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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43 views

Trying to make unreversable operation in the quantum circuit

I want to make a 2 qubit circuit such that the ununitary program will transform the regular basis in the way that: $|0 0\rangle \to |00\rangle$ $|0 1\rangle \to |01\rangle$ $|10\rangle \to |01\...
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Implementing B92 protocol on IBM Qx

I wanted to implement the B92 protocol on IBM Qx. Implementing the protocol would require that a particular qubit should not be measured when using a particular base i.e. there should be no output at ...
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1answer
40 views

Dephasing in graph states

In a recent paper Graph States as a Resource for Quantum Metrology. In the Appendix it states: We model an $n$ qubit graph state $G$ undergoing iid dephasing via $$G \to G^{\text{dephasing}} = \...
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2answers
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How to build a CNOT out of universal CCNOT gates?

By the classic theory of computation, every classic gate can be build with NAND operation, for example XOR ("the classic CNOT") is build by net of NANDs, I saw that the quantum analogue for NAND can ...
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2answers
177 views

Query on paper on entanglement in graph states

Quick question on the paper Entanglement in Graph States. On page 14. a definition of a graph state: Given $|+\rangle=\frac{1}{\sqrt{2}}(|0\rangle + |1\rangle)$. Let $G=(V,E)$ be a graph. The ...
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1answer
35 views

How to factor Ising YY coupling gate into product of basic gates?

Let us consider Pauli YY coupling gate of the following form $$ YY_\phi= \left(\begin{matrix} \cos(\phi) & 0 & 0 & i \sin(\phi) \\ 0 & \cos(\phi) & -i \sin(\phi) & 0 \\ ...
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Exact functions of a single-iteration Grover Search Algorithm's operators

I'm doing a practice assignment where I'm asked to identify specific features of the Grover Search Algorithm's second operator (picture in post, further on "$Us$"), which mirrors the system relative ...
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1answer
34 views

Decomposing a controlled phase gate into CNOTs

I'm trying to understand the following derivation of decomposing a controlled $R_k$ (phase) gate into a combination of CNOTs and single qubit gates, but there's one main thing about the process that ...
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3answers
129 views

How do I prove that the Hadamard satisfies $H\equiv e^{i\pi H/2}$?

How can I demonstrate on the exponential part equality of the Hadamard matrix: $$H=\frac{X+Z}{\sqrt2}\equiv\exp\left(i\frac{\pi}{2}\frac{X+Z}{\sqrt2}\right).$$ In general, how can I demonstrate on: $\...
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2answers
102 views

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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1answer
107 views

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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31 views

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 ...
4
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1answer
72 views

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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2answers
75 views

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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2answers
111 views

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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1answer
44 views

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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Could the Hadamard gate have been constructed differently with similar characteristics?

Say we had a Hadamard-like gate with the -1 in the first entry instead of the last. Let's call it $H^1$. $$H = \begin{bmatrix}1&1\\1&-1\end{bmatrix}$$ $$H^1 = \begin{bmatrix}-1&1\\1&...
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1answer
54 views

How many ancilla qubits to use with Multiple-Control Toffoli (mct) gate in Qiskit?

The Multiple-Control Toffoli (mct) gate takes as input: 1. a register containing the control qubits, 2. the target qubits and 3. a register containing ancilla qubits. I don't know how many ...
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Code for implementing MCT in qiskit [duplicate]

I am trying to implement 7 control toffoli gate in qiskit .
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54 views

Physical Interpretation of Pauli Matrices as Polarization Check

We know that the Pauli matrices are: $$\sigma_x = \begin{bmatrix}0 & 1 \\ 1 & 0\end{bmatrix}, \sigma_y = \begin{bmatrix}0 & -i \\ i & 0\end{bmatrix}, \sigma_z = \begin{bmatrix}1 & ...
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2answers
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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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3answers
163 views

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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1answer
280 views

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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1answer
300 views

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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435 views

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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1answer
63 views

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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1answer
80 views

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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1answer
66 views

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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3answers
67 views

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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1answer
46 views

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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1answer
69 views

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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2answers
124 views

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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4answers
185 views

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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1answer
61 views

How are measurements on $Z$ and $X$ axes interpreted in the Bloch sphere?

I'm having trouble understanding how the measurement on $z$ and $x$ axes can be interpreted in terms of the Bloch sphere representation. . I know that the state can be written as $$∣𝜓⟩=\cos(𝜃/2)|...
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1answer
168 views

Why use U2 and U1 gate in IBM quantum computers?

I was wondering why IBM's computer were using U1 and U2 gates as part of there basis gates since as I understood, they are particular cases of the U3 gate. Why not just use U3 gate instead ? Thanks ...
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73 views

Can one operator commute with four other operators?

I want to know whether I can have a operator $A$ which commutes with four other operators $M_1$, $M_2$, $M_3$, and $M_4$ (for instance, drawing the operators $M_j$ from $\{H,I,X,Y\}$). When can we ...
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Is $M = a \mathbb{I} - ib \sigma_Z$ a valid representation in terms of logic gates?

I have a matrix $M= \begin{pmatrix} a - ib & 0 \\ 0 & a + ib \end{pmatrix}$, where $a$ and $b$ are real numbers and $i = \sqrt{-1}$. I need to represent this matrix in terms of the quantum ...
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1answer
64 views

How to reduce circuit elements of a decomposed $C^2(U)$ operation?

This question refers to Nielsen and Chuang's Exercise 4.22: Prove that a $C^2(U)$ gate (for any single-qubit unitary U) can be constructed using at most eight one-qubit gates, and six controlled-not ...
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204 views

How is the Controlled Z Gate implemented?

How are 2 qubit Controlled Z gates (1 control / 1 target) typically implemented? Do we seek physical realizations of this gate, or have an alternate decomposition?
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140 views

How do 2 Hadamard gates act on a single qubit?

When I perform $2$ Hadamard $H$ gates on a single qubit, why is the probability of getting $0$ as the outcome 100%? Why is it not 50% 0 and 50% 1 instead? Why is the second $H$ gate not putting the ...
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1answer
48 views

Does the general form of a unitary operator define strict signs for the second column?

As per IBM's documentation for quantum circuits, the general unitary operator is defined as: $$\hat{U}=\begin{bmatrix}\cos(\frac{\theta}{2})&-e^{i\lambda}\sin(\frac{\theta}{2})\\e^{i\phi}\sin(\...
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1answer
48 views

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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1answer
60 views

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 ...
2
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1answer
45 views

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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1answer
39 views

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....
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1answer
37 views

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.
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How to make a time rotation in Qsharp like in Quirk spinning gates?

Qsharp have Rx Ry and Rz gates for rotation, but I need to apply a gate that leaves the Qbuit rotating continuosly like in Quirk spinning gates. https://algassert.com/quirk#circuit=%7B%22cols%22%3A%5B%...