# 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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### What's $(\langle 0|\otimes I)(|00\rangle + |11\rangle)$ simplified?

It's a rather simple question. I think I am confused by the fact that using $\langle0|$ on a qubit doesn't result in another qubit. So I'm not sure if I should interpret $\langle 0|$ as the $1\times2$ ...
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### Recover local systems from composite systems

Define $A,B$ as two linear operator of two local systems. Define $C:= A \otimes B$ as the composite systems. How to recover $A$ and $B$ given $C$? For example, we set \begin{align} A=\left[\begin{...
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### Tensor product of the state of a system after partial measurement

I am trying to solve the question below: While solving the post measurement state, I understand we can take the 1st and last qubit common using tensor product if they are the same(1st part of the ...
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### Where am I going wrong in my understanding of qubit associativity?

I am studying the basics of quantum computing math and am confused about qubit associativity. As I understand it, in quantum math, multiple qubits are represented as the tensor product of the qubits ...
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### Qiskit.opflow can't conbine Pauli Tensor sum

I have the problem when I run my code ...
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### How to find the matrix representation of a given many-qubit Hamiltonian?

I have the following Hamiltonian H = - Z1Z2 - Z2Z3 - Z1Z3 - 6(Z1 + Z2 + Z3) Here, Z1, Z2, Z3 represent the Pauli-Z operators acting on qubits 1, 2, and 3, ...
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### Matrix representation for biproduct mixed states

Nielsen and Chuang [10e, p. 74] introduce the Kronecker product $A\otimes_K B$ as a matrix representation of the tensor product $A\otimes B$ of the operators $A$ and $B$ (for clarity I use a subscript ...
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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 ...
• 123
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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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