# Questions tagged [quantum-gate]

For questions regarding usage, performance, implementation, application or theory related to quantum gates.

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### Conjugation of Unitary Matrices in Quantum Channel

A quantum channel is given in the form $U(\rho)=\sum_{j}p_jK_j\rho K_j^\dagger$. I have read in another thread that a quantum channel is the generalized version of a quantum gate (represented by a ...
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### Conditional unitary based on output of a function

I read about dynamic circuits in Qiskit which uses an if-test. My question is how can we give a custom function in the if-test? Based on its documentation, we can only provide a classical register to ...
222 views

### How to represent Beam-Splitter and Kerr gates as basic quantum logic gates?

I want to know how to convert these exponential forms to tensor products of well known logic gates (like the ones built into Qiskit). My goal is to program the Beam-splitter-Kerr ansatz circuit for ...
129 views

### Origin of the names of S-gate and T-gate [duplicate]

I have had several opportunities to explain quantum computers to the general public, and I am always at a loss to explain S gate and T gate. Could someone please tell me if there is an origin of the ...
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### When does CNOT entangle?

Let $|\psi_1\rangle$ and $|\psi_2\rangle$ be qubit states such that $\text{CNOT}|\psi_1\rangle \otimes |\psi_2\rangle$ is entangled. I'm interested in if there is a simple condition that this imposes ...
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### Decomposition of rotational matrix using {$H, T$} only

We know that {$H,T$} is universal. However, I don't understand how we can generate any rotational matrix from this set. For example, how can I build \begin{bmatrix} cos(\pi/8) & sin(\pi/8)\\ ...
1 vote
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### Does every code have a strongly transversal Pauli group?

A transversal logical gate for an $n$ qubit code is a gate from the group of local unitaries $$\bigotimes_{i=1}^n U(2)$$ which also preserves the codespace. For an $((n,K,d))$ code we say a ...
33 views

### defining a unitary isometry

I am defining the coefficient unitary in full details but stuck. I tried many ways so that the cross terms gets cancelled and the diagonal terms has one.
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### How to implement the -I matrix using Pauli gates

I'm trying to build a quantum walk circuit. I have the C0 matrix as follows import numpy as np C0 = np.array([[-1, 0], [0, -1]]) As we can see, it's the (-)...
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1 vote
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### Is it possible to use quantum state to store and read information without destorying it?

Like building a ROM device? Please consider the influence of the non-cloning theorem and better show some papers. Thanks! PS: I heard that error-correction methods might help to achieve this goal. Is ...
1k views

### How does one perform amplitude encoding using only unitary gates?

How does one perform amplitude encoding using only unitary gates ? Could you show me a concrete example ?
107 views

### Time complexity of block-encoded matrices

A lot of modern quantum computation has this idea of "block-encoding" matrices; loosely, this is encoding a non-unitary matrix into the top left corner of a larger unitary matrix. This ...
1 vote
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### Controlled Z gate entanglement

In order to prove that the Controlled Z gate can create entanglement, I'm trying to show that using these two arbitrary $2\times 2$ matrices and their tensor product:  \begin{bmatrix}a_1&b_1\\...
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1 vote
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### Sorting two numbers using quantum computing

To better understand how quantum computing works, I am trying to sort two numbers using unitary matrix. Based on this definition, I understand a quantum Turing machine to have the automorphism (...