Towards Non-Abelian Quantum Signal Processing: Efficient Control of Hybrid Continuous- and Discrete-Variable Architectures
Bibliographic record
Abstract
Quantum Signal Processing (QSP) transforms a unitary parameterized by a classical variable $θ$ into one governed by a polynomial function $f(θ)$. Though quantum mechanics is linear, such highly nonlinear transformations arise naturally from the curvature of the qubit Bloch sphere. The QSP primitive underpins most quantum algorithms and finds broad utility in robust control by decreasing sensitivity to parameter errors, and in quantum sensing by increasing sensitivity to target parameters. In this work, we extend QSP to a new multivariate class, non-Abelian QSP, that utilizes a set of non-commuting (operator-valued) control parameters $\{\hatθ_1, \hatθ_2, \dots\}$. Experimental instantiations of this richer algebraic structure are currently being explored in hybrid oscillator-qubit systems realized in superconducting and trapped-ion processors, where the non-commuting variables are oscillator positions and momenta. We demonstrate the utility of our construction, the Gaussian-controlled-rotation (GCR) which is a canonical instance of this class, across three domains: fully analytical state preparation circuits whose performance matches state-of-the-art machine-learning protocols for preparing squeezed, cat, GKP, and Fock states; a complete analytical framework for universal control of GKP bosonic error-corrected qubits, including logical readout and error-corrected gate teleportation --with mid-circuit error detection and generalization to arbitrary lattices, qudits, and multi-mode codes uniquely enabled by the analytical structure; and a construction closing a key gap in oscillator-aided quantum phase estimation algorithms. These results establish non-Abelian QSP as a powerful new frontier, one that is not merely of theoretical interest but ready to be put to work in the laboratory today.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".