Improving Hamiltonian encodings with the Gray code
Bibliographic record
Abstract
Due to the limitations of present-day quantum hardware, it is especially critical to design algorithms that make the best possible use of available resources. When simulating quantum many-body systems on a quantum computer, straightforward encodings that transform many-body Hamiltonians into qubit Hamiltonians use $N$ of the available basis states of an $N$-qubit system, whereas ${2}^{N}$ are in theory available. We explore an efficient encoding that uses the entire set of basis states, where terms in the Hamiltonian are mapped to qubit operators with a Hamiltonian that acts on the basis states in Gray code order. This encoding is applied to the commonly studied problem of finding the ground-state energy of a deuteron with a simulated variational quantum eigensolver (VQE). It is compared to a standard ``one-hot'' encoding, and various trade-offs that arise are analyzed. The energy distribution of VQE solutions has smaller variance than the one obtained by the one-hot encoding even in the presence of simulated hardware noise, despite an increase in the number of measurements. The reduced number of qubits and a shorter-depth variational Ansatz enables the encoding of larger problems on current-generation machines. This encoding also demonstrates improvements for simulating time evolution of the same system, producing circuits for the evolution operators with reduced depth and roughly half the number of gates compared to a one-hot encoding.
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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 | 0.001 | 0.003 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| 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".