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Where can I find runtime of ibm quantum gates?

You can find the gate length from the backend properties: ...
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Finite subgroup of $U(4)$ containing a non-Clifford gate and all local Cliffords

No. There is no way to add a non Clifford gate to the local Clifford group $ Cl_1^{\otimes 2} $ and get a finite group. Definitions: A subgroup $ G $ of $ GL_n(\mathbb{C}) $ is reducible if we can ...
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The relationship between number of shots and performance of quantum agent

I bet you already have looked this over, but here is the documentation for QASM sim: https://qiskit.org/documentation/stubs/qiskit.providers.aer.QasmSimulator.html There is a command to do the max ...
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What are the transversal gates of Shor's [[9,1,3]] code?

Superpositions are too entangled The logical computational basis of the Shor's nine-qubit code is $$ \begin{align} |0\rangle_L=\frac{((|000\rangle+|111\rangle)(|000\rangle+|111\rangle)(|000\rangle+|...
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1 vote

What are the transversal gates of Shor's [[9,1,3]] code?

The code is not symmetric in $X$ and $Z$ type stabilizers $|S_X|=6$ and $|S_Z|=2$; so $H_L=H^{\otimes 9}$ doesn't preserve the codespace and you can't have a transversal $H_L$. $U=H P$ is transversal ...
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2 votes

When we say that 4 qubits can represent $2^4$ binary bit sequences, how do we iterate to the desired bit sequence?

Quantum computing can solve certain problems exponentially faster, but not all. A classical computer with $n$ bits can store a single number with value up to $2^n$, while a quantum computer with $n$ ...
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1 vote
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What are the transversal gates of the [[5,1,3]] code?

This paper (page 4) lists Paulis + $HS$ gate.
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1 vote

When we say that 4 qubits can represent $2^4$ binary bit sequences, how do we iterate to the desired bit sequence?

Even if qubits can represent those combinations at the same time, when I need a definite answer, how does the path to that answer differs from the path followed in binary bit computer? That's not how ...
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How to deterministically add two integers on a quantum computer

I think you’ve got the basic idea, but a few concepts mixed up. Every QC will give a probabilistic output only if it is in superposition. If you do not put it into superposition, addition behaves ...
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1 vote

Where can I find runtime of ibm quantum gates?

There are some ways to do this: There is an archived repository of IBM Quantum on GitHub containing some old as well as current backends of Qiskit: https://github.com/Qiskit/ibmq-device-information/...
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6 votes

Finite subgroup of $U(4)$ containing a non-Clifford gate and all local Cliffords

This partial answer places additional restrictions on $U$. Constructing unitaries with infinite order By KAK decomposition, $U$ can be written as $$ U=(A_1\otimes A_0)e^{i\alpha X\otimes X + i\beta Y\...
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2 votes

Is there a general way to parametrize 2-qubit unitaries?

There is some parametrized matrix form for a 2-qubit unitary, but it would be extremely inconvenient to work with. An $n$-qubit gate is an element of the group $SU(2^n)$, which has dimension $2^{2n} - ...
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Is there a general way to parametrize 2-qubit unitaries?

What I propose here could possibly be simplified further, but that's at least a first direction. First, any unitary can be written as $U=e^{-it/\hbar \widetilde{H}}$ for some $t$ and $\widetilde{H}$ (...
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1 vote

Finite subgroup of $U(4)$ containing a non-Clifford gate and all local Cliffords

Here's an example for the real Pauli and Clifford groups : $$P_1=<X_1,Z_1>; |P_1|=8;$$ $$P_2=<X_1,Z_1,X_2,Z_2>; |P_2|=32;$$ $$C_1=<X_1,Z_1,H_1>; |C_1|=16;$$ $$C_1^{\otimes 2}=<X_1,...
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2 votes

How does a Hadamard gate impact the initial/previous values of a Qubit?

I think you might just be misunderstanding the Hadamard gate slightly. In the computational basis, $H= \frac{1}{\sqrt{2}}\begin{pmatrix} 1 & 1 \\ 1 & -1\end{pmatrix}$ maps $|0\rangle \...
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How to deterministically add two integers on a quantum computer

There are quite a few ways to make an adder on QC. I recommend watching Circuit Sessions with Ali Javadi, demo notebook from the talk so, a simple explanation, what makes a quantum computer faster ...
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4 votes

Are the SDG and TDG gates hermitian?

A matrix $A$ is a Hermitian if and only if $$ A = A^\dagger$$ So if $A^\dagger$ is Hermitian then that means $A^\dagger = (A^\dagger)^\dagger = A$ and so of course $A$ is hermitian. By the way, by ...
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Can a polynomial-sized superposition of computational basis states be prepared with a polynomial-sized quantum circuit?

I think so. Let me rephrase what you're asking and hopefully it captures what you want: Suppose you have $N$ distinct circuits $U_i$ such that $U_i|0\rangle = |\psi_i\rangle$, each with complexity $O(...
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Clarification about QTF proof regarding equality of QFT application and circuit application

I suppose there are two sources of confusion here -- one is the reversed order of the qubits between the circuit and the unitary, and the other is the use of $x$. In terms of qubit ordering, I think ...
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1 vote
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Definitions of a quantum circuit's depth and connectivity

I would like to give explicit definitions of the circuit depth and connectivity. I assume that the meaning of terms like vector state, quantum circuit, wires, and 1- and 2-qubit gates is understood. I'...
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4 votes

Definitions of a quantum circuit's depth and connectivity

The traditional definitions of classical Boolean circuits work perfectly well here: https://en.wikipedia.org/wiki/Boolean_circuit. This is the definition that gives you Niel de Beaudrap's definition. ...
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Composing the CNOT gate as a tensor product of two level matrices

Although $CNOT$ cannot be written as $A\otimes B$, it can be written as a sum of such terms. For example: $CNOT=I\otimes I +\frac12Z\otimes I+\frac12 I\otimes X - \frac12 Z\otimes X$.
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2 votes

Definitions of a quantum circuit's depth and connectivity

Let me try to provide a more precise definition of connectivity in a quantum circuit. Every quantum circuit defines a graph (network), with vertices (nodes) given by qubits. There is an edge $q_1 q_2$ ...
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Controlled phase shift gate

The phase shift is a family of single-qubit gates that map the basis states ket(0) to ket(0) and ket(1) to exp(i theta)* ket(1) so by using this we can find matrix of controlled phase shift operator....
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1 vote

How to write a code to separate two qubits?

Maybe it should be useful tu use qutip to better understand what you desire (if you are familiar with python) by visualizing exactly the 2 qubits and its state vectors (which I believe is what you ...
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I am getting an error like this 'Invalid input data format for Statevector'

Tips for you to understand error: take a look at qiskit docs, what is the valid data input, learn more about Statevector class https://qiskit.org/documentation/stubs/qiskit.quantum_info.Statevector....
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5 votes

Is there a quantum gate that can turn any superposition $|\varphi \rangle $ into a unit column vector $|00\cdots 1\cdots 0\rangle $

It depends on what you mean. For a given state $|\varphi\rangle$, it is always possible to find a gate $U_\varphi$ such that $U_\varphi|\varphi\rangle=|i\rangle_{10}$ for some given $i$. However, it ...
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2 votes

How can I write if conditions on quantum registers using qiskit

If "some operations" in your question means quantum operations, then you can use Gate.c_if() to apply a gate based on a value in a classical register as ...
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1 vote
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Speed of Superconducting Qubit Architectures

Google's Sycamore processor for which they claimed quantum supremacy (https://doi.org/10.1038/s41586-019-1666-5) performs two-qubit operations in 12 ns, so that would be some 80 MHz. Of course ...
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