# Questions tagged [tensor-product]

A tensor is an abstract object generalising a scalar or vector and can be represented by a number, a 1D array, 2D matrix or higher order generalisations thereof. A tensor product is a product defined on these tensors yielding other tensors or a method to define or represent tensors. If appropriate, also use the [mathematics] tag.

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### Applying CNOT operator to specific qubits in a composite system

In the given problem statement, How do I apply the fourth operation i.e. how to apply a $CNOT_{c=3,t=1}$ to a 3-bit composite system: Approach: First, each bit is set to the state 0. Therefore ...
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### Encoding arbitrary quantum gates using qubits

Given an arbitrary 3-qubit state $\sum_{xyz} c_{xyz}|xyz\rangle$, is there a circuit (possibly with measurement) that creates the state $\sum_{xy} c_{xyy}|x\rangle$, up to a normalization constant? As ...
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### How to write down product operators acting on non-adjacent subsystems?

Given the following fusion gate (type-2) which is projecting 2 qubits to an even state $$F_{ZZ}=(\langle00|+\langle|11|)$$ I would like to find the operator for the bigger space. For example, if I ...
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### What is the tensor product expression for the following quantum circuit? [duplicate]

Qiskit generates the following matrix for this 3-qubit CNOT circuit. Can anyone explain how do we get this mathematically ? This is the Quantum Circuit This is the Output of Unitary Simulator
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### How do I represent my 3-qubit state in the computational basis?

I have taken the tensor product of $|0\rangle \otimes |-\rangle \otimes |+\rangle$ which resulted in the matrix $$\begin{bmatrix} 1/2\\ 1/2 \\ -1/2 \\ -1/2 \\ 0 \\ 0\\ 0\\ 0\\ \end{bmatrix}.$$ How ...
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### Does $\mathrm{tr}(A \otimes B) = \mathrm{tr} (A) \otimes \mathrm{tr}(B)$ hold for partial trace?

I was reading this question from this site answered by DaftWullie. I would like to request you to read the question there. The answer says However, in this particular case, the calculation is much ...
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### Are the two ways of interpreting the expression $(|a\rangle\otimes|b\rangle)(\langle c|\otimes\langle d|)(|e\rangle\otimes |f\rangle)$ equivalent?

Reading Nielsen and Chuang, I am under the impression that a linear operator on the tensor product can be written in two ways: \begin{equation} (\left|a\right> \otimes \left|b\right>)(\left<c\...
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### Writing state $|\Psi⟩ =\frac{1}{\sqrt{2}}|00⟩+\frac{i}{\sqrt{2}}|01⟩$ as separate qubits (qiskit textbook)

While going through the IBM qiskit textbook online, I came across the following question in section 2.2: Write the state: $|\Psi⟩ =\frac{1}{\sqrt{2}}|00⟩+\frac{i}{\sqrt{2}}|01⟩$ as two separate ...
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### Show that the two circuits are equivalent mathematically

This exercise wants me to prove the equivalence of the two circuits using their mathematical representations. Circuit 1: Circuit 2: Circuit 1 (q1 CNOT ...
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