# Questions tagged [quantum-gate]

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

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### What is quantum gate's correponding circuit implementation? [on hold]

We know that the symbol of a quantum gate like "x gate", "z gate" is an abstraction notation. For example, the Not-gate in classical computer is composed of 2 transistors. How can we know quantum gate'...
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### How to decompose a unitary transform into two-level unitary matrices?

I'm struggling to understand the process of how to decompose a unitary transform into two-level unitary matrices. I've been trying to understand the process as detailed in arXiv:1210.7366, but I don't ...
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### Transforming the first Bell state into the other Bell states

As I understand it, you can transform the different Bell states into one another by applying various gates. Wikipedia has the Bell states written out as follows: And says that you can generate bell ...
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### Understanding shared Bell states from quantum entanglement

I'm trying to understand an entanglement swapping derivation provided in this PDF (pages 2 - 3) I have several things about this process that I don't understand, and I was hoping someone could ...
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### How to check if a two-qubit gate is entangling?

I would like to know if there's an analog for Schmidt rank that can tell me if a two-qubit unitary is entangling? Suppose I have a parametrized two-qubit unitary $U^{(2)}(\theta)$. I would like to ...
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### Why does a controlled gate not constitute a measurement?

I have recently listened to a talk on quantum computing and was fascinated to learn about IBM Q Experience. Between the explanations in the User Guide and in Nielsen's book, I came to the following ...
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### How and why does swap test works?

I am having some trouble understanding why a SWAP test would work. I meant I read that and understood the concepts as follows: If the two input states are equal, the output register always results in ...
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### What's the difference between observing in a given direction and operating in that same direction?

So starting with an up particle: $$\lvert \uparrow \rangle = \begin{bmatrix} 1 \\ 0 \\ \end{bmatrix}$$ My understanding is that you can measure $\lvert \uparrow \rangle$ in $X$ and have ...
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### Input and output qubit notation in quantum gates

I am new to quantum computing and I am having trouble understanding the notation used for input/output qubits in quantum gates. I will use the CNOT gate as an example. In several (most) references I'...
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### Is there a way to develop a multiple controlled X or Z gate on Qiskit without using ancillary qubits?

I know for instance I can derive a cccX gate using 2 Toffoli gates on 5 qubit wire or ccccX with 3 Toffoli gates and 7 qubits and so on. you will notice the depth is increasing as the number of ...
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### Can everything in QM be described with degrees instead of matrices and vectors?

I found this explanation. "The Hadamard gate can also be expressed as a 90º rotation around the Y-axis, followed by a 180º rotation around the X-axis. So $H=XY^{1/2}H = X Y^{1/2}H=XY^{1/2}$." Can ...
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### Understanding Google's “Quantum supremacy using a programmable superconducting processor” (Part 3): sampling

In Google's 54 qubit Sycamore processor, they created a 53 qubit quantum circuit using a random selection of gates from the set $\{\sqrt{X}, \sqrt{Y}, \sqrt{W}\}$ in the following pattern: ...
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### Understanding Google's “Quantum supremacy using a programmable superconducting processor” (Part 2): simplifiable and intractable tilings

In Google's 54 qubit Sycamore processor, they created a 53 qubit quantum circuit using a random selection of gates from the set $\{\sqrt{X}, \sqrt{Y}, \sqrt{W}\}$ in the following pattern: ...
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### Understanding Google's “Quantum supremacy using a programmable superconducting processor” (Part 1): choice of gate set

I was recently going through the paper titled "Quantum supremacy using a programmable superconducting processor" by NASA Ames Research Centre and the Google Quantum AI team (note that the paper was ...
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### How can we construct a square root of NOT gate in Qiskit and IBMQ circuit composer using universal gates?

I have tried it with decomposing controlled S then conjugating with H gate. But I want to construct it using a minimum number of gates.
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### How to implement the controlled square root of NOT gate on the IBM Q composer?

I already know how to do that for Z, Y, and H gates. How can I make a controlled sqrt-of-NOT gate? I mean the controlled version of the gate described here.
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### Can someone show the linear algebra calculations for X, H, and CNOT gates?

I am on Ch.1 of the Mike & Ike book. On page 18, the text shows an X gate that essentially flips the $\alpha$ and $\beta$ amplitudes. The text shows the $X$ matrix but it doesn't show those for ...
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### How to factor the output of a CNOT acting on the input $|-,+\rangle$

I am trying to implement the Deutsch oracle in classical computer, using direction from this talk. There is this slide where they show how the CNOT gate modify 2 Hadamard transformed Qubits: While ...
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### How do these alternative Q# algorithms produce the same set of Bell states?

In the "Superposition" Microsoft quantum katas (https://github.com/microsoft/QuantumKatas/blob/master/Superposition/ReferenceImplementation.qs) the solution for Task 7 looks like this: ...
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### Can we simulate quantum many-body systems with IBMQ Experience?

Consider physical systems such as electrons in metals, or Bose-Einstein condensates, or any crystal, which are realised in the real three-dimensional space. If we want to simulate these systems on a ...
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### Are all operations simply matrix multiplication?

In the most simple example I can think of, we have: a linear operator $A$, which is also a 2 x 2 matrix. a vector $|v_i⟩$, which can be considered a 2 x 1 matrix. If we see an example of an ...
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### What is the name for quantum gates that can be reversed?

Sorry if this question sounds too basic. But I can't find a word for those quantum gates than can be reversed (exchanging the target qubit with the control qubit) and still performs the same operation....
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### How to derive the way a controlled $U$ gate acts on an input state?

Wikipedia states that a controlled U gate maps the basis states to the following:  |00\rangle \mapsto |00\rangle\\ |01\rangle \mapsto |01\rangle\\ |10\rangle \mapsto |1 \rangle \otimes U |0 \...
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### Understanding how control gates are written in tensor notation

I'm very confused about the tensor representation of Control gates. I had thought that all control gates were of the form $P_0 \otimes I+P_1\otimes \hat{A}$, where this does nothing to the first qubit ...
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### The control phase gate in Quantum fourier transform and the question it brings up regarding control gates in general

I have a question that's arose from reading "Quantum computing explained" by David McMahon. On page 212 there's an aspect of his description of the quantum Fourier transform which I don't understand . ...
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### Why is $Z_1Z_2$ spanned by this set ? Surely it's too small?

In the context of stabilizer codes my lecturer writes that $Z_1Z_2$ is spanned by $\{|000\rangle,|001\rangle,|110\rangle\, |111 \rangle \}$. But I don't see how this spans the matrix as it's given by ...
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### Help with understanding Unitary Operator of Quantum Optical Fredkin Gate

I'm referring to the textbook "Quantum Computation and Quantum Information" 10th Anniversary Edition by Nielsen and Chuang. Chapter 7.4 has a Box 7.4 which introduces the Quantum Optical Fredkin Gate....
### How to do a $C-PH$ gate in google cirq
I know that I can just use the $RZ$ gate to replace the $PH$ phase gate. But I need a way to implement the controlled phase gate $C-PH$ this cannot just be replaced with a $CRZ$ gate.