Spin and Quantum Computers
I recently attended one of the Massey Lectures given in Montreal by the Director of the Perimeter Institute (PI), Professor Neil Turok, “The Universe Within: From Quantum to Cosmos”. He succeeded in explaining physics to the public for a radio broadcast without the use of visuals. His talk was particularly interesting to me because of two of the points he raised. One was the importance of the imaginary number i,
Quantum phases, exp(iφ) , are always there from spin states to Feynman path integrals, to anything with waves. In my study of spin ½ a small but significant change to its definition was made. Rather than the three Pauli spin operators (σX,σY,σZ), I added an i: (σX,iσY,σZ). Although non-Hermitian states seemed strange, why not? But as I played with them, things started to work out all right. Besides, such forms often crop up. There are the raising and lowering operators, a± = aX ± iaY , e.g. angular momentum, J± = JX ± iJY , Euler’s formulae,
exp(iφ) = cosφ ± isinφ
Then there are trajectories and many others places the imaginary number arises in physics. In my case that small change to the spin operator makes a huge difference to the description of spin, if it happens to be right. First it gives structure to spin rather than the current point-particle view with a single axis of quantization. Introducing that i gives spin two axes of quantization not one: one along a Z axis and the other along the X. The term, iσY, is a phase and orients the two axes in 3D space. In the end this makes spin real and unveils new properties: ones that cannot be measured because they are hidden in inaccessible states.
Another point Professor Toruk raised was that quantum computing will usher in a new revolution in progress. Everyone would be able to put every book ever written on their computer. It would be a move from the digital world back to continuous states by controlling the superpositions of waves. (by use of phases like above). Rather than having states that give yes:no; or 1:0; or up, down; or +1, -1; quantum bits, or qubits, will take over,
In a recent blog I talked about the Bloch sphere shown in the figure. Any two antipodal points can be states like, |±>Z; but other states,|±>θ,φ , cover the surface of the sphere and there are an infinite number of them. By varying these angles the amount of information that can be carried jumps from the two digital classical bits of yes:no, to the infinite superposition of yes:no offered by qubits.
In part, I share this view and believe quantum computers will one day replace the classical ones we have today. However quantum computing, and the field of quantum information in general, depends upon quantum entanglement and non-locality. Entanglement may turn out not be a property of Nature but rather of quantum mechanics. Non-locality is a concept that no-one understands. It is largely upon these shaky notions that quantum information theory rests.
One day I am sure that physics will view Nature as real rather than statistical. Throughout history initial ideas of non-local effects, also called “spooky action-at-a-distance”, have been repudiated and replaced with something more physically reasonable. The most well-known examples are the early attempts to understand gravity and electromagnetism. So it will be with non-locality between entangled particles.
A new way of looking at spin could lead to some new revelations. Elementary particles all have spin ½ or 1, (except the Higgs Boson). Spin influences much of science all the way from elementary particles to Magnetic Resonance Imagining. Spin plays important roles in the ways we communicate. Spin is presently treated as a point particle but if it has structure, our present understanding of the interactions must change. If correct, the challenge of the future will be how to understand properties of Nature that cannot be measured and are hidden from us. Ways will have to be found to manipulate these properties that are due to local hidden variables.