Eigenpath traversal by phase randomization
Why this work is in the frame
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Bibliographic record
Abstract
A computation in adiabatic quantum computing is implemented by traversing a path of nondegenerate eigenstates of a continuous family of Hamiltonians. We introduce a method that traverses a discretized form of the path: At each step we apply the instantaneous Hamiltonian for a random time. The resulting decoherence approximates a projective measurement onto the desired eigenstate, achieving a version of the quantum Zeno effect. If negative evolution times can be implemented with constant overhead, then the average absolute evolution time required by our method is $\cO(L^{2} /\Delta)$ for constant error probability, where $L$ is the length of the path of eigenstates and $\Delta$ is the minimum spectral gap of the Hamiltonian. The dependence of the cost on $\Delta$ is optimal. Making explicit the dependence on the path length is useful for cases where $L$ is much less than the general bound. The complexity of our method has a logarithmic improvement over previous algorithms of this type. The same cost applies to the discrete-time case, where a family of unitary operators is given and each unitary and its inverse can be used. Restriction to positive evolution times incurs an error that decreases exponentially with the cost. Applications of this method to unstructured search and quantum sampling are considered. In particular, we discuss the quantum simulated annealing algorithm for solving combinatorial optimization problems. This algorithm provides a quadratic speed-up in the gap of the stochastic matrix over its classical counterpart implemented via Markov chain Monte Carlo.
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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 it