SWAP test inputs
$begingroup$
I'm using the SWAP test circuit for implementing a qubit registers comparison
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
edited Feb 8 at 14:17
Blue♦
6,15831354
asked Feb 8 at 13:43
Gianni CasonatoGianni Casonato
555
$endgroup$
add a comment |
$begingroup$
I'm using the SWAP test circuit for implementing a qubit registers comparison
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
edited Feb 8 at 14:17
Blue♦
6,15831354
asked Feb 8 at 13:43
Gianni CasonatoGianni Casonato
555
$endgroup$
$begingroup$
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
add a comment |
$begingroup$
I'm using the SWAP test circuit for implementing a qubit registers comparison
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
edited Feb 8 at 14:17
Blue♦
6,15831354
asked Feb 8 at 13:43
Gianni CasonatoGianni Casonato
555
$endgroup$
I'm using the SWAP test circuit for implementing a qubit registers comparison
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
edited Feb 8 at 14:17
Blue♦
6,15831354
asked Feb 8 at 13:43
Gianni CasonatoGianni Casonato
555
edited Feb 8 at 14:17
Blue♦
6,15831354
asked Feb 8 at 13:43
Gianni CasonatoGianni Casonato
555
edited Feb 8 at 14:17
Blue♦
6,15831354
edited Feb 8 at 14:17
Blue♦
6,15831354
edited Feb 8 at 14:17
Blue♦
6,15831354
6,15831354
asked Feb 8 at 13:43
Gianni CasonatoGianni Casonato
555
asked Feb 8 at 13:43
Gianni CasonatoGianni Casonato
555
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
add a comment |
$begingroup$
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
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
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.
answered Feb 8 at 14:45
Siddhānt SinghSiddhānt Singh
985116
$endgroup$
1
$begingroup$
Thanks for the answer. Fully clear now.
$endgroup$
– Gianni Casonato
16 hours ago
add a comment |
$begingroup$
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.
answered Feb 8 at 14:09
cnadacnada
2,389213
$endgroup$
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
add a comment |
Your Answer
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
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.
answered Feb 8 at 14:45
Siddhānt SinghSiddhānt Singh
985116
$endgroup$
1
$begingroup$
Thanks for the answer. Fully clear now.
$endgroup$
– Gianni Casonato
16 hours ago
add a comment |
$begingroup$
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.
answered Feb 8 at 14:45
Siddhānt SinghSiddhānt Singh
985116
$endgroup$
1
$begingroup$
Thanks for the answer. Fully clear now.
$endgroup$
– Gianni Casonato
16 hours ago
add a comment |
$begingroup$
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.
answered Feb 8 at 14:45
Siddhānt SinghSiddhānt Singh
985116
$endgroup$
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.
answered Feb 8 at 14:45
Siddhānt SinghSiddhānt Singh
985116
answered Feb 8 at 14:45
Siddhānt SinghSiddhānt Singh
985116
answered Feb 8 at 14:45
Siddhānt SinghSiddhānt Singh
985116
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
add a comment |
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
add a comment |
$begingroup$
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.
answered Feb 8 at 14:09
cnadacnada
2,389213
$endgroup$
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
add a comment |
$begingroup$
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.
answered Feb 8 at 14:09
cnadacnada
2,389213
$endgroup$
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
add a comment |
$begingroup$
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.
answered Feb 8 at 14:09
cnadacnada
2,389213
$endgroup$
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.
answered Feb 8 at 14:09
cnadacnada
2,389213
answered Feb 8 at 14:09
cnadacnada
2,389213
answered Feb 8 at 14:09
cnadacnada
2,389213
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
add a comment |
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
add a comment |
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$begingroup$
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