Questions tagged [quantum-gate]
For questions regarding usage, performance, implementation, application or theory related to quantum gates.
285
questions
3
votes
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views
types of states that can be created with a given number of entangling gates
I want to know if it is possible to say something in general about the "richness" or "complexity" of quantum states that can be created using a given number of entangling 2-qubit ...
- 1,180
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votes
2
answers
157
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Expressing CNOT in the eigenbasis of $X$ (Preskill lecture notes eq. 7.6)
In chapter 7, equation 7.6 says CNOT works as follows:
CNOT: $\frac{1}{\sqrt{2}} (|0\rangle + |1\rangle )\otimes |x\rangle \rightarrow
\frac{1}{\sqrt{2}} (|0\rangle + (-1)^x |1\rangle ) \otimes |x\...
- 549
3
votes
2
answers
460
views
How to implement the exponential of an outer product?
In exercise 6.7 page 258 in Nielsen and Chuang book, they have a Hamiltonian $H = \left| x \right\rangle \!\!\left\langle x \right| + \left| \psi \right\rangle \!\!\left\langle \psi \right|$ and the ...
- 335
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How do I embed classical data into qubits?
How do I embed classical data into qubits? I have a classical data [0 1] and I want to encode it as quantum amplitude to a superposition? What are the gates used to achieve that? I am a beginner to ...
- 61
3
votes
1
answer
895
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Matrix representation and CX gate [duplicate]
I am having hard time figuring out how the CX (controlled-NOT) gate is represented in the matrix representation.
I understood that tensor product and the identity matrix are the keys, and I ...
- 4,702
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votes
1
answer
190
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Eastin Knill Theorem and groups of transversal gates
The Eastin-Knill Theorem shows that the transversal gates always form a group and that moreover this group is a finite subgroup of the group of all unitaries.
For many codes, for example all self dual ...
- 2,556
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votes
1
answer
280
views
How to use Cirq to transpile circuit to custom native gate set?
I am trying to use Cirq to compile arbitrary quantum circuits to custom native gate sets, e.g., to use the Cirq compiler to generate quantum circuits for different quantum computers (IBM, Rigetti, ...
- 33
3
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1
answer
1k
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Quantum addition and modulo operation using gates
I have a matrix equation $X_{\text{new}}=AX_{\text{old}}$, where $A=\begin{bmatrix}1 & 1 & 1\\
2 & 3 &2\\
3&4&4
\end{bmatrix}\bmod 64$, and $X_{\text{old, new}}\in \{1,2,...64\}...
- 1,400
3
votes
4
answers
195
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Can you use Rz to flip from $|+\rangle$ to $|-\rangle$?
Here's the Rz matrix:
$$
Rz(\theta) =
\begin{bmatrix}
e^{-i\theta/2} & 0 \\
0 & e^{i\theta/2}
\end{bmatrix}
$$
As I understand it, Rz rotates around the Z axis on the Bloch sphere. Since $|+\...
- 3,978
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1
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How does quantum gate teleportation differ from state teleportation?
As described e.g. in this post, quantum gate teleportation can be framed as a variation of quantum state teleportation where a gate is applied beforehand on the receiver, and this results in the final ...
glS♦
- 21.7k
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2
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Measuring T1 and T2 constants on IBM Q
We have been asked to measure relaxation and dephasing times T1 and T2 on the IBM Q using the composer only, Qiskit not allowed. I am a bit confused about the way to do so. Can someone explain the ...
- 39
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votes
2
answers
133
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What is the name of this "ancilla based" process to implement gates
I just want to know if there is a specific name for the implementation of a gate on the top qubit with the help of the bottom qubit, represented on this image:
It looks like gate teleportation but it ...
- 1,142
3
votes
2
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170
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Minimal quantum OR circuit
The quantum OR circuit between $|a\rangle$ and $|b\rangle$ can be made out of 1 Toffoli and 2 CNOT gates, 1 ancillary qubit. Is there any other implementation? Or is this the minimal in the sense of ...
- 1,400
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Clifford gates are transversal What exactly does this transversal mean? What is the difference between non-Clifford gates and Clifford gates?
Clifford gates are transversal What exactly does this transversal mean? What is the difference between non-Clifford gates and Clifford gates? Why is it simple for Clifford gates to implement ...
- 69
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1
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Can the ancilla for Qiskit's mcx with mode="recursion" be dirty?
I think their implementation is close to the one from here which does use a dirty ancilla, but I just want to make sure
- 500
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442
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How does the cnx gate work in Qiskit (Python)?
Could somebody explain the cnx operator, and how it operates on its qubit parameters to flip the target qubit in Qiskit (Python)?
- 377
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0
answers
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Clock matrix vs matrix clock
In the process of research leading up to my previous question, I found out about matrix, vector & logical clocks.
The citation in the aforementioned question mentions clock and shift matrices. ...
- 3,272
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votes
1
answer
120
views
In quantum teleportation, does Bob's qubit depend on Alice's $\alpha$ and $\beta$ coefficients?
Does applying an operation to one half of an entangled pair affect the other?
As in the case of quantum teleportation when Alice applies CNOT to her half of the pair and the qubit she wants to send ($\...
3
votes
1
answer
371
views
Can we understand multi-qubit gates in terms of rotation groups?
I'm trying to reconcile (i) the statement that swapping two subsystems constitutes a rotation by $2\pi$ and (ii) the angle that is implied by the Hermitian generator of a SWAP gate.
I haven't tracked ...
- 5,715
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votes
1
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701
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What is the connection between $RX$ gates and $X$ gates (similar for $Y$ and $Z$)?
I am new to quantum gates but do not understand the connection between the $RX$ and $X$ gates. I know that
$$R X(\theta)=\exp \left(-i \frac{\theta}{2} X\right)=\left(\begin{array}{cc}
\cos \frac{\...
- 33
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votes
3
answers
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How can we construct a square root of NOT gate in Qiskit and IBMQ circuit composer using universal gates?
I have tried it with decomposing controlled S then conjugating with H gate. But I want to construct it using a minimum number of gates.
3
votes
1
answer
262
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Grover's Algorithm on a Database with more than 50% matching entries
The Setup for Grover's Algorithm is the following:
Given an oracle $f_O^{\pm}$ representing a Query on a Database with total $N$ entries $N$ of which $k$ are matching. Grover's Algorithm is used to ...
- 762
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votes
2
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607
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Computing expectation value of $|\langle z|C|0^n\rangle|^2$ over Haar random circuit
I am trying to understand the integration on page 4 of this paper. Consider a Haar random circuit $C$ and a fixed basis $z$. Each output probability of a Haar random circuit (given by $|\langle z | C |...
- 1,119
3
votes
1
answer
95
views
Does every code have a strongly transversal Pauli group?
A transversal logical gate for an $ n $ qubit code is a gate from the group of local unitaries
$$
\bigotimes_{i=1}^n U(2)
$$
which also preserves the codespace. For an $ ((n,K,d)) $ code we say a ...
- 2,556
3
votes
1
answer
375
views
Is it possible to express $U_1(\lambda)$ through the gates $R_x, R_y, R_z$ while maintaining the phase? In Qiskit for example
Is it possible to express gate $U_1(\lambda)$ through the gates $R_x, R_y, R_z$ while maintaining the phase? Both in principle and in practice (in Qiskit for example)?
The single gate $R_z(\lambda)$ ...
2
votes
1
answer
68
views
How to write an $n$-qubits parametric unitary as a linear combination of tensor products between parametric 2$\times$2 matrices?
As far as I understood, it should always be possible to decompose any $n$-qubits unitary $U$ into a linear combination of tensor products between $n$ complex matrices $W_i \in \mathbb{M}_{2 \times 2}$ ...
- 1,320
2
votes
4
answers
251
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Quantum circuit with one unknown gate
You are given a quantum circuit with around 4-5 gates connected. The catch is that you know all the gates and the connection except one gate.
For as many times as you want you can check what the ...
- 115
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votes
1
answer
288
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How to Construct Swap Gates from Permutation Matrix?
This is a follow-up question from here.
Let's say after an LUP decomposition, we have an 8x8 permutation matrix:
$ P^{-1} = \begin{bmatrix}
1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\
...
- 72
2
votes
2
answers
404
views
Is there a good way to mathematically write a CNOT operation over non-neighboring qubits in a circuit? [duplicate]
I was wondering if there is any way to present the CNOT matrix as we usually present single qubit operations
$$... 1 \otimes NOT \otimes 1 ...$$
I know that for adjacent qubits in a circuit we can ...
2
votes
1
answer
184
views
How do Hadamard and CNOT gates work on Qiskit SDK? Why is the output reversed?
Here is the code that I have been using on IBM Q Experience (should be the latest version of Qiskit). From my understanding it seems like the outputs of Hadamard and CNOT gates are reversed in a 2-...
- 23
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votes
2
answers
318
views
Matrix representation of SWAP on two qubit registers?
There is a matrix that can represent a swap gate-- a gate that essentially swaps two qubits. This matrix, $S$, is:
$$
\begin{bmatrix}
1 & 0 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & ...
- 373
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votes
0
answers
114
views
Is there a quantum operation that can transform a superposition of states into its complement?
Given a superposition of states "B" which is a subset of the suoerposition "A" of all possible states of a set of qbits, is there a quantum operation that produces superposition $R=...
- 235
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2
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291
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How can I find a quantum channel connecting two arbitrary quantum states?
Given two arbitrary density matrices $\rho, \sigma\in \mathcal{H}$ (they have unit trace and are positive), how do I go about finding a possible quantum channel $\mathcal{E}$ such that $\mathcal{E}(\...
- 137
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votes
2
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232
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Quasiprobability decomposition of the CZ-gate
I was trying to obtain the quasiprobability decomposition of the CNOT gate by using the information in this paper.
The authors give us the example for the CZ gate (Figure 2, i.e. the one below).
The ...
- 333
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votes
2
answers
224
views
Do quantum gates rotate a qubit around the Bloch sphere, or do quantum gates rotate the Bloch sphere around a qubit?
Do quantum gates rotate a qubit around the Bloch sphere?
Or do quantum gates rotate the Bloch sphere around a qubit?
"The simplest quantum gates are the Paulis: X, Y, and Z. Their action is to ...
- 303
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votes
1
answer
146
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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 ...
- 123
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votes
2
answers
210
views
Why does gate teleportation allow to implement nonlocal operations via local ones?
In (Gottesman and Chuang 1999), when discussing quantum gate teleportation, they mention how it can be used to implement nonlocal gates such as a CNOT, by only using (classically controlled) local ...
glS♦
- 21.7k
2
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1
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155
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How to generate matrix for swap(a, b) gate for n qubits
I am trying to simulate a swap gate that swaps two qubits of indices a and b where there are n qubits total. I understand how to make a truth table and generate a matrix based off of that for each ...
2
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3
answers
1k
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Creating a parameterized Operator in Qiskit
I'm trying to run a VQE for a specific custom Anzats. The Anzats is built up of an unitary matrix $U_H$, which I'm trying to created in this way:
...
2
votes
1
answer
312
views
Circuit construction and Dirac notation of the following operation
I have a state $$ |\tilde{\Phi_2}\rangle =\dfrac{1}{2^{3l/2}}\sum_{x=0}^{2^l-1}\sum_{y=0}^{2^l-1}\sum_{z=0}^{2^l-1}|0\rangle^{\otimes q}\otimes |x\rangle^{\otimes l}\otimes |y\rangle^{\otimes l}\...
- 1,400
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votes
1
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588
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FANOUT with Toffoli Gate
Figure 1.16: FANOUT with the Toffoli gate, with the second bit being the input to the FANOUT (and the other two bits standard ancilla states), and the output from the FANOUT appearing on the second ...
2
votes
1
answer
137
views
How does measuring a value of one operator affect the probability of measuring a value for another operator?
Suppose I have two non-commuting operators, $U_1$ and $U_2$ with eigenvalues $\lambda_{1,1}, \lambda_{1,2}$ and $\lambda_{2,1}, \lambda_{2,2}$, respectively. In order to determine how measuring one ...
- 21
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votes
1
answer
89
views
Is $e^{i\beta} R_Z(-2\beta)$ equivalent to $U_1(2\beta)$?
As far as I know the single qubit gate
$$
e^{i\beta\sigma_z} =
\begin{bmatrix}
e^{i\beta} & 0 \\
0 & e^{-i\beta}
\end{bmatrix}
= e^{i\beta}
\begin{bmatrix}
1 & 0 \\
0 & e^{-i2\beta}
\...
- 197
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votes
1
answer
164
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How would I compute a density matrix of a 2 qubit mixed state?
I am currently reading Nielsen & Chuang, and one of the questions asks to calculate a density matrix with the following mixed states, how would I do this?
$$
|00> \;with \;probability \; 2/4 \\
...
- 101
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votes
2
answers
313
views
How to construct a CU3 gate using only CX and U3 gates?
Knowing that CX and U3 (taking 3 parameters $\theta, \phi$ and $\lambda$) form a set of universal gates how can I construct an arbitrary CU3 gate using a decomposition of only CX and arbitrary U3 ...
- 45
2
votes
1
answer
272
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How do we perform a measurement of an arbitrary 1-qubit quantum state in any arbitrary orientation?
Let's imagine we have an arbitrary 1-qubit quantum system $\alpha \vert 0 \rangle + \beta \vert 1 \rangle$ Making a measurement in the +/- basis is equivalent to performing a Hadamard gate and then ...
- 85
2
votes
1
answer
145
views
Gate corresponding to $-I$
I am implementing a quantum circuit in Qiskit. I create the equal superposition state
$$
-|00\rangle + |01\rangle + |10\rangle +|11\rangle
$$
but I want to obtain the quantum state
$$
|00\rangle - |...
- 451
2
votes
1
answer
408
views
If CNOTs and single qubit gates are universal then why do we need to prove that controlled U operations can be composed by them as well?
In the book by Chuang and Nielsen they prove that controlled U operations can be made out of CNOTs and single qubit gates. But then they go on to prove that they are universal by showing that every n ...
- 841
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votes
1
answer
670
views
Can SWAP operators change trace of a product state? [closed]
I am currently reading https://arxiv.org/abs/1501.03099.
In the third part of the paper, "Measuring and detecting quantumness", the authors define the SWAP operators, use them on the initial ...
2
votes
1
answer
607
views
How do I compute the square root of the $Y$ gate?
I am trying to compute the square root of the Y gate.
$$Y_\theta =\begin{pmatrix}
\cos\theta & -\sin\theta \\
\sin\theta & \cos\theta
\end{pmatrix}$$
There are many ways for doing this. I ...
