Linear and Non-linear Relational Analyses for Quantum Program Optimization
Bibliographic record
Abstract
The phase folding optimization is a circuit optimization used in many quantum compilers as a fast and effective way of reducing the number of high-cost gates in a quantum circuit. However, existing formulations of the optimization rely on an exact, linear algebraic representation of the circuit, restricting the optimization to being performed on straightline quantum circuits or basic blocks in a larger quantum program. We show that the phase folding optimization can be re-cast as an affine relation analysis , which allows the direct application of classical techniques for affine relations to extend phase folding to quantum programs with arbitrarily complicated classical control flow including nested loops and procedure calls. Through the lens of relational analysis, we show that the optimization can be powered-up by substituting other classical relational domains, particularly ones for non-linear relations which are useful in analyzing circuits involving classical arithmetic. To increase the precision of our analysis and infer non-linear relations from gate sets involving only linear operations – such as Clifford+ t – we show that the sum-over-paths technique can be used to extract precise symbolic transition relations for straightline circuits. Our experiments show that our methods are able to generate and use non-trivial loop invariants for quantum program optimization, as well as achieve some optimizations of common circuits which were previously attainable only by hand.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.006 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.007 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".