Efficient Training of Layerwise-Commuting PQCs with Parallel Gradient Estimation
Bibliographic record
Abstract
Variational quantum algorithms, such as the variational quantum eigensolver (VQE), have a very high cost due to the large number of measurement outcomes that must be acquired from the quantum device during training. This is due in large part to the use of the parameter shift rule for estimating the gradient at each step, which requires two circuit evaluations per parameter. It was recently shown that if all the gate generators in the ansatz commute with each other, then the complete gradient vector can be found from a single evaluation of an augmented circuit (Bowles et al., 2023), and this has the potential to significantly reduce the quantum cost. Unfortunately, this is quite a severe restriction, as it prevents the ansatz from having a nontrivial dynamical Lie algebra (DLA). In order to obtain a more expressive ansatz than permitted by the commutation requirement, we construct it iteratively and train it in a layerwise fashion using the parallel gradient method. For VQE training of an 8-qubit transverse field Ising model (TFIM) on an ideal simulator, we show that this approach is able to reach a lower energy using fewer circuit evaluations than the parameter shift rule with a more conventional ansatz.
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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 | 0.000 | 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 | 0.000 | 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".