# 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.

87 questions
Filter by
Sorted by
Tagged with
28 views

### How to apply 2x2 matrix transformation gates upon 1x4 tensor product columns of two tensored qubits?

The tensor product of two qubits yields a 4-row column vector. Once tensored, how are we supposed to apply common gates such as NOT on just one of the qubits, an operation which expects 2x2 or at ...
33 views

### why is $H^{⊗2}$ used to denote the parallel action of two Hadamard gates?

Why is the tensor product used here, what's its meaning? I learned tensor products as an operation between 2 matrices, and have an effect such as the follows: How does the tensor product above relate ...
73 views

### Negative Probability — Reality vs Description [closed]

I understand that quantum physics supports the concept that the probability of a qubit collapsing into (say) 1, can be negative or positive… and that quantum computing uses this as a feature, adding ...
142 views

### Confusion regarding the tensor product usage in book

I have recently started with quantum computing, and I've found great book about it - Learn Quantum Computing with IBM Quantum Experience, which explains a lot of things in quite a simple language. ...
94 views

### Python shorthand for tensor product (Kronecker product)

When using numpy or tensorflow in Python, we can simply write C = A @ B for matrix ...
89 views

223 views

### Is it possible to retrieve $|\psi_1\rangle,|\psi_2\rangle$ from their tensor product $|\psi_1\rangle\otimes|\psi_2\rangle$?

Consider two quantum states$$\left| \psi_1 \right> = \alpha \left|0\right> + \beta\left|1\right>$$ and $$\left| \psi_2 \right> = \gamma \left|0\right> + \delta\left|1\right>$$ Now ...
65 views

### Understanding the quantum circuit for the quantum adder Toffoli gate

I am trying to understand the toffoli operation for the quantum adder below: (especially for the second toffoli gate) but I am stuck in understanding the calculation to get the correct outputs. The ...
98 views

### In the hidden subgroup problem for finite Abelian groups, where does the state $\frac{1}{\sqrt{|G|}}\sum_{g\in G} |g,0\rangle$ come from?

I am new to the concept of HSP. Previously, I saw how to solve hidden subgroup problem over $\mathbb{Z}_2^n$, which was Simon's algorithm. Over there the first step was to apply $H^{\otimes n}$, which ...
77 views

### What is the "quantum mean value problem"?

What is the "Quantum mean value problem"? A definition I found was that it is "estimating the expected value of the tensor product observable on the output state of a quantum circuit&...
36 views

### How would I apply rotations to both qubits in a 2 qubit system?

Say I have the two qubit system $\frac{1}{\sqrt{2}}\begin{bmatrix} 0 \\ 1 \\ 1 \\ 0 \end{bmatrix}$. I have two 2x2 unitary gates, one is a rotation ...
97 views

### How to create an observable: 'Identity \tensor Pauli gate' in Cirq

I am working on an implementation of the RQAOA algorithm on the Maxcut problem in Cirq. My graph G has n vertices. And after running a QAOA circuit with n qubits I obtain a state gammabeta (a vertical ...
110 views

### Can we express $\mathrm{tr}_A((A\otimes B)\rho_{AB})$ in terms of $A$, $B$, $\rho_A$ and $\rho_B$?

For a density matrix $\rho_{AB}$ and some operators $A, B$, is there a way to express $$\text{Tr}_A((A\otimes B)\rho_{AB})$$ using the reduced states $\rho_A$ and $\rho_B$ and operators $A$ and $B$? ...
166 views

### If you apply a unitary transformation to an entangled state, is it still entangled?

See title. If this is not true, is there a counter example? If it is not true, does it hold true for certain combinations of unitaries and entangled states?
97 views

### How does the sum of two operators act on a two-level system of qubits?

I am confused how the sum of N operators will act on an N-level system of qubits. Here, lets say N=2 so the state is $|00⟩_{CD}$. Then how will this operator $X_{C} + Z_{D} ⊗ I_{C} + X_{D}$ act on ...
133 views

91 views

### Can every bipartite state be written as $\rho_{AB} = \sum_{ij} c_{ij}\sigma_A^i\otimes \omega_B^j$?

Can every bipartite quantum state (including entangled ones) be written in the following way $$\rho_{AB} = \sum_{ij} c_{ij}\sigma_A^i\otimes \omega_B^j$$ where $\sigma_A^i$ and $\omega_B^j$ are ...
124 views

### Quantum tensor product closer to Kronecker product?

Coming more from a computer science background, I never really studied tensor products, covariant/contravariant tensors etc. So until now, I was seeing the "tensor product" operation mostly ...
117 views

### 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 ...
92 views

### 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 ...
180 views

### 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 ...
350 views

### 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 ...
539 views

### 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 ...
52 views

### 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 ...
111 views

### 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 ...
68 views

### Tensor Product in Q#

Does anyone know how you can obtain a new state |z> from two pre-existing states |x> and ...
228 views

### 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 ...
72 views

78 views

### 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?
95 views

### 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 ...
569 views

### 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 ...
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 ...