Partitioning qubits in hypergraph product codes to implement logical gates
Why this work is in the frame
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Bibliographic record
Abstract
The promise of high-rate low-density parity check (LDPC) codes to substantially reduce the overhead of fault-tolerant quantum computation depends on constructing efficient, fault-tolerant implementations of logical gates on such codes. Transversal gates are the simplest type of fault-tolerant gate, but the potential of transversal gates on LDPC codes has hitherto been largely neglected. We investigate the transversal gates that can be implemented in hypergraph product codes, a class of LDPC codes. Our analysis is aided by the construction of a symplectic canonical basis for the logical operators of hypergraph product codes, a result that may be of independent interest. We show that in these codes transversal gates can implement Hadamard (up to logical SWAP gates) and control-Z on all logical qubits. Moreover, we show that sequences of transversal operations, interleaved with error correction, allow implementation of entangling gates between arbitrary pairs of logical qubits in the same code block. We thereby demonstrate that transversal gates can be used as the basis for universal quantum computing on LDPC codes, when supplemented with state injection.
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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 | 0.001 | 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 | 0.001 | 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