The Task
Variable tracing is a fundamental reasoning task that requires tracking the value of a variable as it changes through a sequence of operations. Given a code snippet with assignments, arithmetic operations, and variable interactions, the model must determine the final value of a queried variable.
This task tests a model's ability to maintain state across multiple steps and correctly handle temporal dependencies—a capability where we hypothesized quantum attention mechanisms would show measurable advantages.
Why This Matters
Variable tracing mirrors real-world code understanding challenges: debugging, code review, and automated program analysis all require tracking state through execution flow. Superior performance on this task indicates potential for practical applications in AI-assisted software development.
Synthetic Dataset
We designed a synthetic dataset with controlled complexity levels to systematically evaluate model capabilities. The dataset includes simple assignments, arithmetic operations, variable references, and confounding reassignments across three difficulty tiers.
Simple
Direct assignments and basic arithmetic. The target variable's value can be determined from a single operation or direct reference.
y = x + 3
→ y = 8
Interaction
Multiple variable interactions requiring tracking of intermediate values and dependencies between variables.
b = a * 3
c = b + a
→ c = 8
Reassignment
Confounding reassignments that require precise temporal tracking. Variables are reassigned after being referenced by others.
y = x
x = 9
→ y = 1
Experimental Setup
We compared our Quantum-Enhanced Transformer Multi-Head Attention (QETMHA) architecture against a classical transformer baseline with identical parameter counts. Both models were trained on the same dataset splits with equivalent training procedures to ensure a fair comparison.
Results
Test Accuracy Over Training
Per-Level Accuracy (Final)
Level 3 (Reassignment) Accuracy
Quantum Advantage Over Training
Key Findings
- Consistent advantage across all difficulty levels: QETMHA outperformed the classical baseline at every complexity tier, with the gap widening as task difficulty increased.
- Faster convergence: The quantum architecture reached high accuracy earlier in training, suggesting more efficient learning of the underlying task structure.
- Robust long-range tracking: Level 3 results demonstrate QETMHA's superior ability to maintain temporal dependencies, the core capability needed for complex code understanding.
- Scalable advantage: The performance gap was most pronounced on the hardest problems, indicating quantum attention provides the greatest benefit where classical methods struggle most.
Implications
These results validate our hypothesis that quantum attention mechanisms provide measurable advantages on tasks requiring precise state tracking across multiple reasoning steps. The pronounced advantage on Level 3 problems—where temporal order and reassignment must be carefully tracked—suggests significant potential for applications in code analysis, debugging assistance, and automated program verification.