I have $n$ states in superposition $|A\rangle=\dfrac{1}{2^{l/2}}\sum_{i=0}^{2^l-1}\sum_{j=0}^{2^l-1}|0\rangle^{\otimes q}|i\rangle^{\otimes l}|j\rangle^{\otimes l}$. Now I have to apply the transform in batches of $4$ i.e for example Let $l=2$, then $$A= \dfrac{1}{2^{2/2}}\left( |0\rangle^{\otimes q}|00\rangle|00\rangle+ |0\rangle^{\otimes q}|00\rangle|01\rangle+|0\rangle^{\otimes q}|00\rangle|10\rangle+|0\rangle^{\otimes q}|00\rangle|11\rangle+|0\rangle^{\otimes q}|01\rangle|00\rangle+|0\rangle^{\otimes q}|01\rangle|01\rangle+|0\rangle^{\otimes q}|01\rangle|10\rangle+|0\rangle^{\otimes q}|01\rangle|11\rangle+|0\rangle^{\otimes q}|10\rangle|00\rangle+|0\rangle^{\otimes q}|10\rangle|01\rangle+|0\rangle^{\otimes q}|10\rangle|10\rangle+|0\rangle^{\otimes q}|10\rangle|11\rangle+|0\rangle^{\otimes q}|11\rangle|00\rangle+|0\rangle^{\otimes q}|11\rangle|01\rangle+|0\rangle^{\otimes q}|11\rangle|10\rangle+|0\rangle^{\otimes q}|11\rangle|11\rangle\right)$$Now as there are $16$ states in superposition here, I need to apply a unitary transform to $4$ states at at a time i.e the first $4$, then the second $4$ , then the third $4$ , then the last $4$. The transform that I apply every time on the four states is on the first register $0\rangle^{\otimes q}$ of each state. The unitary transform between these states is $P$. How would the tensorial notation of this state look like is my question? How do I give the right notation that the operator acts on $4$ states and then the next four is my doubt.

  • $\begingroup$ can somebody suggest ? $\endgroup$
    – Upstart
    Jun 1, 2019 at 15:51
  • $\begingroup$ The normalisation factor is off. It is a superposition of 16 states and each is 1/2. $\endgroup$ Jun 2, 2019 at 9:53
  • $\begingroup$ Terms of a superposition cannot be separated like that. Generally we talk about applying transforms on a set of qubits. What is the context? $\endgroup$ Jun 2, 2019 at 9:54

1 Answer 1


You'd need to apply $P$ controlled on the second register. I assume you want a different operation for each of the 4 sets? In terms of a tensor product you'd need operators like

$$P_1\otimes |00\rangle\langle00|\otimes I$$ $$P_2\otimes |01\rangle\langle01|\otimes I$$ $$P_3\otimes |10\rangle\langle10|\otimes I$$ $$P_4\otimes |11\rangle\langle11|\otimes I$$


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.