Boosting quantum amplitude exponentially in variational quantum algorithms
Bibliographic record
Abstract
Abstract We introduce a family of variational quantum algorithms, which we coin as quantum iterative power algorithms (QIPAs), and demonstrate their capabilities as applied to global-optimization numerical experiments. Specifically, we demonstrate the QIPA based on a double exponential oracle as applied to ground state optimization of the H 2 molecule, search for the transmon qubit ground-state, and biprime factorization. Our results indicate that QIPA outperforms quantum imaginary time evolution (QITE) and requires a polynomial number of queries to reach convergence even with exponentially small overlap between an initial quantum state and the final desired quantum state, under some circumstances. We analytically show that there exists an exponential amplitude amplification at every step of the variational quantum algorithm, provided the initial wavefunction has non-vanishing probability with the desired state and that the unique maximum of the oracle is given by λ 1 > 0 , while all other values are given by the same value 0 < λ 2 < λ 1 (here λ can be taken as eigenvalues of the problem Hamiltonian). The generality of the global-optimization method presented here invites further application to other problems that currently have not been explored with QITE-based near-term quantum computing algorithms. Such approaches could facilitate identification of reaction pathways and transition states in chemical physics, as well as optimization in a broad range of machine learning applications. The method also provides a general framework for adaptation of a class of classical optimization algorithms to quantum computers to further broaden the range of algorithms amenable to implementation on current noisy intermediate-scale quantum computers.
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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 | 0.005 | 0.021 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| 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".