Quantum computing for multi-qubit systems using Schwinger’s paired bosons representation of angular momentum

Abstract

The fundamental difference between calculations performed using quantum and classical computers is that, unlike a bit, a quantum bit (qubit) is a linear combination of quantum states |1/2, 1/2 > and |1/2, −1/2 > of effective spin S = 1/2. The states of an N-qubit system can be characterized by spin wave functions |S, MS > (𝑀𝑆 = 𝑆, S - 1, S - 2, …, 2 - S, 1 - S, - S) of effective spin S = 2𝑁−1 – 1/2 [1]. These 2S + 1 spin wave functions, given traditionally in the spinor representation, can also be written using the paired bosons representation proposed by J. Schwinger