Quantum Mechanics promises an exponential speed-up of computing. Shor Algorithm famously demonstrates the promise of quantum weirdness. Ironically, the Shor Algorithm also displays the fundamental inconsistencies of Quantum Mechanics. The magical ‘Phase Kickback’ transfers the unobservable complex eigenvalue of a Modular Exponentiation (ME) operator to qubits of a control registry. An Inverse Fourier Transform and a following measurement collapse the wavefunction of the ME work register, and the control register produces the phase of the non-observable complex ME eigenvalue.
The exponential speed-up of phase estimation is implied by the number of computational basis states. For n-qubits, the number of computational bases grows as 2n. Quantum Mechanics implies that ME acts on all 2n states at once. As n increases, 2n exceeds the number of particles in the universe. No wonder more universes are needed for an explanation. How n-qubits with n-states turn into 2n states remains a mythical miracle. Unless one has a reasonable explanation of how 2n states emerge from n-qubits, the claimed quantum exponential speed-up has no physical foundation.
If ME operator has a measurable phase, why cannot we measure or calculate it directly? Why bother with a control registry and Inverse Fourier Transform? Obviously, to measure the ME eigenvalues one needs to prove that it is an observable. Without a Physical Ontology that may provide a justification, Quantum Mechanics denies any physical meaning to the ME eigenvalues and their phases. There is no known method of eliminating the superfluous registry and its operations.
On the contrary, Corpuscular Quantum Mechanics describes how to calculate the eigenstates of the ME operator acting on n-qubits. The 2n computational states and their entanglement do not arise anywhere. “Phase Kickback” and “Acting on all 2n states” are misleading metaphors arising from the inconsistent postulates and mathematical recipe of Quantum Mechanics.