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?
> - 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.
westurner|2 years ago
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