Questions tagged [quantum-gate]
For questions regarding usage, performance, implementation, application or theory related to quantum gates.
890
questions
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After creating the Ising Hamiltonian, how it can be used in QAOA to find the optimal solution? Instead of using quadratic program
qubitOp, offset = qp.to_ising()
print('Offset:', offset)
print('Ising Hamiltonian:')
print(str(qubitOp))
5
votes
2answers
2k views
What is the square root of the NOT gate?
I have encountered different matrix of operator "the Square Root of NOT gate".
For example, the matrix is specified here:
$\sqrt {NOT} = \frac{1}{2}\left( {\begin{array}{*{20}{c}}
{1 + i}&...
4
votes
1answer
50 views
CNOT error rate of 1 in IBM Quantum Experience
I have noticed that some CNOT gates (for instance, between qubits 1 and 2 in ibmq_casablanca) display an error rate of 1 while typical error rates are of course ...
2
votes
1answer
40 views
What's free evolution for a period T?
I am currently studying a model of a quantum (atomic) clock. And in this paper, I came across the term "Free evolution for a period T":
Free evolution for a period T where a phase ...
0
votes
0answers
40 views
How do you build the modified Toffoli gate using only local unitary and CNOT operations?
How do you build a circuit for a modified Toffoli gate using only local unitary operations and CNOT operations? The two-qubit unitary operation is given by: $\text{diag}\{1, 1, 1, e^{i\phi}\}$.
1
vote
1answer
24 views
Quantum gates with respect to phase angles
We can say that
$X (\cos \frac{\theta}{2} |0\rangle + e^{i \phi}\sin \frac{\theta}{2} |1\rangle) = \cos \frac{\pi-\theta}{2} |0\rangle + e^{-i \phi}\sin \frac{\pi-\theta}{2} |1\rangle$,
a fact that ...
2
votes
1answer
27 views
Gate Cost to Transform Superposition of Hamming weight 1 states to superposition of arbitrary basis states?
Say you have something like a general-coefficient $n$-qubit W-state, i.e.,
$$
|\psi\rangle\equiv\sum_{j=1}^n a_j X_{j}|0\rangle^{\otimes n} \ ,
$$
where $a_j$ are normalized complex coefficients. ...
3
votes
1answer
42 views
How does $|00\rangle$ evolve through an Hadamard and a CNOT gate?
If we have this given circuit:
So the output for $|0\rangle$ will be: $\frac{1}{\sqrt{2}}\left(|00\rangle + |11\rangle\right)$
And we have this given circuit:
What will be the output for $|00\rangle$...
3
votes
1answer
42 views
Toffolli upside down - an equivalent circuit
It is known that an "upside-down" CNOT is equivalent to a "normal CNOT" surrounded by Hadamard gates as shown in this picture.
I am wondering whether there is a similar circuit ...
2
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1answer
68 views
Is RYY gate not available in IBM Quantum Composer?
If so, why? How to create the RYY-gate in the composer?
0
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1answer
54 views
constructing a CNOT gate using a CZ and H gates
How can I construct a CNOT gate using a CZ and H gates?
And I also need to prove it using these identities:
\begin{equation}
H = (1/\sqrt{2})(X+Z)\\
XZ = -ZX\\
X^2 = Z^2 = H^2 = 1\\
HXH = Z\\
HZH = X\\...
2
votes
2answers
148 views
Making a Controlled-Z from a CNOT
How can we draw a circuit that is based on the gates $H, CZ$ that implements $CNOT$.
I know that the $H$ gate is like that:
And also the $CZ$ gate is:
But I'm not sure how to draw this with the ...
2
votes
1answer
43 views
How do you compute the compiled unitary of a quantum circuit comprised of different $n$-input gates?
Given a quantum circuit consisting of two qubits, how is the compiled unitary of the circuit computed when we have different input type gates? (X-gate, H-gate are single-input gates, CNOT is a 2-input ...
2
votes
1answer
46 views
Formulate Controlled-Not as mapping (including modulo-2 addition)
We often see that the controlled-not gate is written as
$CNOT |x y \rangle = |x\rangle |x \oplus y\rangle$.
Now, would it be possible to further expand this to get a general equation?
$$(\alpha_0 |0\...
3
votes
2answers
40 views
Method to derive Matrix description of a circuit [duplicate]
This question is about finding a matrix description of a specific circuit. I am learning quantum computing through edX's Quantum Information Science lecture series. The question below is the one I am ...
0
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1answer
62 views
Does a CNOT quantum gate violate no cloning theorem? [duplicate]
I am a curious quantum computing learner. :)
Once observe the CNOT gate:
as you can see there it converts a |+> to |-> in the top or to say in another way it clones the |->
state. So does ...
0
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0answers
47 views
Is there a simple quantum gate that shows off the power of Quantum interference?
I'm trying to build a deep understanding of where the power of quantum computing comes from when compared to probabilistic computing. A naive observation might be that probabilistic computing would be ...
2
votes
0answers
19 views
What is the relationship between the (sx) error rate listed in calibration and the angle/amplitude errors calculated using the fitter?
The IBM Quantum services website lists calibration statistics for their devices, including the (sx) error rate per qubit, which is listed as a single number. One can also manually calibrate a device ...
4
votes
1answer
87 views
If $C$ is a Clifford circuit, is there necessarily a Clifford circuit $C'$ such that $CT=TC'$?
Let $C$ be a Clifford circuit, is there necessarily a Clifford circuit $C'$ such that $CT=TC'$ (where $T$ is taken as applying the $T$ gate to the same qubit on both sides)?
3
votes
1answer
49 views
Why are 3, rather than 2 gates used in quantum variational circuits?
In the hello many worlds tensorflow tutorial and in the lockwood paper (2020) I have seen that often in QVC the following combination of gates is used:
$R_z(\theta), R_y(\theta), R_x(\theta)$
I am ...
4
votes
2answers
178 views
Can I use Grover's algorithm for a function that has multiple arguments which satisfy it?
Let's say we have a function $f(x)$, where $f(011) = 1$, and $f(111) = 1$.
Can I still use Grover's algorithm with this function, and receive the result of either $011$, or $111$?
2
votes
1answer
57 views
How to calculate the evolution of ket states through a simple quantum circuit?
I am having difficulties with the calculations of qubits.
I think I can do them, but it feels so massivly inefficient!
In this tutorial grover's algorithm for example, there's a simple oracle given ...
1
vote
2answers
113 views
Intuitions about probabilities relating to evolving a two-qubit state through a CNOT gate
If the initial state of $|x_0\rangle = \alpha |0\rangle + \beta |1\rangle$ and $|x_1\rangle =|0\rangle$, and the final state at the barrier is $|10\rangle$ (in the form $|x_1x_0\rangle$), what would ...
1
vote
2answers
106 views
Given 2 unknown qubits, which series of gates can put them in an equal superposition of $\vert 00 \rangle$ and $\vert 11 \rangle$?
You have 2 qubits, the states of which are unknown to you. They are either in the state $\vert 0 \rangle$ or $\vert 1\rangle$. Which sequences of gates can be applied so as to put the system in the ...
1
vote
1answer
77 views
How to keep angles in degrees into quantum circuit using qiskit?
Qubit in polar form $$\left|\psi\right\rangle=\cos(\theta/2)\left|0\right\rangle+\sin(\theta/2)\left|1\right\rangle $$
Now lets say i want to keep $\cos(\theta/2) = 50.400 $ degrees angle and $\sin(\...
3
votes
1answer
65 views
How do I show that $R_z(\theta)=e^{-iZ\theta/2}$?
I know that an $R_z (\theta)$ gate is equivalent to the unitary transformation $e^{-iZ * \theta/2}$ but I'm not sure how we get there.
I know that for every Hermitian matrix there is a corresponding ...
0
votes
1answer
28 views
What is the outcome when you apply 2 hadamard gates on CNOT
So when I run through risk, it displayed it had an equal 25% chance to get 00 01 10 11 respectively.
I know how the CNOT output looks like when you apply hadamard gate on control part before CNOT, but ...
2
votes
1answer
42 views
Can we convert two single qubit states into single mixed state?
Consider two qubits
$$\left| \psi_1 \right> = \alpha \left|0\right> + \beta \left|1\right>$$ and $$\left| \psi_2 \right> = \alpha_1 \left|0\right> + \beta_1 \left|1\right>$$
Is it ...
5
votes
1answer
137 views
Does anyone know the list of all known universal sets of quantum gates?
Does anyone know the list of all known universal sets of quantum gates? I know only two such sets: Cliffords + $T$ and rotations + CNOT.
0
votes
1answer
45 views
Transformation of Operation Order for H,T Single Quantum Gate
Suppose I want to apply an $H$-gate transformation to an arbitrary quantum state $|\sigma\rangle$, and then a $T$-gate transformation to the arbitrary quantum state $|\sigma\rangle$.
The quantum state ...
3
votes
0answers
60 views
Calculating length of code words in quantum information(compression)
I was studying this article by Boestrom and Felbinger.
We define the significant length of the codewords in the preparation of the communication protocol : $$L_c(w_i) = \lceil log_k(i) \rceil$$
We ...
2
votes
0answers
74 views
is it possible to eliminate a certain possibility of an outcome of 3+ qbits
Let's say I have n qbits each in a superposition $\begin{pmatrix} \frac{1}{\sqrt{2}}\\ \frac{1}{\sqrt{2}} \end{pmatrix}$ so each possible outcome has a probability of $\frac{1}{2^n}$. Is it possible ...
3
votes
2answers
115 views
Basic gates sets
There are several basic gate sets allowing to construct any gate on a quantum gate-based computer, e.g.:
$H$, $T$, $CNOT$ (sometimes enriched to $H$, $T$, $S$, $X$, $CNOT$),
rotations $Rx$, $Ry$ and $...
2
votes
2answers
98 views
Estimating output amplitudes of quantum circuits as GapP functions
Let's fix a universal gate set comprising of a Hadamard gate and a Toffoli gate. Consider an $n$ qubit quantum circuit $U_{x}$, made up of gates from that universal set, applied to initial state $|0^{...
3
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1answer
94 views
How to prove the fundamental equation in the theory of angular momentum $\sum_{l=x,y,z}\langle J_l^2\rangle\le\frac{N(N+2)}{4}$?
How to prove the inequality$$\sum_{l=x,y,z}\langle J_l^2\rangle\le\frac{N(N+2)}{4}$$
where $J_l = \mathop{\Sigma}_{i=1}^N \frac{1}{2}\sigma_l^{i}$, and $\sigma_l^i$ is pauli matrix acting on the $i$th ...
1
vote
1answer
80 views
Why is a 15-qubit IBM quantum computer not working correctly?
I just wanted to implement an algorithm for adding two 2-bit binary numbers. And it works, but only on an IBM 32-qubit simulator. And on a real 15-qubit computer, ibmq_16_melbourne, it produces very ...
2
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0answers
31 views
When writing data into qRAM, can I do it in a superposition state?
In general, quantum algorithms are said to be hybrid algorithms.
Especially when storing data in qRAM, it seems to be done through classical calculations.
Is it possible to write this part directly to ...
7
votes
2answers
955 views
Characteristics of the IBM quantum computer
On the IBM Quantum Composer website, there are characteristics of qubit computers. For example, ibmq_16_melbourne.
But there is no description anywhere of what:
...
1
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1answer
75 views
What is the name for the gate rotating around $Z$ by $\pi/8$?
I think similar to $R_z\big(\frac{\pi}{4}\big)$ gate named T gate, how to standardize the name $R_z\big(\frac{\pi}{8}\big)$?
0
votes
1answer
42 views
Understanding Deutsch Algorithm
From the image below, if we focus on the first qubit, we know after Hadamard (state 1) $|0\rangle$ will become $|+\rangle$ and the second qubit $|1\rangle$ will become $|-\rangle$.
What exactly would ...
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2answers
68 views
Exercise 4.6 in Quantum Computing and Quantum Information Nielsen and Chuang
Question 4.6: One reason why the
$R_\hat{n}(θ)$ operators are referred to as rotation operators is the following fact, which
you are to prove. Suppose a single qubit has a state represented by the ...
0
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0answers
31 views
After a photon passes through the phase shifter, does it gain the geometric phase or dynamical phase?
In Quantum Mechanics, the phase can be divided into geometric phase and dynamical phase. In mach-zehnder interferometer, after the photon passes through the phase shifter, what kind of phase does it ...
2
votes
2answers
124 views
Is Grover's algorithm suitable for this search problem?
I wonder if we can utilize Grover's algorithm to solve the following search problem.
Leetcode 33. Search in Rotated Sorted Array
Example 1:
Input: nums = [4,5,6,7,0,1,2], target = 0
Output: true
...
4
votes
1answer
100 views
Do global phases matter when a gate is converted into a controlled gate?
Let's say that we have a unitary matrix M such that:
$$
M = e^{i\pi/8}\begin{pmatrix}
1 & 0 \\
0 & e^{i\pi/12} \\
\end{pmatrix}
$$
If we were to apply this unitary matrix to the state $|1\...
1
vote
0answers
38 views
Iterative Phase Estimation with noise vs standard Quantum Phase Estimation with noise
I am doing Qiskit Lab 4 about Iterative Phase Estimation. I created a circuit implementing IPE for theta = 1/3 (phase of 2pi/3). Here's the circuit:
It seems to do okay if I run it without noise in a ...
1
vote
2answers
69 views
How do I get the Unitary matrix of this circuit without using 'unitary_simulator'? [duplicate]
I am using jupyter notebook and qiskit. I have a simple quantum circuit and I want to know how to get the unitary matrix of the circuit without using 'get_unitary' from the Aer unitary_simulator.
i.e.:...
4
votes
1answer
74 views
I don't understand unitary of ${e^{iAt}}$ from HHL algorithm
I tried to implement the following circuit in the image below but with the red circled gates replaced with a unitary controlled ${e^{iAt/2}}$ and controlled ${e^{iAt/4}}$
The image came from this ...
0
votes
1answer
27 views
Why is my unitary matrix using linear algebra not matching the 'get_unitary' simulation?
I am using jupyter notebook and qiskit. I have a simple quantum circuit and I want to know how to get the unitary matrix of the circuit without using 'get_unitary' from the Aer unitary_simulator.
i.e.:...
3
votes
3answers
320 views
Can we write Pauli-Y gate without even complex part?
I was just curious, why is the quantum gate Y-gate (Pauli-Y gate) written in terms of complex numbers? We can actually write Pauli-Y gate as
$$
Y = i * \begin{bmatrix} 0 & -1 \\ 1 & 0 \end{...
4
votes
2answers
91 views
Are these two 'divided by two' terms related?
I have a question about the two equations:
Any matrix in $SU(2)$ could be parametrized as
$$
R_{\hat{n}}(\theta) = \cos\left(\frac{\theta}{2}\right)I-i\sin\left(\frac{\theta}{2}\right)(\hat{n}\cdot\...
