Freeze the finite-bit input and numerical-stability contract.
Acceptance: All arbitrary-real comparisons and small pivots have explicit handling.
planned; no claimed closure
Structure before circuit tricks
Fault-tolerant resource trade-offs for structured preparation
A small number of arbitrary real rotations is not a complete fault-tolerant resource estimate.
research target setting:structured-clifford-t-connectivity
\[\mathcal R=(T,\operatorname{Toffoli},d,q_{\rm anc},Q_{\rm oracle},\epsilon)\]
Frozen target and input model
Compile the exact-real structured route into a finite gate set with a proved error budget and declared connectivity.
Access model: Finite-bit source data and a fixed Clifford+T gate set, connectivity graph, tolerance and ancilla policy.
- Input/separation and conditioning promises exposed
- Each angle approximation and synthesis error budget explicit
- Count or bound the actual emitted primitive list
Desired result, not an achieved bound
A source-to-finite-bit theorem and a model-matched resource frontier; do not claim simultaneous global optimality of every coordinate.
The Hermite exact-real primitive theorem is already a useful substrate. Full bit complexity and stable angle generation are additional obligations.
Dependency-ready execution route
Bound coefficient, canonicalization and angle errors.
Acceptance: A normalized-state error theorem tied to supplied bit precision.
planned; no claimed closure
Compose finite-gate synthesis and connectivity routing.
Acceptance: T/Toffoli/depth/ancilla accounting plus final state error and cleanup.
planned; no claimed closure
Next bounded advance: Treat the current Hermite bit-complexity boundary as the first local target rather than reopening its exact-real correctness proof.
Reusable mathematics
Named Lean substrates below have their own exact signatures. They do not certify every sentence or proposed generalization on this page.
QuantumBlockEncoding.ConstructiveHermitePreparation.prepare_spec
Lower-bound comparison contract
source-audit-pending
Compare ancilla/depth trade-offs only in the same finite gate and connectivity model.
Same-model key: setting:structured-clifford-t-connectivity
Diagnostic examples, not proofs
- Hermite baseline versus structured route at matched error
- Connectivity-constrained local TT compilation
Primary-source ledger
primary-text-checked Results: circuit complexity lower bound; construction of LCU-based block-encoding; Methods: state preparation
Explicit access construction is not a free oracle. PREPARE together with SELECT and uncomputation can supply a block encoding; a single prepared state alone does not determine an arbitrary operator.
primary-metadata-checked Abstract and publication version notice: published arXiv v2; later v3 exists
Baseline for arbitrary and controlled state preparation and ancilla/depth trade-offs. Pin a version and gate model before comparing bounds.
Download bounded agent / contributor packet
python3 website/scripts/research_atlas.py context --route spw-fault-tolerant