Bang-bang algorithms for quantum many-body ground states: A tensor network exploration
Bibliographic record
Abstract
We use matrix product techniques to investigate the performance of two algorithms for obtaining the ground state of a quantum many-body Hamiltonian $H={H}_{A}+{H}_{B}$ in infinite systems. The first algorithm is a generalization of the quantum approximate optimization algorithm and uses a quantum computer to evolve an initial product state into an approximation of the ground state of $H$ by alternating between ${H}_{A}$ and ${H}_{B}$. We show for the one-dimensional (1D) quantum Ising model that the accuracy in representing a gapped ground state improves exponentially with the number of alternations. The second algorithm is the variational imaginary time ansatz, which uses a classical computer to simulate the ground state via alternating imaginary time steps with ${H}_{A}$ and ${H}_{B}$. We find for the 1D quantum Ising model that an accurate approximation to the ground state is obtained with a total imaginary time $\ensuremath{\tau}$ that grows only logarithmically with the inverse energy gap $1/\mathrm{\ensuremath{\Delta}}$ of $H$. This is much faster than imaginary time evolution by $H$, which would require $\ensuremath{\tau}\ensuremath{\sim}1/\mathrm{\ensuremath{\Delta}}$.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.001 |
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".