Quantum States and Probabilities

To understand how quantum gates precisely calibrate the quantum states of qubits in programs, we need a systematic way to represent blended states. To model such states in code, let’s start with a qubit containing seven pentagon images/_pragprog/svg-17.png qubelets and three inverted triangle images/_pragprog/svg-18.png qubelets, shown here:

images/quantum_states_algebra/Qubelets_7_Pentagons_3_Triangles.png

Looking at this qubit, we can deduce the following:

  • When measured, the pentagon images/_pragprog/svg-17.png qubelets have a greater chance of being selected than the triangle images/_pragprog/svg-18.png qubelets; in other words, the qubit is skewed toward collapsing to the images/_pragprog/svg-17.png idealized state than the images/_pragprog/svg-18.png idealized state.

  • Qubelets can be inverted, such as the triangle ones in the figure.

We express these observations for the quantum state of the qubit with the following equation:

The magnitudes of the coefficients and

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