Research problems on numerical ranges in quantum computing
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Abstract We describe some instances in quantum information processing where numerical range techniques arise. We focus on two basic settings: higher-rank numerical ranges and their relevance in theoretical quantum error correction, and the classical numerical range and its use for comparing quantum information processing operations. We present the basic theory, discuss examples and formulate open problems. Keywords: numerical rangehigher-rank numerical rangequantum information processingquantum error correctiongate fidelityAMS Subject Classifications: 15A6015A9047N5081P68 Acknowledgements D.W. Kribs is grateful for several interesting conversations with participants of WONRA08, and for helpful conversations with M.B. Ruskai. D.W. Kribs was partially supported by NSERC grant 400160, by NSERC Discovery Accelerator Supplement 400233, and by Ontario Early Researcher Award 048142. A. Pasieka was partially supported by an Ontario Graduate Scholarship. M.P. da Silva and C. Ryan were partially supported by NSERC, M. Laforest was partially supported by NSERC and FQRNT.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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 it