Essential Mathematics for Quantum Computing

Chapter 6: Complex Numbers

"What is unpleasant here, and indeed directly to be objected to, is the use of complex numbers. Ψ is surely fundamentally a real function."

– Letter from Schrödinger to Lorentz. June 6, 1926.

Even the great physicist Erwin Schrödinger was perplexed by the occurrence of complex numbers in quantum mechanics. Yet, complex numbers have been found to be inherent to quantum mechanics and, hence, quantum computing. Up until now, we have concentrated on the real numbers to make concepts easier to get across. It is time now to cross the Rubicon and make our way into the complex plane. You have probably come across complex numbers before, but we will go into great depths about them in this chapter. I think it is unfortunate ...