Matrix-Product Entanglement Characterizing the Optimality of State-Preparation Quantum Circuits
Bibliographic record
Abstract
Multipartite entanglement offers a powerful framework for understanding the complex collective phenomena in quantum many-body systems that are often beyond the description of conventional bipartite entanglement measures. Here, we propose a class of multipartite entanglement measures that incorporate the matrix product state (MPS) representation, enabling the characterization of the optimality of quantum circuits for state preparation. These measures are defined as the minimal distances from a target state to the manifolds of MPSs with specified virtual bond dimensions χ, and thus are dubbed as χ-specified matrix product entanglement (χ-MPE). We demonstrate superlinear, linear, and sublinear scaling behaviors of χ-MPE with respect to the negative logarithmic fidelity F in state preparation, which correspond to excessive, optimal, and insufficient circuit depth D for preparing χ-virtual-dimensional MPSs, respectively. Specifically, a linearly growing χ-MPE with F suggests H_{χ}≃H_{D}, where H_{χ} denotes the manifold of the χ-virtual-dimensional MPSs and H_{D} denotes that of the states accessible by the D-layer circuits. We provide an exact proof that H_{χ=2}≡H_{D=1}. Our results establish tensor networks as a powerful and general tool for developing parametrized measures of multipartite entanglement. The matrix product form adopted in χ-MPE can be readily extended to other tensor network Ansätze, whose scaling behaviors are expected to assess the optimality of quantum circuit in preparing the corresponding tensor network states.
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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 | 0.009 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.001 | 0.004 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".