feat(Complexity): BQP / EQP / QNC complexity classes#38
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Bridges QuantumQuery and QuantumCircuit into QuantumInfo's semantic types (𝐔[d], MState, CPTPMap) via a syntactic query layer. - QuantumQuery carries only syntactic data (gate tags, Fin n indices, rational phase); unitaryOf maps each constructor to its genuine 𝐔[Fin n → Fin 2] via embedQubitGate / cnotUnitary / phaseGate. - QuantumCircuit's toCPTP interprets the tree into CPTPMap via ofUnitary / compose / prod, with par threading through finFunSplitEquiv. - Retires QState, IsUnitary, tensorGate, measureDistribution, every gateX function and gateX_isUnitary lemma, QuantumCircuit.eval. - Projective computational-basis measurement as POVM. - Adds Physlib dependency in lakefile; Algolean.lean becomes non-module because QuantumInfo is non-module.
Bumps Physlib to v4.29.1 (which modularizes QuantumInfo), transitively pulling Mathlib and the Lean toolchain to v4.29.1 as well. With the QuantumInfo dep now a module, Algolean.lean and the three Quantum/* files that import it can be modules themselves, matching the rest of the project. - Convert Algolean.lean, Quantum/Circuit, Quantum/Embed, Quantum/Oracle to `module` + `public import` + `@[expose] public section`. - Drop `private` on helper defs/lemmas referenced from exposed public decls (fin2_sub_sub_self, cnotAction, cnotAction_involutive in Embed; qubitIndicator in Oracle). - Add PolytimeBasicClasses, RandomSample, ReadWriteVec to the Algolean.lean roll-up; they'd landed on the branch but were never imported. - Delete Algolean/Models/QuantumCircuit.lean and QuantumOracle.lean, superseded by the Quantum/ subdirectory in 3a97291.
Defines the `UniformFamily` abstraction in `Complexity/Basic.lean` and uses it to state `BQP`, `EQP`, `QNC^k` in `Complexity/BQP.lean`. - `UniformFamily Q α`: family of `Prog Q (α n)` indexed by input size. - `Uniform` / `SatisfiesSpec` predicates capture cost and correctness. - `BQP` is defined against `SingleTapeTM` as the classical generator model: classical `Prog (TMQuery tm)` generates quantum circuits whose `toCPTP` decides `L` with bounded error on first-qubit measurement. Both layers measured by `Prog.time`. - Containments: `EQP ⊆ BQP`, `QNC^k ⊆ BQP`. Showcases the `Prog` framework across classical and quantum models.
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Defines the standard uniform quantum complexity classes against the new QuantumInfo-based circuit model.
What's added
UniformFamilyinAlgolean/Complexity/Basic.lean— a small abstraction for families of programs(n : ℕ) → Prog Q (α n)indexed by input size, withUniform(cost-bound predicate) andSatisfiesSpec(correctness predicate). Reusable for any complexity class of this shape.Algolean/Complexity/BQP.lean—BQP,EQP, andQNC^kdefined as cross-model statements: a classicalProg (TMQuery tm)generator produces aQuantumCircuit nfor each input size, bounded inTMCost.stepsby a polynomial; the generated circuit'stoCPTPinterpretation decides the language with the class's error discipline, measured by first-qubit POVM. Includes containmentsEQP ⊆ BQPandQNC^k ⊆ BQP.