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
    Feb 8 at 14:09


















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
    Feb 8 at 14:09
















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 Feb 8 at 14:17









Blue♦

6,15831354




6,15831354










asked Feb 8 at 13:43









Gianni CasonatoGianni Casonato

555




555












  • $begingroup$
    I think your question is similar to mine, and I found the answer over here Inner product of quantum states.
    $endgroup$
    – Aman
    Feb 8 at 14:09




















  • $begingroup$
    I think your question is similar to mine, and I found the answer over here Inner product of quantum states.
    $endgroup$
    – Aman
    Feb 8 at 14:09


















$begingroup$
I think your question is similar to mine, and I found the answer over here Inner product of quantum states.
$endgroup$
– Aman
Feb 8 at 14:09






$begingroup$
I think your question is similar to mine, and I found the answer over here Inner product of quantum states.
$endgroup$
– Aman
Feb 8 at 14:09












2 Answers
2






active

oldest

votes


















2












$begingroup$

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




    $begingroup$
    Thanks for the answer. Fully clear now.
    $endgroup$
    – Gianni Casonato
    16 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









$endgroup$









  • 3




    $begingroup$
    or even more simply, the SWAP operation does not make sense if they have different sizes
    $endgroup$
    – glS
    Feb 8 at 16:24






  • 1




    $begingroup$
    Thanks to you both too.
    $endgroup$
    – Gianni Casonato
    16 hours ago











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2 Answers
2






active

oldest

votes








2 Answers
2






active

oldest

votes









active

oldest

votes






active

oldest

votes









2












$begingroup$

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




    $begingroup$
    Thanks for the answer. Fully clear now.
    $endgroup$
    – Gianni Casonato
    16 hours ago
















2












$begingroup$

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




    $begingroup$
    Thanks for the answer. Fully clear now.
    $endgroup$
    – Gianni Casonato
    16 hours ago














2












2








2





$begingroup$

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 Feb 8 at 14:45









Siddhānt SinghSiddhānt Singh

985116




985116








  • 1




    $begingroup$
    Thanks for the answer. Fully clear now.
    $endgroup$
    – Gianni Casonato
    16 hours ago














  • 1




    $begingroup$
    Thanks for the answer. Fully clear now.
    $endgroup$
    – Gianni Casonato
    16 hours ago








1




1




$begingroup$
Thanks for the answer. Fully clear now.
$endgroup$
– Gianni Casonato
16 hours ago




$begingroup$
Thanks for the answer. Fully clear now.
$endgroup$
– Gianni Casonato
16 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









$endgroup$









  • 3




    $begingroup$
    or even more simply, the SWAP operation does not make sense if they have different sizes
    $endgroup$
    – glS
    Feb 8 at 16:24






  • 1




    $begingroup$
    Thanks to you both too.
    $endgroup$
    – Gianni Casonato
    16 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









$endgroup$









  • 3




    $begingroup$
    or even more simply, the SWAP operation does not make sense if they have different sizes
    $endgroup$
    – glS
    Feb 8 at 16:24






  • 1




    $begingroup$
    Thanks to you both too.
    $endgroup$
    – Gianni Casonato
    16 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 Feb 8 at 14:09









cnadacnada

2,389213




2,389213








  • 3




    $begingroup$
    or even more simply, the SWAP operation does not make sense if they have different sizes
    $endgroup$
    – glS
    Feb 8 at 16:24






  • 1




    $begingroup$
    Thanks to you both too.
    $endgroup$
    – Gianni Casonato
    16 hours ago














  • 3




    $begingroup$
    or even more simply, the SWAP operation does not make sense if they have different sizes
    $endgroup$
    – glS
    Feb 8 at 16:24






  • 1




    $begingroup$
    Thanks to you both too.
    $endgroup$
    – Gianni Casonato
    16 hours ago








3




3




$begingroup$
or even more simply, the SWAP operation does not make sense if they have different sizes
$endgroup$
– glS
Feb 8 at 16:24




$begingroup$
or even more simply, the SWAP operation does not make sense if they have different sizes
$endgroup$
– glS
Feb 8 at 16:24




1




1




$begingroup$
Thanks to you both too.
$endgroup$
– Gianni Casonato
16 hours ago




$begingroup$
Thanks to you both too.
$endgroup$
– Gianni Casonato
16 hours ago


















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