Our response is YES. Quantum computing has arrived, as an expression of that.
Numbers do obey a physical law. Massachusetts Institute of Technology Peter Shor was the first to say it, in 1994 [cf. 1], in modern times. It is a wormhole, connecting physics with mathematics, and has existed even before the Earth existed.
So-called "pure" mathematics is, after all, governed by objective laws. The Max Planck Institute of Quantum Optics (MPQ) showed the mathematical basis by recognizing the differentiation of discontinuous functions [1, 2, 3], in 1982.
This denies any type of square-root of a negative number [4] -- a.k.a. an imaginary number -- rational or continuous.
Complex numbers, of any type, are not objective and are not part of a quantum description, as said first by Erwin Schrödinger (1926) --
yet,
cryogenic behemoth quantum machines (see figure) consider a "complex qubit" -- two objective impossibilities. They are just poor physics and expensive analog experiments in these pioneering times.
Quantum computing is ... natural. Atoms do it all the time, and the human brain (based on +4 quantum properties of numbers).
Each point, in a quantum reality, is a point ... not continuous. So, reality is grainy, everywhere. Ontically.
To imagine a continuous point is to imagine a "mathematical paint" without atoms. Take a good microscope ... atoms appear!
The atoms, an objective reality, imply a graininess. This quantum description includes at least, necessarily (Einstein, 1917), three logical states -- with stimulated emission, absorption, and emission. Further states are possible, as in measured superradiance.
Mathematical complex numbers or mathematical real-numbers do not describe objective reality. They are continuous, without atoms. Poor math and poor physics.
It is easy to see that multiplication or division "infests" the real part with the imaginary part, and in calculating modulus -- e.g., in the polar representation as well as in the (x,y) rectangular representation. The Euler identity is a fiction, as it trigonometrically mixes types ... avoid it. The FFT will no longer have to use it, and FT=FFT.
The complex number system "infests" the real part with the imaginary part, even for Gaussian numbers, and this is well-known in third-degree polynomials.
Complex numbers, of any type, must be deprecated, they do not represent an objective sense. They should not "infest" quantum computing.
Quantum computing is better without complex numbers. software makes R,C=Q --> B={0,1}.
What is your qualified opinion?
REFERENCES
[1] DOI /2227-7390/11/1/68
[2] https://lnkd.in/gdbMitAJ
[3] June 1982, Physical review A, Atomic, molecular, and optical physics 26:1(1).
[4] https://lnkd.in/gsgfN_hB
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