Effective prime factorization via quantum annealing by modular locally-structured embedding
Bibliographic record
Abstract
This paper investigates novel techniques to solve prime factorization by quantum annealing (QA). First, we present a very-compact modular encoding of a multiplier circuit into the architecture of current D-Wave QA devices. The key contribution is a compact encoding of a controlled full-adder into an 8-qubit module in the Pegasus topology, which we synthesized using Optimization Modulo Theories. This allows us to encode up to a 21 × 12-bit multiplier (and a 22 × 8-bit one) into the Pegasus 5760-qubit topology of current annealers. To the best of our knowledge, these are the largest factorization problems ever encoded into a quantum annealer. Second, we investigated the problem of actually solving encoded PF problems by running an extensive experimental evaluation on a D-Wave Advantage 4.1 quantum annealer. In the experiments we introduced different approaches to initialize the multiplier qubits and adopted several performance enhancement techniques. Overall, 8,219,999 = 32,749 × 251 was the highest prime product we were able to factorize within the limits of our QPU resources. To the best of our knowledge, this is the largest number which was ever factorized by means of a quantum annealer; also, this is the largest number which was ever factorized by means of any quantum device without relying on external search or preprocessing procedures run on classical computers.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".