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20 May 2010 Rotations on the Bloch Sphere In order to relate unitary operations on a qubit state |?? to rotations By the definition of the outer product ? =.
22 Dec 2007 For example, if we perform the above construction in R3, we obtain real . rotation of the Bloch sphere that permutes the coordinate axes (both
26 Sep 2016 Your 2×2 unitary is mostly determined by its action on the state vector ( 1 0 ) . This is because 1) in a 2-d Hilbert space, for any given vector there is a single other
Qubit: The standard quantum mechanical notation for a vector in a vector space is . ? is a Example: a spanning set for the vector space is Rotation operators.
a closed quantum system does not interact with any other system. QSIT07.2 Page 1 example: on the Bloch sphere: this is a rotation around the equator with
Example composite rotation. 7. References. 9. I. WHAT IS A QUBIT? Let us begin by introducing some notation: 1 state (called “minus” on the Bloch sphere).
1 Mar 2013 then two rotation steps are sufficient for implementing a single-qubit gate, and one rotations in three or fewer steps, for example, by using.Introduction to quantum computing: Bloch sphere. will discuss about a very intuitive representation of a single qubit: the Bloch sphere. .. Let’s see some examples. . are exactly the matrices that rotate/invert representations on the sphere.
z. Rotation about the n axis. ) (. 2 sin. 2 cos. )2/?? exp(. )( ?. ZnYnXn. iI ni. R z y x n. +. +. ?. = ?. ?. ? ? ? ? ? ?. ?. ?. ?. ?. ?. ?. ?. ?. ?. ?. = z y x n n n n?. Example.

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