I am working on coming up with practice problems for a QC course. I have a problem that considers two qubits as so:

$$|\psi_a\rangle = \alpha_a |0\rangle + \beta_a |1\rangle$$

$$|\psi_b\rangle = \alpha_b |0\rangle + \beta_b |1\rangle$$

But I found the alphas and betas combined with a's and b's very confusing. I was just wondering if there was a standard notation for this type of thing or any notation others have found easier to understand.

  • $\begingroup$ The metacharacters \langle and \rangle give you the left and right angle brackets. $\endgroup$
    – jecado
    Aug 20 '21 at 0:05
  • $\begingroup$ $|\psi_a\rangle=a_0|0\rangle + a_1|1\rangle$ and $|\psi_b\rangle=b_0|0\rangle + b_1|1\rangle$? $\endgroup$
    – Mauricio
    Aug 20 '21 at 13:13

I am not sure if this helps in any way but you could consider the state of an arbitrary qubit $i$ as:

$$ |\psi_i \rangle = \alpha_i |0\rangle + \beta_i |1\rangle $$

So if $|\psi_1 \rangle$ and $|\psi_2 \rangle$ correspond to the state of qubit $q_1$ and $q_2$ then we have $$ |\psi_1 \rangle = \alpha_1 |0\rangle + \beta_1 |1\rangle $$ $$ |\psi_2 \rangle = \alpha_2 |0\rangle + \beta_2 |1\rangle $$

This avoids mixing $\alpha$, $\beta$ with $a$ and $b$. Again, these are just dummy variables so you can change them to whatever you want.

  • 1
    $\begingroup$ Yep, this is what I would do. Sometimes I go even further and use just a single symbol $c$ for all coefficients, with an extra subscript giving the basis state. For example: $|\psi_1\rangle=c_{01}|0\rangle+c_{11}|1\rangle$. But this has a high risk of getting confused with multi-qubit basis states, so the answer above is probably best for a course. $\endgroup$
    – jecado
    Aug 20 '21 at 0:03

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