What is the j in the single qubit state equation in the Quantum Phase section? https://quantum-computing.ibm.com/composer/docs/iqx/guide/introducing-qubit-phase it's not defined in the page itself (that I can see)

$$ |\psi\rangle=\sqrt{(1-p)}|0\rangle + e^{j\phi}\sqrt{p}|1\rangle$$

I can see something similar referred to as i in https://en.wikipedia.org/wiki/Qubit#Bloch_sphere_representation and this other stackexchange seems to imply that they are interchangeable

When defining the state vector of a qubit in qiskit, what difference does putting "j" make?

Is "j" in this equation just the imaginary number i?


1 Answer 1


Yes, $j$ is just the imaginary number $i$.
The use of $j$ comes from the world of electrical engineers who use it instead of $i$ so there is not confusion with notation for current which is already noted $i$.


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