Quantum Computing: Is there a number system?
Hi, Is there a way to simple way to explain the number system in quantum computing? Also is the number system of quantum computing what makes this type of computing so much more powerful than traditional computing.? I didn’t find the right solution from the internet. References: https://www.physicsforums.com/threads/quantum-computing.843946/
The link in your question in broken. By number system, if you mean Hilbert space, it is complex indeed!
A 1 qubit QC can be visualized nicely with the Bloch Sphere. The quantum gates applied on the Bloch sphere can be though of as vector rotations. Even dephasing and decoherance can be visualized. However, there is no equivalent visualization for multiple qubits.
It’s not that the QC are based on a specific number system and that’s why it is powerful. It’s because QC is based on Quantum Mechanics, and explaining QM requires these kind of mathematical constructs. Simply think of 1 qubit as a Hydrogen atom (from high school chemistry) with an electron either in the ground state (0) or the first excited state (1). The power of QC is derived from 2 main QM phenomena, superposition and entanglement. Superposition means, a particle can be both 0 and 1 at the same time. But measurement is projective, meaning, whenever we try to probe it, we will only see it in either 0 or 1 state (technically called the Eigenstates of the Hamiltonian). Since it is based on such physical processes that indeed behave counter intuitively, it is difficult to reason it out. But, it’s not the number system that gives it the power, it’s the weirdness of Nature at quantum scales.