equal-width workloads, measured U-C controls and amplified candidates came from different hardware records, making their measured comparison descriptive rather than calibration-matched.The exact analytic U-C control is calibration-independent but is not a hardware measurement.Source: §5 · p. 9
• Repeated reference-circuit endpoints provide a local calibration check, but do not bound fluctuations between anchors or describe another day or device.Endpoint probability changes were at most 0.031 for component circuits and 0.020 for bundled circuits; whole-form changes were −0.020 and +0.039.Source: §5 · p. 9
• The two whole-predicate compiler constructions agreed on marked assignments and probabilities to 1.68 × 10^-14 in statevector checks.The constructions used PhaseOracleGate and a truth-table diagonal phase.Source: §5 · p. 9

6.2 Whole-form amplification versus uniform sampling

• 6.7–104.0× more active device time: whole-form amplification showed no resolved probability improvement over measured controls across four conditions.This observation applies to the two whole-predicate compiler constructions evaluated.Source: Figure 2 · p. 10, §6.2 · p. 12

6.1 Primary resource results

• The table reports 95%-completion counts using policy-specific outcome rules, with Dactive/N95 giving mean scheduled duration per counted physical-circuit execution.For S and A, comparable one-attempt probabilities are products of separately measured component probabilities, marked †.Source: §6.1 · pp. 9–10, Table 2 · p. 11

6.2 Whole-form amplification versus uniform sampling

• For the three-component W circuit, the selection half gives probability 0.136, while the evaluation half gives 0.081; reporting selection would raise the point estimate approximately 68% relative to the held-out value.Source: §6.2 · p. 12

6.3 Component-visible amplification

• For the three-component workload, valid fractions 1/4, 3/4, and 1/2 yield selected tuple (1, 0, 0); one round on all components would reduce ideal joint-valid probability from 0.3750 to zero.The selected round tuples are chosen separately by component.Source: §6.3 · p. 12
• 2.20–4.00× fewer N95 executions: F reduces exact-U-C counts from 28 to 7, 28 to 8, 13 to 4, and 11 to 5.The 4.63× reduction against measured U-C on equal-width mapping 2 is descriptive because the records differ.Source: Table 4 · p. 13, §6.3 · p. 13
• Every F interval lies above exact round-zero probability; measured U-C and F intervals are disjoint in all four conditions, but only two comparisons share a calibration record.Measured equal-width comparisons remain descriptive.Source: §6.3 · p. 13
• On the unequal-width workload, exact-U-C to F cuts executions from 13 to 4 but raises active time from 7.44 to 9.81 µs; neither dominates across (N95, Dactive, H).Against measured U-C, the same case is fourteen executions and 8.01 µs versus four executions and 9.81 µs.Source: §6.3 · p. 13
• In the extended job, the largest anchor endpoint change was 0.031 versus amplified-minus-round-zero gaps of 0.342 and 0.253, but this does not establish replication across windows, days, or devices.The comparison is descriptive.Source: §6.3 · p. 14

6.4 Joint-shot versus fixed aggregation

• For the same bundled circuit, every joint-shot completion is also a fixed-aggregation completion, so PF(k) ≥ PJ(k) and N95 cannot favor J.Source: §6.4 · p. 14
• Policy F reduces N95 from 14 to 7, 17 to 8, 6 to 4, and 8 to 5; identical circuit durations and job counts make active device time fall in the same proportions.Source: §6.4 · p. 14

6.5 Bundled versus separated packaging

• F bundles all components in one circuit, whereas S runs one component circuit at a time; F uses fewer executions on both equal-width mappings and the unequal-width workload.Source: §6.5 · p. 14
• Even assuming separately measured component probabilities multiply without cross-submission drift or provider failures, F uses fewer executions than S in all four conditions and fewer than A in three, tying once.Source: §6.5 · p. 14
• On equal-width mapping 2, S has a larger one-attempt product than F, 0.2362 versus 0.1641, yet needs twelve physical-circuit executions rather than eight.Source: §6.5 · p. 14

6.6 Static versus adaptive retention

• Adaptive retention lowers the 0.95-quantile execution count from 14 to 10, 12 to 8, 6 to 5, and 11 to 8, but raises provider jobs from one to 9, 6, 4, and 4.Source: §6.6 · p. 15

6.7 Overhead sensitivity

• F is selected in 99 of 108 tested overhead settings and is no worse than the other tested amplified policies on executions, active device time, or jobs; U-C is selected in the remaining nine zero-execution-overhead settings.Source: §6.7 · p. 15

6.8 Whole-form construction

• For unequal-width and three-component workloads, the alternative whole-form lowering reduces native depth from 356 to 221 and 965 to 431, while cross-component gates fall from 56 to 52 and 301 to 157.Source: §6.8 · p. 15
• The alternative lowering raises full-record valid-result point estimates from 0.064 to 0.104 and 0.066 to 0.109, but these records include selection shots and a gap remains against component bundles.Source: §6.8 · pp. 15–16

• Bundled fixed aggregation is at least as good as other tested amplified policies on executions, active device time, and provider jobs, while unequal-width amplification saves ten executions but adds 1.80 µs of active device time.Source: §7 · p. 16
• Fixed aggregation cannot do worse than joint-shot validation for the same bundled circuit, and useful amplification-round counts depend on each component’s valid fraction.Source: §7 · p. 16
• The study covers exhaustively checkable workloads, zero or one amplification round, and three IQM Garnet jobs; policy order may change for deeper circuits, more components, or another device.Source: §7 · p. 16

• Across four workload–mapping conditions, component-visible amplification reduces point-estimate fixed-batch execution counts by 2.20–4.00× versus exact round-zero aggregation, while bundled fixed aggregation is selected in 99 of 108 modeled-cost settings.Source: §8 · p. 16
• On one workload, executions fall from thirteen to four while active device time rises from 7.44 to 9.81 µs, leaving the runtime measurements to inform whether amplification is worthwhile.Source: §8 · pp. 16–17
• Future work will study adaptive scheduling that jointly chooses amplification rounds, circuit bundles, and resubmission batches as search progress, device conditions, and provider costs change.Source: §8 · p. 17