Quantum computing is incompatible with Born Rule and the related measurement postulates, the qubit reading capability is falsified experimentally, and the Feynman-Deutsch quantum computing theory is low-strict, low-testable and infeasible.
Authors: Liu Bowen 
Published: April 2022

(1) Deutsch stated: it is shown that quantum theory and the ‘universal quantum computer’ are compatible with the principle, that is, it is shown the compatibility of quantum computing with quantum mechanics. Born Rule and Time Evolution Postulate are the important ingredients of quantum theory. Deutsch et al. did not provide a proof of the compatibility of quantum computing with Born Rule (and Time Evolution Postulate), avoided the extraction of unitary transformation results in their papers, and defaulted that the output probability density can map to the observation-space CSC and to be read. We attribute the proof of the incompatibility of quantum computing with quantum mechanics to the proof of the incompatibility of quantum computing with Born Rule. The basic form of Born Rule is that \({\left| \psi \right|^2}\) represents the probability density for particles; if the system is in a state \(\left| \psi \right\rangle\), then the probability that the eigenvalue λi of Q is found when Q is measured is P(λi) =\({\left| {\left\langle {{\lambda _n}} \right|\left. \psi \right\rangle } \right|^2}\). We show that in the technical scheme of quantum computing, there is an imposed strong constraint on Born Rule, that is, double \({\left| \psi \right|^2}\) hypothesis (i.e., Feynman-Deutsch’s \({\left| \psi \right|^2}\)(double) reading hypothesis), which requires that there is such a mapping from the state-space CSM to the observation-space CSC: \({\left| {{\psi _M}} \right|^2}\)→\({\left| {{\psi _C}} \right|^2}\), where \({\left| {{\psi _M}} \right|^2}\)is the probability density of the wavefunction \({\text{a}}\left| 0 \right\rangle +b\left| 1 \right\rangle\) of the single-qubit, \({\left| {{\psi _C}} \right|^2}\) is the probability density of the corresponding outcomes within CSC, and \({\left| {{\psi _C}} \right|^2}\) is equivalent to \({\left| {{\psi _M}} \right|^2}\). The original Born Rule does not assert the mapping \({\left| {{\psi _M}} \right|^2}\)→\({\left| {{\psi _C}} \right|^2}\). We demonstrate that in the technical scheme of quantum computing it is assumed that the single-qubit carrier-symbol snapshot traceability is the basis for the realization of the double \({\left| \psi \right|^2}\). We, using the Stern-Gerlach experiment and the chip engineer's contraction mapping experiment, experimentally falsify the single-qubit carrier-symbol snapshot traceability, and thus experimentally falsify the Feynman-Deutsch’s \({\left| \psi \right|^2}\)(double) reading hypothesis. In this way, we show that quantum computing is incompatible with Born Rule and the related measurement postulates, and the Feynman-Deutsch quantum computing theory is not feasible. The principal error of the Feynman-Deutsch theory is the mapping \({\left| {{\psi _M}} \right|^2}\)→\({\left| {{\psi _C}} \right|^2}\); the root of all errors in quantum computing is the double probability density hidden in the technical scheme, which is the false Born Rule. (2) The Feynman-Deutsch theory is a low-strict, low-testable and non-transparent theory for the following reasons: postulate-level assumptions are hidden in the technical scheme; the testability (falsifiability) of various parts of quantum computing has never been publicized. It has long been believed that quantum computing centers on unitary transformation sequence. We show that qubit reading is the only falsifiable part of quantum computing. Because falsifiable issue takes precedence over unfalsifiable issue, and principle-level issue takes precedence over non-principle-level issue, the priority of quantum computing research is the inapplicability of Born Rule to quantum computing rather than the applicability of unitary transformation. i.e., the real heart of quantum computing is the existence of \({\left| \psi \right|^2}\) mapping from CSM to CSC. We prove the fact that although algorithm and the algorithm’s output within CSM are carried out in the name of quantum technology, the "double \({\left| \psi \right|^2}\)" is actually independent of Born Rule, and independent of quantum mechanics. The methodological error of the Feynman-Deutsch theory is to exclude the inapplicability of Born Rule from the research field. (3) We re-examined the effectiveness of three published quantum computing (Shor factoring) experiments, and show that they are invalid in the sense of falsifiability criterion and the traversal criterion. The high risk of the infeasibility of quantum computing is completely underestimated. (4) In the last sections, we examine a topic with a higher degree of generality: the traceability (direction non-constraint) of single-particle information process. Using the “reproducible effect” method suggested by Popper, we show that the realization of quantum computing violates human's existing knowledge about the contraction mapping experiments of two spaces. The proofs in this paper show that the compression mapping experiment in meso-micro scale and the physical version of Gödel's incompleteness theorem are more profound principles of quantum physics (including Born Rule and the related measurement postulates).