Why is it difficult to understand quantum computing?

 

It's not difficult if you know a little bit of math, physics and electronics and can solve the Schrödinger equation that describes quantum systems, at least for a few simple systems, to understand the foundation, strength and limits of these systems. The Schrödinger equation in quantum systems is similar to Maxwell's equations for electrical systems or, more applied, similar to Ohm's and Kirchhoff's laws for digital systems, without which the essence of digital computers cannot be understood. The apparent difficulty of quantum computing comes from excessive marketing, and by excessive and unrealistic (unphysical) mathematical extrapolation of quantum systems, without building a real device to confirm or disprove those extrapolations. Without experimental confirmation, any description, even if is mathematical or algorithmic, is not scientific and implicitly is not technologically feasible. There are currently many mathematical and algorithmic extrapolations assumed to be related to quantum computing, but which in the absence of experimental confirmation represent only extrapolations/utopias or even technological noise, noise that contributes to the apparent difficulty to understand quantum computing for a beginner.

Essentially, after someone plays a little bit with basic quantum systems and solves the Schrödinger equation related to them and experiments a little bit with real physical systems confirming the theoretical solutions, he finds out that systems that have at least two quantum states can be used as units of quantum information, i.e. qubits (quantum bits): which can be: an electron's spin pointing up for 1 noted ∣1⟩ or down for 0 noted ∣0⟩ or vice versa, a photon's polarization, a microscopic magnetic state, etc. The quantum system thus identified with the two states ∣0⟩ and ∣1⟩ can be described in general through a state vector ∣ ⟩ which represents the quantum superposition of the two states, mathematically described through ∣ ⟩ = α∣0⟩ + β∣1⟩ which represents an informational "and" of the two states.

Quantum information processing means any transformation performed on quantum information unit (qubit) ∣ ⟩, through various quantum transformations (quantum gates) such as: as spin rotations, photon polarization changes, energy level transitions, phase shifts, etc. These transformations essentially modify at the single bit level the values ​​of α and β which establish the probabilistic weight of the basic states ∣0⟩ and ∣1⟩ between which there is the normative constraint ∣𝛼∣² + ∣𝛽∣² = 1.

To extract information from a quantum system, in this case from a processed qubit, we must apply a macroscopic measuring device that operates according to digital logic which describes digital (classical) bits b in which the states 0 and 1 are not superposed but can be exclusively either 0 or 1.

The measurement process (i.e. extracting information from a quantum system and using it at the macroscopic level, representing the transformation of ∣ ⟩ into b) involves probabilistic collapsing of the quantum system ∣ ⟩ into one of its basic states ∣0⟩ or ∣1⟩ (which now become real digital/macroscopic bits 0 or 1 ) with the respective probabilities ∣𝛼∣² or ∣𝛽∣² due to the macroscopic interaction with the quantum system and represents the greatest limitation/challenge of quantum computers.