# 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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### Bell state preparation

I was watching some lectures on qubits. They were talking about how to generate a Bell state. They described it as follows: Prepare state 00: $$\left |0 \right> \otimes \left |0 \right>$$ Apply ...
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### Changing the Basis

I am attempting to use a VQE algorithm to find the ground state of a deuterium nucleus by applying a constructed hamiltonian to an ansatz state with one parameter created by a circuit. While I am ...
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### Is there a good way to mathematically write a CNOT operation over non-neighboring qubits in a circuit? [duplicate]

I was wondering if there is any way to present the CNOT matrix as we usually present single qubit operations $$... 1 \otimes NOT \otimes 1 ...$$ I know that for adjacent qubits in a circuit we can ...
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### Is the tensor product of two states commutative?

I'm reading "Quantum Computing Expained" of David McMahon, and encountered a confusing concept. In the beginning of Chapter 4, author described the tensor product as below: To construct a ...
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### Show that a $CZ$ gate can be implemented using a $CNOT$ gate and Hadamard gates

Show that a $CZ$ gate can be implemented using a $CNOT$ gate and Hadamard gates and write down the corresponding circuit. Recall from Quantum Information Theory that $Z=HXH$. As $CNOT$ is a ...
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### Grover oracle result: vectors (0,1) & (0,1) => two Hadamards => product of two H results => CZ = (.5, .-5, -.5, -.5)

According to the Grover's algorithm section in the IBM Quantum Experience, if I have two qubits in the "one" state (vectors (0,1) and (0,1)), and I apply a Hadamard gate to each of them, and then ...
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### Generic maths for two-qubit gates [closed]

With regard to this question/answer: How's the generalized behaviour of a two-qubit gate for the resulting two qubits? Here e.g. CNOT: If I apply the CNOT matrix to the tensor product, also the ...
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### Tensor Product in Q#

Does anyone know how you can obtain a new state |z> from two pre-existing states |x> and ...
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### How do I compute the output of quantum circuit involving multiple gates?

I'm new in quantum computing, I have this question. Qubits $x$ and $y$ are in $\mathbb{C}^2$ (column vector) and $A, B$ are unitary matrices ($A$ 8x8 and $B$ 4x4 matrix). If I'm not wrong the input ...
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### 2 qubit gate operation on multi qubit systems

Considering a 3 qubit system, what does the matrix operation will look like if I apply CNOT on qubit 1 and qubit 2 and then apply CNOT on qubit 1 and qubit 3?
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### Is kronecker product identifiable?

I have a unitary matrix $U$ and a quantum state $\vert \Psi \rangle$ such that $$U \vert \Psi \rangle = e^{i \theta} \vert \Psi \rangle.$$ I also know that my unitary matrix and my quantum state can ...
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### Quantum Principal Component analysis by Seth Lloyd

I am currently reading the paper quantum principal component analysis from Seth Lloyd's article Quantum Principal Component Analysis There is the following equation stated. Suppose that on is ...
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### How to obtain the tensor-product of two quantum operations (superoperators) explicitly?

I have an amplitude damping channel, denoted as a superoperator $\mathcal{E}$ with operator elements \begin{matrix} E_1=\begin{pmatrix} 1 & 0 \\ 0 & \sqrt{1-r} \end{pmatrix},\quad ...
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### Writing the transformation matrix for the following in terms of Kronecker products of elementary 2-qubit gates

I have a set of transformations that transforms $|11001\rangle\to |10101\rangle$ which is basically keeping the leftmost qubit as it is and then it is just the CNOT between the successive qubits, I ...
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### What is the tensorial representation of the quantum swap gate?

I need to write the tensorial representation of the Controlled Swap Gate, what I have written is $\operatorname{CSWAP}=|0\rangle\langle0|\otimes I\otimes I+|1\rangle\langle1|\otimes U$, where U is ...
In my lecture notes on quantum information processing my lecturer gives an example of composite systems as $|\phi\rangle=|0\rangle |0\rangle=|00\rangle$. I understand that if we have two qubits then ...