# Questions tagged [quantum-gate]

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

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### How does an $\sqrt{X}$ error propagates through an $T$ gate?

I wonder whether there is a compact way of describing a noise $\sqrt{X}$ propagating through a $T$ gate. Possibly in terms of Pauli and/or Clifford operators.
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### Multi qubit states and the CNOT gate

I'm stuck on this passage from a book: Suppose we try to copy a qubit in the unknown state $|ψ\rangle = a|0\rangle + b|1\rangle$ in the same manner by using a $\text{CNOT}$ gate. The input state of ...
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### math behind rotation gate

$R_Z(\theta) = e^{-i\frac{\theta}{2}Z}$ and $R_{ZX}(\theta) = e^{-i\frac{\theta}{2}XZ}$ My question is, why is the rotation gate defined in an exponential format? Where does the $\frac{1}{2}$ come ...
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### Gate times for photonic quantum computers

I am trying to understand the landscape of one- and two-qubit gate times for various quantum computing architectures. It is not so hard to find gate times for various gates such as Hadamard, CNOT and ...
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### Is 60% accuracy high when calculating 1+1 on a quantum computer?

A financial firm has criticized the quantum computer of a company called IonQ. Part of the content is that IonQ's quantum computer is only 60% accurate for 1+1 calculations, and only 50% for 2+3 ...
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### Counting the number of CCX and CX gates in controlled modular addition

If we do a controlled modular addition of an adder with 2n ccx and 4n cx gates for example the CDKMRippleCarryAdder, what will be the resultant count of ccx and cx ...
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### How do I generate gates for qudits with $d=4$?

So I was working on a project with qudits (specifically d = 4) and came across a problem. How do I generate gates for these? I can construct Hadamard and X gates for these, but how does one approach ...
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### What is the average amount of gates needed to implement a random Clifford gate?

Given a Clifford gate acting on $n$ qubits is implemented using its generators, what is the average number of gates needed to implement a random Clifford gate as a function of $n$?
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### How does a quantum computer find the correct password faster than classical computers using brute-force?

I didn't get this part right! For example, we have an online box with a 16-digit password, and we don't know what the password is! How can a quantum computer find the correct password faster than ...
1 vote
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### Standard name for CZ gate conjugated by Hadamards?

Is there a standard name for a $CZ$ gate conjugated by $H \otimes H$ gates? See below for circuit
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### Direction of rotation operators

The rotation operators for a single qubit are defined as $R_{v}(\theta) = e^{-i \theta X/2}$, with $v \in \{ X,Y,Z\}$. If we look at the direction of rotation of $R_v$ w.r.t. the positive eigenvalue, ...
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### What justifies using tensor product of matrices for parallel gates when applying them to an entangled state?

In my university we defined tensor product of two matrices $A$, $B$ as a matrix $A \otimes B$ such that for any vectors $\left| \phi \right>$, $\left| \psi \right>$ the following is satisfied: ...
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### Does the CX gate always leave the first qubit unchanged and swap the amplitudes of the second one?

I'm a self-learner of quantum computing and is at the very beginning. I do have some math and coding background though. I'm trying to understand how working with entangled qubits helps performing ...
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### Is there relation between IonQ native gates and the rotation gates $R_x$, $R_y$, $R_z$? [closed]

I know $GZ = R_z$ and $XX = MS$ but what about $GPI$ and $GPI2$?
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### How to extract solution from HHL statevector on qskit?

I want to extract the HHL solution from the StateVector. I am doing this on a $4\times4$ matrix. For a $2$ by $2$ the solution is available in the StateVector $8$, $9$. However for a $4$ by $4$ matrix ...
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### Local Hermitian operators can be written as sums over local error operators?

In this paper, near the bottom of the left half of page 3, the authors claim that any local Hermitian operator (one which acts only on a single subsystem of a larger composite system) can be expressed ...
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### Quantum Gate - Negating qubit whose state is known to lie in the equatorial x-y plane

Given a qubit whose state is known to lie in the equatorial x–y plane in the Bloch sphere is it possible to find a quantum gate that will always negate this qubit? If so, exhibit such a gate. If not, ...
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