SWAP test inputs












2












$begingroup$


I'm using the SWAP test circuit for implementing a qubit registers comparison
enter image description here



From the documentation I could find I've understood it can be applied to input qubits |$alpharangle$ and |$betarangle$ of the same size.



Is that really a constraint? Or it can be also applied to general cases of qubits of different size?






quantum-gate circuit-construction







share|improve this question











$endgroup$












  • $begingroup$
    I think your question is similar to mine, and I found the answer over here Inner product of quantum states.
    $endgroup$
    – Aman
    13 hours ago


















2












$begingroup$


I'm using the SWAP test circuit for implementing a qubit registers comparison
enter image description here



From the documentation I could find I've understood it can be applied to input qubits |$alpharangle$ and |$betarangle$ of the same size.



Is that really a constraint? Or it can be also applied to general cases of qubits of different size?






quantum-gate circuit-construction







share|improve this question











$endgroup$












  • $begingroup$
    I think your question is similar to mine, and I found the answer over here Inner product of quantum states.
    $endgroup$
    – Aman
    13 hours ago
















2












2








2





$begingroup$


I'm using the SWAP test circuit for implementing a qubit registers comparison
enter image description here



From the documentation I could find I've understood it can be applied to input qubits |$alpharangle$ and |$betarangle$ of the same size.



Is that really a constraint? Or it can be also applied to general cases of qubits of different size?






quantum-gate circuit-construction







share|improve this question











$endgroup$




I'm using the SWAP test circuit for implementing a qubit registers comparison
enter image description here



From the documentation I could find I've understood it can be applied to input qubits |$alpharangle$ and |$betarangle$ of the same size.



Is that really a constraint? Or it can be also applied to general cases of qubits of different size?






quantum-gate circuit-construction




quantum-gate circuit-construction






share|improve this question















share|improve this question













share|improve this question




share|improve this question








edited 13 hours ago









Blue♦

6,12831354




6,12831354










asked 13 hours ago









Gianni CasonatoGianni Casonato

455




455












  • $begingroup$
    I think your question is similar to mine, and I found the answer over here Inner product of quantum states.
    $endgroup$
    – Aman
    13 hours ago




















  • $begingroup$
    I think your question is similar to mine, and I found the answer over here Inner product of quantum states.
    $endgroup$
    – Aman
    13 hours ago


















$begingroup$
I think your question is similar to mine, and I found the answer over here Inner product of quantum states.
$endgroup$
– Aman
13 hours ago






$begingroup$
I think your question is similar to mine, and I found the answer over here Inner product of quantum states.
$endgroup$
– Aman
13 hours ago












2 Answers
2






active

oldest

votes


















1












$begingroup$

Qubits can be only with a size of 2, which means a dimensionality of 2.



For $|alpha rangle,|betarangle$ here, for the SWAP gate to make sense, they must be of the same dimensionality (in the operating Hilbert space), then only there is a meaningful correspondence for the SWAP to work.



In case if it happens that they are not (suppose one qubit and other qtrit), then the extra degrees of freedom of the qtrit would not take part in the algorithm governed by the Hamiltonian which mimics the SWAP gate.






share|improve this answer









$endgroup$





















    4












    $begingroup$

    Yes they should be the same size. Otherwise, if you use it for getting the inner product between them, it would not make sense they aren't.






    share|improve this answer









    $endgroup$









    • 2




      $begingroup$
      or even more simply, the SWAP operation does not make sense if they have different sizes
      $endgroup$
      – glS
      11 hours ago











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    2 Answers
    2






    active

    oldest

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    2 Answers
    2






    active

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    active

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    active

    oldest

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    1












    $begingroup$

    Qubits can be only with a size of 2, which means a dimensionality of 2.



    For $|alpha rangle,|betarangle$ here, for the SWAP gate to make sense, they must be of the same dimensionality (in the operating Hilbert space), then only there is a meaningful correspondence for the SWAP to work.



    In case if it happens that they are not (suppose one qubit and other qtrit), then the extra degrees of freedom of the qtrit would not take part in the algorithm governed by the Hamiltonian which mimics the SWAP gate.






    share|improve this answer









    $endgroup$


















      1












      $begingroup$

      Qubits can be only with a size of 2, which means a dimensionality of 2.



      For $|alpha rangle,|betarangle$ here, for the SWAP gate to make sense, they must be of the same dimensionality (in the operating Hilbert space), then only there is a meaningful correspondence for the SWAP to work.



      In case if it happens that they are not (suppose one qubit and other qtrit), then the extra degrees of freedom of the qtrit would not take part in the algorithm governed by the Hamiltonian which mimics the SWAP gate.






      share|improve this answer









      $endgroup$
















        1












        1








        1





        $begingroup$

        Qubits can be only with a size of 2, which means a dimensionality of 2.



        For $|alpha rangle,|betarangle$ here, for the SWAP gate to make sense, they must be of the same dimensionality (in the operating Hilbert space), then only there is a meaningful correspondence for the SWAP to work.



        In case if it happens that they are not (suppose one qubit and other qtrit), then the extra degrees of freedom of the qtrit would not take part in the algorithm governed by the Hamiltonian which mimics the SWAP gate.






        share|improve this answer









        $endgroup$



        Qubits can be only with a size of 2, which means a dimensionality of 2.



        For $|alpha rangle,|betarangle$ here, for the SWAP gate to make sense, they must be of the same dimensionality (in the operating Hilbert space), then only there is a meaningful correspondence for the SWAP to work.



        In case if it happens that they are not (suppose one qubit and other qtrit), then the extra degrees of freedom of the qtrit would not take part in the algorithm governed by the Hamiltonian which mimics the SWAP gate.







        share|improve this answer












        share|improve this answer



        share|improve this answer










        answered 12 hours ago









        Siddhānt SinghSiddhānt Singh

        853115




        853115

























            4












            $begingroup$

            Yes they should be the same size. Otherwise, if you use it for getting the inner product between them, it would not make sense they aren't.






            share|improve this answer









            $endgroup$









            • 2




              $begingroup$
              or even more simply, the SWAP operation does not make sense if they have different sizes
              $endgroup$
              – glS
              11 hours ago
















            4












            $begingroup$

            Yes they should be the same size. Otherwise, if you use it for getting the inner product between them, it would not make sense they aren't.






            share|improve this answer









            $endgroup$









            • 2




              $begingroup$
              or even more simply, the SWAP operation does not make sense if they have different sizes
              $endgroup$
              – glS
              11 hours ago














            4












            4








            4





            $begingroup$

            Yes they should be the same size. Otherwise, if you use it for getting the inner product between them, it would not make sense they aren't.






            share|improve this answer









            $endgroup$



            Yes they should be the same size. Otherwise, if you use it for getting the inner product between them, it would not make sense they aren't.







            share|improve this answer












            share|improve this answer



            share|improve this answer










            answered 13 hours ago









            cnadacnada

            2,340213




            2,340213








            • 2




              $begingroup$
              or even more simply, the SWAP operation does not make sense if they have different sizes
              $endgroup$
              – glS
              11 hours ago














            • 2




              $begingroup$
              or even more simply, the SWAP operation does not make sense if they have different sizes
              $endgroup$
              – glS
              11 hours ago








            2




            2




            $begingroup$
            or even more simply, the SWAP operation does not make sense if they have different sizes
            $endgroup$
            – glS
            11 hours ago




            $begingroup$
            or even more simply, the SWAP operation does not make sense if they have different sizes
            $endgroup$
            – glS
            11 hours ago


















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