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--- en:mathematics_at_the_rescue [2021/01/10 19:16]
jaddawyn [Superposition]
+++ en:mathematics_at_the_rescue [2021/01/16 10:29] (current)
@@ Line 43: / Line 43: @@
 Computed amplitudes are correct.
-==== Superposition ====
+===== Superposition =====
 Like Schrödinger's cat, quantum particles are in superposition between the generator and the detector. That is to say dead **and** alive.\\
-The same for particles: when superposed it is both |0> and |1>.\\
+The same for qubits: when superposed it is both |0> and |1>.\\
 This state is described with the following equation:\\
 ;#;
@@ Line 52: / Line 52: @@
 ;#;
 With:
-  * <m>delim{|}{psi}{}></m> the particle state,
+  * <m>delim{|}{psi}{}></m> the qubit state,
   * <m>alpha</m> the amplitude of <m>delim{|}{0}{}></m>,
   * <m>beta</m> the amplitude of <m>delim{|}{1}{}></m>.
 \\
 \\
-Between the generator and the detector the particle is in a quantum state balanced by probabilities between |0> and |1>. When particle hits the detector we read the result and get |0> or |1>.\\
+Between the generator and the detector the qubit is in a quantum state balanced by probabilities between |0> and |1>. When qubit hits the detector we read the result and get |0> or |1>.\\
 \\
 \\
-If the generator is calibrated to launch particles with perfect balanced probabilities to get |0> and |1>, here is the state of particle between the source and the detector:\\
+If the generator is calibrated to launch particles with perfect balanced probabilities to get result |0> and |1>, here is the state of qubit between the source and the detector:\\
 ;#;
 <m 15>delim{|}{psi}{}> = 1/sqrt{2} delim{|}{0}{}> + 1/sqrt{2} delim{|}{1}{}></m>
@@ Line 68: / Line 68: @@
 Which is, for the poor cat:\\
 ;#;
-<m 15>delim{|}{psi}{}> = 1/sqrt{2}</m> |{{:en:catalive.jpg?30|}}> <m 15>+ 1/sqrt{2}</m> |{{:en:catdead.jpg?50|}}>
+<m 15>delim{|}{psi}{}> = 1/sqrt{2}</m> |{{:en:catalive.png?30|}}> <m 15>+ 1/sqrt{2}</m> |{{:en:catdead.png?50|}}>
 ;#;
-XXX Schrödinger's cat equation XXX
+===== Quantum matrices =====
-XXX Conseiller Octave XXX
+I'll push a bit further with mathematics because there is another important way to describe quantum states: using matrices.\\
+\\
+The quantum state <m>delim{|}{psi}{}> = alpha delim{|}{0}{}> + beta delim{|}{1}{}></m> can also be defined with the following matrix:
+;#;
+<m 15>delim{[}{matrix{2}{1}{alpha beta}}{]}</m>
+;#;
+The top entry is the amplitude for |0> and the bottom entry the amplitude for |1>.
+\\
+\\
+If you are not comfortable with matrices I invite you to review how it works and specifically how to multiply it. I won't do that here and you'll find plenty of courses about that on the web. For instance:\\
+;#;
+[[https://www.wikihow.com/Understand-the-Basics-of-Matrices]]
+;#;
+\\
+\\
+The matrix representing a qubit perfectly balanced between |0> and |1> is:\\
+;#;
+<m 15>delim{[}{matrix{2}{1}{1/sqrt{2} 1/sqrt{2}}}{]}</m>
+;#;
+===== A little detail concerning amplitudes ... =====
+There is a little joke concerning amplitudes: they are complex numbers...No don't leave!!!\\
+It is not a big deal because the most of the time we are using them as normal numbers. \\
+\\
+I wanted to indicate this detail because it shows how crazy quantum world is.
+\\
+\\
+<columns 100% 50% ->
+Previous: [[en:this_little_thing_called_qubit|This little thing called qubit]]
+<newcolumn>
+;;#
+Next: [[en:quantum_registers|Quantum registers]]
+;;#
+</columns>

Quantum leap

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