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# Questions tagged [quantum-gate]

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

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### CNOT quasiprobability decomposition with $\gamma = 3$

In this paper of Christophe Piveteau and David Sutter, they prove that the $\gamma$-factor of the quasiprobability decomposition of the CNOT gate is equal to $3$ (if we don't allow classical ...
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### How to use more than 3 classical registers in a single quantum circuit in Qiskit without getting error: not enough memory slots?

I'm trying to run a quantum circuit on qasm simulator which has more than 3 classical registers. It gives error when I try to execute it. The circuit looks ...
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### What are the relations between the permutation group and the Clifford group?

I'm trying to understand the relation between the permutation group on all the $2^n$ bitstrings and the Clifford group. My question arises from the fact that the Toffoli gate (which can be thought of ...
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### Finding controlled Y gate?

I was working with qiskit textbook --> Basic Circuit Identities where I get that I can write a CY gate with s CNOT and sdg gate but I want to find out the unitary matrix for that circuit without ...
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### Is there any shortcut to create a controlled gate or any technique?

I was solving Controlled H gate from qiskit textbook -> Basic Circuit Identities There I tried to find the unitary matrix for CH gate but it get's really complicated when I use tensor product or ...
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### Is the mathematical expression between the CNOT gates arranged in this way a tensor product or a concatenated product?

Is the mathematical expression between the CNOT gates arranged in this way a tensor product or a concatenated product? That is \begin{matrix} \text{CNO}{{\text{T}}^{\otimes n}} & or & \prod\...
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### How can we represent a CNOT gate using a cascade of rotation gates?

I have been working using qiskit to implement the CNOT decomposition into a cascade of rotation gates from this source. After computing the unitary matrix, the resultant matrix is not the same as the ...
1 vote
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### How to calculate c not, toffoli gate with additional line

How to calculate cnot gate(or toffoli) in red box Why is there additional line? And is it same as the two toffoli gate?
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### Equivalent $[\![n,k,d]\!]$ codes and transversal gates

An operator on the Hilbert space of $n$ qubits is called a local unitary if it is of the form $$U=\bigotimes_{i=1}^n g_i$$ where each $g_i$ is a $2 \times 2$ unitary matrix. In other words if ...
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### Quantum Algorithm to Solve a Maze

I am trying to understand the paper "Quantum Algorithm to Solve a Maze - Converting the Maze Problem into a Search Problem" by Debabrata Goswami and Niraj Kumar (here the reference https://...
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### Decompose 8x8 Unitary Matrix into tensor product of three phased gate

We try to decompose 8x8 unitary matrices \begin{pmatrix} e^{ia} & & & & & & \\ & e^{ib} & & & & & \\ & & e^{ic} & & ...
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As I was reading Qiskit textbook and there is this problem ... How can I swap a $|+\rangle$ to a $|-\rangle$ Qiskit textbook --> Basic Circuit Identities
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### What other discrete non-trivial non-Clifford groups of gates are there?

I do not know many groups (as in group theory) of quantum gates. Aside from trivial ones, I know there is Pauli group and the Clifford group. Recently I discovered another interesting group generated ...
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### How can the result of 1 million transformations on a qubit be verified to be correct?

I tried to do almost a million transformations on a qubit. I made a three qubit circuit with equal superposition of |0> and |1> (using Hadamard gate) and on the first qubit (qubit 0), added one ...
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### Padding a quantum circuit to increase the amplitude by a constant

Let us be given the description of a quantum circuit $\mathsf{Q}$, acting on $n$ qubits, such that $$\langle 0^n|\mathsf{Q}|0^n\rangle = \frac{\#0_f - \#1_f}{\sqrt{2^n}},$$...
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### How to read data from multiple qubits and feed it to a MLP

Being new in the field of quantum computing, I tried with the implementation of "https://qiskit.org/textbook/ch-machine-learning/machine-learning-qiskit-pytorch.html" using a single qubit. ...
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### How to generate CNOT-gates via Bell pairs

In this paper from Christophe Piveteau and David Sutter, the authors use Bell pairs to generate CNOT-gates. The procedure is shown in Fig.2 and Fig.3 of the paper. By doing the calculations about that ...
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### Preparing a superposition state modulo $k$

Consider being given the description of a function $f: \{0, 1\}^n \rightarrow \{0, 1\}^m$ and the binary representation of an integer $k$. Is the state |\psi_{f, k}\rangle = \frac{1}{\...
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### Sample random unitary at a given distance from a given unitary

Is it possible? I.e., what is the most natural procedure of such sampling? The sampling has to be 'uniform' in a vicinity (of radius $\epsilon$) of given $U$ (can I say "according to Haar measure ...
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### How to intuitively understand why $T$ gate can't be implemented transversally?

Suppose we have all to all connectivity and can implement fault-tolerant logical gates in the Clifford group. Why can't we just apply a physical $T$ gate to every physical qubit in the code block? (...
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### Are there Clifford gates that preserve some computational basis states while otherwise generating superpositions?

Consider a two-qubit Clifford gate that maps $|00\rangle$ to $|00\rangle$, up to a phase. Can it map at least one of the other computational basis states $|10\rangle, |01\rangle, |11\rangle$ into a ...
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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 ...
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### Does a fidelity of $\mathcal{F}(U_1|0\rangle, U_2|0\rangle)=1$ imply that $U_1=U_2$?

I'm now studying quantum ML and now studying about fidelity ($\mathcal{F}$). To my knowledge, fidelity means the distance between two quantum states, $\textit{i.e.,}$ if $\mathcal{F} ==1$, then the ...
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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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### If you had a 1000 qubit NISQ machine with arbitrary connectivity, what would you do?

Many current devices are constrained to nearest neighbor connectivity or small system sizes, but suppose that a NISQ machine with 99-99.5% level two-qubit gate fidelities and arbitrary connectivity ...
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### Can a Quantum computer simulate classical hack and exploit in a network ? Also how would it be any different from the classical computer [closed]

I'm trying to write a realistic story around Quantum computing and was wondering how different a network exploit/hack would look if a Quantum computer was to hack into a private network, instead of ...
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### Does the ZX calculus allow for Y-axis rotations?

I'm trying to understand how Y-axis rotations are represented in ZX Calculus. In the paper, wikipedia, everywhere I look, it's as if there is no such thing as Y-axis rotations, only X and Z. I ...
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### Mapping a classical cipher into quantum implementation of Grover Oracle

I am translating simple ciphers into quantum implementation in order to create oracle for Grover algorithm. I have started the task with a light weight SPECK cipher (got both classical and quantum ...
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