Questions tagged [swap-test]

For questions related to the "Swap test": a quantum algorithm whose purpose is to quantify the distance between two given quantum states.

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Amplitude encoding: distinction between negative and positive real values

I want to encode two vectors into qubits and compute a distance between them that corresponds/is proportional to the euclidian distance of the real vectors. The encoding I use is A) qiskit ...
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Quantum check sample implementation

I've been trying to figure out how to create a simple circuit in Qiskit to create a check (cheque ) generation and verification as described in this paper. I started with 3 qubits, first one with the ...
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1answer
70 views

How do you test a pair of unknown qubits for orthogonality with certainty?

If you want to check if a pair of unknown qubits are the same, a standard test is the controlled SWAP test. This gives a result of 0 with certainty if the states are the same and 1 with a 50% chance ...
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1answer
106 views

How to calculate inner product of quantum states with other method than swap test? [duplicate]

In connection to this question, I am wondering how to calculate value $\langle \psi|\phi \rangle$ for arbitrary quantum states $|\psi\rangle$ and $|\phi\rangle$. A swap test is able to return only $|\...
2
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1answer
66 views

In the swap test, how is the final probability $P(0)$ calculated?

Does anyone know much about quantum dot product: Lets say: $$|\psi \rangle = \frac{|0\rangle_1|\overrightarrow{x_i}\rangle_2 + |1\rangle_1|\overrightarrow{x_j}\rangle_2}{\sqrt 2}$$ $$|\phi \rangle = \...
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1answer
31 views

In a Swap Test why is the control qubit influenced and aren't the target qubits altered?

I am in a study group learning about quantum computing using O'Reilly - Programming Quantum Computing. I'm a developer, not a physicist. :) I feel like my question is rudimentary but I can't seem to ...
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2answers
2k views

How and why does swap test works?

I am having some trouble understanding why a SWAP test would work. I meant I read that and understood the concepts as follows: If the two input states are equal, the output register always results in ...
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2answers
322 views

Distance calcluation between two vectors

In Quantum Machine Learning for data scientists, Page 34 gives an algorithm to calculate the distance between two classifical vectors. As mentioned in this question, it is not clear how the SwapTest ...
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3answers
512 views

Swap Test for vector difference - how are different sized inputs combined?

I'm working on a similar problem of that raised by Aman in Inner product of quantum states Concerning the use of Swap Test for calculating the difference of two vectors. An example of the original ...
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2answers
489 views

Can the SWAP test only compare registers with the same number of qubits?

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 |$\alpha\rangle$ and |$\beta\...