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# Questions tagged [quantum-gate]

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

225 questions with no upvoted or accepted answers
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### CNOT gate path interference

I have a question on paper https://doi.org/10.1038/nature02054. In this paper, the CNOT gate is realized using a beam displacer for higher stability. The figure below shows a 1:1 mapping from (a) to (...
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1 vote
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### What is the relationship between the number of shots and the performance of a quantum agent?

What is the relationship between number of shots and the performance of quantum agent in Quantum neural network? and what is the limit of number of shoots in QASM simulator?
1 vote
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### Faithful description of a photonic setting with the circuit model

The above picture comes from this paper. The circuit on the left and the one on the right are equivalent (up to the basis). However, there is an important difference: the circuit makes the input -- i....
• 1,958
1 vote
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### What's the best way to design a circuit with logic gates that use the same input lines?

I am implementing a Carry Select Adder, the problem is that the circuit is quite complex to translate in Qiskit. I need to use one (or multiple) line(s) as input for two (or more) gates. In particular,...
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1 vote
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1 vote
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### How to measure the error rate (or fidelity) of a particular gate (such a H, T) by Qiskit

We know the calibration data of IBM's quantum devices can be retrieved through the randomized benchmarking method, which is included in Qiskit. However, the calibaration data about gates just gives ...
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1 vote
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### Matrix for $U^{2^j}$ from Shor's algorithm for any $a$ and $N$

I'm implementing Shor's algorithm from scratch and therefore want to implement a unitary gate $U$ such that $U^{2^j}|y\rangle = |a^{2^j}y \: \text{mod} \: N\rangle$. I know that an efficient way of ...
• 2,895
1 vote
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### In (O'Brien et al. 2004), why is the target qubit not affected when the control is $\vert 0\rangle$?

I'm currently reading this paper https://arxiv.org/abs/quant-ph/0403062 but I fail to understand how the input of the control qubit affects the output of the target qubit. I do understand that when ...
1 vote
210 views

### 3-qubit phase shift gate/circuit implementation without any Ancilla qubits

Hi, I need help me with figuring out the 3-qubit phase shift circuit without any ancillas similar to the 2-qubit circuit shown in below attached picture....... Please do let me know! Thanks in advance!...
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1 vote
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### Axis and Angle of rotation of $\frac{1}{\sqrt{2}}\begin{bmatrix}-i&-1\\1&i\end{bmatrix}$

I have made use of the following formulas, \begin{align} \theta&=2\cos^{-1}\bigg(\frac{e^{-i\alpha}Tr(X)}{2}\bigg)\\ n_i&=\frac{e^{-i\alpha}Tr(X\sigma_x)}{2\sin\theta/2}\\ e^{i\alpha}&=\...
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### Proof that if W is the image of a Unitary operator with an $n^O(1)$ size quantum circuit, then $R_W$ has an $n^O(1)$ circuit as well

I have been working on the following problem Suppose $H$ is the Hilbert space of n qubits. Let $W_0$ be the subspace of $H ⊗ H$ with basis $|x_0⟩$, x = 0,...,N −1 where $N = 2^n$. Suppose $U$ is a ...
25 views

### What is the role of color in color code? ( theoritically and exprimentally)

We know that the color code has an extra element relative toric code . It is color . I want to know what is the role of color ?
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### How to deal with logical gates which map Logical Paulis to non-Pauli products?

I am trying to figure out the action of logical gates on quantum codes. I am trying to check the logical operations that the logical gate performs on the code. I can do it in simple cases, for example ...
• 585
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### How to decompose a permutation matrix into two-level unitary matrices?

Assume a have a SBox and want to make quantum circuit for it. The unitary transform matrix for a SBox is special - a permutation matrix. I found an algorithm to decompose any unitary matrix into two-...
• 93
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### Diffuser's hadamard logic in equal superposition with negative phases

This is with reference to the question here: How to understand intuitively the Grover diffusion operator? Overall it makes sense on how H^n of the diffuser logic creates the |000..0> from an equal ...
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### Spin Hamiltonian to Quantum Circuits and are there any group theory associated with the quantum circuits?

Can we think of Quantum Circuits as another representation to describe the dynamics of a system other than its Hamiltonian? How can we go from the spin Hamiltonian version (for eg: SSH Model ...
61 views

### IBM quantum composer possible bug?(state amplitudes of quantum circuit)

I have this quantum circuit: and from the IBM quantum composer I get this state amplitudes: I wanted to flip the target qubit and keep only its pure state however this is not what I am getting.I am ...
151 views

### Qiskit cant run circuit with reset gate with error

In qiskit if i have a reset gate in a circuit. If i want to add noise to the circuit it wont transpile. For example: ...
• 31
162 views

### How do qubits interact to form logic gates?

How do qubits interact to form, say, CNOT gates? There are very few comprehensive explanations of how quantum computing works. They all use obscure metaphors that don’t make sense (like Schrödinger’s ...