Quantum Computing 9/23/21

Science with Richard Bleil

While looking at the spectrum of light emitted from gases (such as the light released from neon lights), scientists noticed something else that is impossible.  Not only was the gas emitting light from having energy passed through it (a phenomenon called “blackbody radiation”, meaning the light is coming from the gas rather than just reflecting light from another source), the light was “quantized” as well.  That means that the energy in the light was not continuous from some maximum value to a minimum, but rather, there were specific energies of light emitted, and no energy between them. 

Nothing in the physics they knew could explain this (“classical” physics, sometimes known as “Newtonian” physics).  Further studies revealed something else that was impossible.  Electrons behaved both like a particle and a wave, rather than one or the other.  This gave Schroedinger an idea.  Instead of using classical particle physics, what would happen if, instead, he tried to explain electron motion as waves?

Sometimes you’ll hear quantum mechanics referred to as “wave mechanics”.  Going to hydrodynamicists, he took their equations of wave behavior and applied it to electrons.  Doing so, his equation gave rise to results that were bizarre in their own rights, and seemingly impossible, and yet wildly accurate when the results were tested experimentally. 

Mathematically, waves can be modeled by trigonometric functions like sine (or, more correctly, sine squared).  The solutions to this function are multiples of pi.  That is sine (squared) is zero at zero, pi, two times pi, three times pi and so forth.  This modeled the quantized energy levels, where you only get valid solutions at 0, 1, 2, and so forth.  Half pi, then, is not a solution since it is not equal to zero, and the energy corresponding to half pi is not seen in the spectrum. 

Honestly, the solutions to Schroedinger’s equation is more complicated than this (but not that much more complicated) and taken to its conclusion gives rise to another fascinating concept called “spin”.  Spin is wildly misrepresented in chemistry and physics classes today as they try to give a physical explanation based on the “direction of rotation” of electrons.  This is nonsense, and Heisenberg’s equation tells us as such.  First of all, electrons are not spheres.  They’re as much waves as they are particles, so to say they’re spheres rotating clockwise or counterclockwise is just wrong.  In fact, spin is a solution of Schroedinger’s equation and, frankly, we really don’t know what it is.  The final solution had a term of the square root of one quarter, and taking a square roots always has both a positive and a negative answer.  Thus, electrons are either positive one half (called “spin up”) or negative one half (called “spin down”).  These are not charges; the electron always has a negative charge.  Instead, it’s just a mathematical solution of some property of the electron that we just don’t understand, and yet, like everything else wave mechanics predicts, “spin” has been verified. 

Computers, in the meantime, are binary devices.  That is to say that the “language” used by computers is written in “bits”, and bits are either one or zero.  This gives the connection to quantum theory.  If we call spin up (plus one half) the binary bit one, and spin down (minus one half) the binary bit zero, then electrons can indeed be used to write (and manipulate) a binary code. 

Of course, just because an idea is simple in principle, that doesn’t make it simple in practice.  In principle, to be married all I have to do is find a partner, but in practice, well, I think you get it.  There are some hurdles to overcome to use spin in a quantum computer means that along with the simple concept of assigning spin states as ones and zeros, we also have to find ways to read electrons spins, and to manipulate them.  Fortunately, engineer and quantum mechanists have been working on this idea and making significant progress. 

To make the electron “gates” for computer chips, the silicon wafer is maybe 275 micrometers, or 275,000 nanometers.  A silicon atom has an approximate diameter of 0.2 nanometers, so the wafer is a million or so silicon atoms thick.  It takes time, energy and space to do this.  Imagine a computer that uses chips just one atom thick.  Far less energy, far smaller chips and incredibly faster chips can be developed.  This potential is enormous, and the very reason that quantum computing is such an exciting topic today. 

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