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Basics of quantum computing: change of basis

Computing requires classical bits, which can hold a value of 0 or 1. Quantum computing gets benefit from superposition of quantum bit (qubit). Qubit is a representation of state of quantum object (electron, proton, photon, etc). The qubit holds a value between 0 and 1 while it is in superposition state. Superposition means the qubit possesses multiple values at the same time so we can harness its power for parallel computing. Once we try to measure the value it can be collapsed into either 0 or 1 based on probability. (Observer collapses wave function simply by observing.) Using bloch sphere, we can represent qubit physically. (The bloch sphere is a physical model to represent a spin state of qubit) A state vector can point to any direction from the center of the sphere. If a vector points to Z+ and Z-, it represents 0 and 1 state respectively. All other vectors represent superposition state in a Z basis. Now, if a vector points to X+, X-, Y+, Y-, all are at a 90-degree angle from
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