An Introduction to Mesoscopic and Nanometer Scale Physics (PDF)
An Introduction to Mesoscopic and Nanometer Scale Physics (PDF)
An Introduction to Mesoscopic and Nanometer Scale Physics (PDF)
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Single qubit quantum operations<br />
The time evolution operation can be represented as a matrix that<br />
operates on a general qubit superposition state α|0> + β|1><br />
where θ=ωt<br />
⎛<br />
P(θ) = 1 0 ⎞<br />
⎜<br />
⎝ 0 e iθ ⎟<br />
⎠<br />
⎛<br />
ψ = α ⎞<br />
⎜ ⎟<br />
⎝ β⎠<br />
Other opera<strong>to</strong>rs:<br />
Identity opera<strong>to</strong>r I takes |0> -> |0>, |1> -> |1><br />
Opera<strong>to</strong>r X switches the two states |0> -> |1>, |1> -> |0><br />
⎛<br />
X = 0 1 ⎞<br />
⎜<br />
⎝ 1 0⎠<br />
The X opera<strong>to</strong>r can be recognized as the analog of the<br />
classical NOT opera<strong>to</strong>r<br />
⎛<br />
I = 1 0 ⎞<br />
⎜ ⎟<br />
⎝ 0 1⎠
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