| A classical universal function approximator is probably not sufficient to approximate quantum systems
(unless there is IDK a geometric breakthrough in classical-quantum correspondence similar to the Amplituhedron). IIUC Church-Turing and Church-Turing-Deutsch say that Turing complete is enough for classical computing, and that a qubit computer can simulate the same quantum logic circuits as any qudit or qutrit computer; but is it ever shown that Quantum Logic is indeed the correct and sufficient logic for propositional calculus and also for all physical systems? From "Quantum logic gate > Universal quantum gates":
https://en.wikipedia.org/wiki/Quantum_logic_gate#Universal_q... : > Some universal quantum gate sets include: > - The rotation operators Rx(θ), Ry(θ), Rz(θ), the phase shift gate P(φ)[c] and CNOT are commonly used to form a universal quantum gate set. > - The Clifford set {CNOT, H, S} + T gate. The Clifford set alone is not a universal quantum gate set, as it can be efficiently simulated classically according to the Gottesman–Knill theorem. > - The Toffoli gate + Hadamard gate.[17] The Toffoli gate alone forms a set of universal gates for reversible boolean algebraic logic circuits which encompasses all classical computation. [...] > - The parametrized three-qubit Deutsch gate D(θ) > A universal logic gate for reversible classical computing, the Toffoli gate, is reducible to the Deutsch gate, D(π/2), thus showing that all reversible classical logic operations can be performed on a universal quantum computer. CCNOT: https://en.wikipedia.org/wiki/Toffoli_gate https://en.wikipedia.org/wiki/Quantum_logic_gate#Toffoli_(CC... CNOT: https://en.wikipedia.org/wiki/Controlled_NOT_gate H: https://en.wikipedia.org/wiki/Quantum_logic_gate#Hadamard_ga... S: https://en.wikipedia.org/wiki/Quantum_logic_gate#Phase_shift... T: https://en.wikipedia.org/wiki/Quantum_logic_gate#Phase_shift... Implicit to a quantum approximator would be at least Quantum statistical mechanics and maybe also Quantum logic: Quantum statistical mechanics: https://en.wikipedia.org/wiki/Quantum_statistical_mechanics Quantum logic: https://en.wikipedia.org/wiki/Quantum_logic |