Questions tagged [quantum-gate]
For questions regarding usage, performance, implementation, application or theory related to quantum gates.
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How to simulate a $CNOT$ only using a single qubit?
I am looking to do a $CNOT$ on itself, i.e., if the qubit is in $|0\rangle$ it stays in $|0\rangle$ and if it is in $|1\rangle$ it becomes $|0\rangle$. We are allowed to use $H$, $X$, $Z$, and $CNOT$ ...
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Qiskit library.gaussian() does not accept parametric expression
I'm trying to build a gaussian pulse in qiskit where I keep the amplitude as a parameter but for the followig code
...
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What are necessary and sufficient conditions for the output of a parametrized unitary $U(\theta)$ to be smooth?
Let us consider a unitary $U$ parameterised by $\theta \in \mathbb{R}$, i.e, $U(\theta)$. What are the necessary and sufficient conditions for the output states of this unitary to be smooth? One ...
glS♦
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Visualizing Y-gate operation to achieve quantum state
In the below snippet how qc.y(1) helps to achieve the quantum state $i|10\rangle$ ?
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How do qubits interact to form logic gates?
How do qubits interact to form, say, CNOT gates? There are very few comprehensive explanations of how quantum computing works. They all use obscure metaphors that don’t make sense (like Schrödinger’s ...
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Can you twist a qubit?
Is it possible to operate on a single qubit by a map which has a nonzero degree?
Let $|c\rangle=c_0|0\rangle + c_1|1\rangle$ represent a qubit state where $c_0,c_1 \in \mathbb{C}$ and $|c_0|^2+|c_1|^2=...
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Sufficient conditions for a single-qubit unitary to be the identity
Say I have a unitary $U = e^{-iHt}$ where $H = \alpha X + Z$.
First, suppose $U = I$. Then it rotates a set of initial states to themselves. Say I'm working on a computational basis, then on the Bloch ...
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How are elementary quantum gates realised?
When expressing computations in terms of a quantum circuit, one makes use of gates, that is, (typically) unitary evolutions.
In some sense, these are rather mysterious objects, in that they perform "...
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Regarding the inductive proof that any Clifford gate can be made of Hadamard, phase and c-not
In Exercise 10.40 of Nielsen and Chunang's textbook, the reader is supposed to construct an inductive proof of Theorem 10.6 that any Clifford gate can be made of Hadamard, phase and c-not. There it is ...
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Are there any other published quantum factoring algorithms that are simpler or more efficient than Shor’s?
How many qubits and what is the minimum number of gate operations needed to factor an n-bit integer? Are there any other published algorithms that are simpler or more efficient?
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Is it physically or algorithmically possible to implement continuous observation of parameter changes in a quantum gate?
Since direct observation of qubits collapses the quantum state and prevents the original state from being obtained, does continuously monitoring the parameters of a quantum gate collapse the quantum ...
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Post-selection on pennylane
I want to do something like this:
For a single-qubit
Apply Hadamard -> Time_evolution -> Phase_damping -> Hadamard -> Post-selection -> Get CFI(classical fisher info)
Density matrix ...
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How to represent two gates addition on Qiskit composer. we can do tensor product and multiplication but how to do Addition
How to represent two gates addition on Qiskit composer we can do it in python code by using qiskit library but I would like to visually see how addition of two operators look like in composer.
I am ...
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How does error accumulate when entangling two distant qubits with limited connectivity?
My goal is to minimize accumulated error when entangling two qubits that cannot be entangled via a single native two qubit gate operation.
I have a coupling map/graph for the qubits of an IBM quantum ...
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A Toffoli gate can be decomposed into a circuit of 1- and 2-qubit gates
While reseaching a way to implement a 3 qubit Toffoli gate, I came across this circuit:
However, I cannot find a proper source for this circuit. Can anyone link a cited paper.
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How to calculate number of qubits required for Grover Algorithm while constructing it's oracle and diffuser for any Specific Algorithm or Hash?
I am reading a paper titled, " (Towards Post-Quantum Secure Symmetric Cryptography:
A Mathematical Perspective)". Here, I am able to understand the gate counts and T-depth calculations. ...
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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
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What are the possible gates that I can use to vary input states before CNOT?
We know that the noise of the $\text{CNOT}$ gate varies depending on the input state before it.
What are the gates that I can put in the place of the 4 identity gates above to change the input state ...
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Application of transformation $U_d$ that maps any qudit state to $|d-1\rangle$
When giving examples of universal gate sets in the paper Qudits and High-Dimensional Quantum Computing, the authors first define the transformation that maps any given qudit state to $|d-1\rangle$:
$$
...
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Is {U, CZ, S} universal for quantum computation, for appropriate single qubit unitary U?
In the paper arXiv:0205115, Shi proves that the gateset $\{CX, U\}$ is computationally universal for quantum computation, where $U$ is a single qubit unitary such that $U^2$ does not preserve the ...
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How can I implement this unitary operation using CNOT and single qubit gates?
How can I implement the following unitary operation using CNOT and single qubit gates?
$$U =\begin{bmatrix}1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0\\
0 & ...
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Given a COMPLEX unitary matrix, how can I construct a unitary gate in Qiskit?
It seems that it is fairly easy to construct a unitary gate given a real unitary matrix. However, I have tried several methods with a complex unitary matrix, but they all seem to be not working. How ...
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Half Adder using CNOT Gates
As per this schematic of qubits, how this explanation is correct --"If you look again at the four possible sums, you’ll notice that there is only one case for which this is 1 instead of 0: 1+1=10....
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What is the quantum circuit complexity of a multi-control Y-gate with n control bits and 1 output bit?
It is known that many multicontrol quantum gates consist of sets of elementary gates, and there seems to be no authoritative way to give the complexity of such multicontrol quantum gates. So using one ...
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What is the quantum circuit to prepare a Bell state?
I was watching some lectures on qubits. They were talking about how to generate a Bell state. They described it as follows:
Prepare state 00:
$$\left |0 \right> \otimes \left |0 \right>$$
Apply ...
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Seeking Programming Projects and Tools for Quantum Gate Decomposition Implementations
The Solovay-Kitaev theorem shows that "this approximation can be made surprisingly efficient, thereby justifying that quantum computers need only implement a finite number of gates to gain the ...
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Can we write a sum of unitary gates as an equivalent product of unitary gates?
If I did it correctly, in an answer to a question about Bell's states preparation, I found true that:
$$CNOT \space \space (H \otimes I) \space CNOT = ( X \otimes X + Z \otimes I ) \frac{1}{\sqrt{...
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Inverse channel of the Pauli 4 POVM
I'm currently grappling with a challenge in comprehending the inverse channel of the Pauli 4 POVM. The POVM elements are defined as follows:
$
M_0 = \frac{1}{3} |0\rangle\langle0|, \quad M_1 = \frac{1}...
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Show how the Bell state arises from the circuit with Hadamard and CNOT, using matrix notation
I understand that starting with
,
we can get to $\vert \Phi^+ \rangle$. First, we start with $\vert Q_1 \rangle \otimes \vert Q_2 \rangle = \vert 0 \rangle \otimes \vert 0 \rangle$ and then applying ...
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Computing the evolution of expectation values of the Pauli observable
I have a quantum state described by $N$ qubits, and I don't know anything about this quantum state except the expectation value of the single-qubit Pauli observables of the $i$-th qubit ($\langle X_i \...
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Conditional quantum circuits
Let's suppose that we have the following $\text{GHZ}$-state
$$|\psi\rangle = \frac{1}{\sqrt{2}}|a_1a_2a_3a_4\rangle + \frac{1}{\sqrt{2}}|b_1b_2b_3b_4\rangle$$
By using quantum gates, can we evaluate $...
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Toffoli Gate Matrices
Here are the different toffolis (or maybe one of them is toffoli and the others are very similar to toffoli gates)
My question is:
we know the matrix of the number 1 Toffoli:
What are the matrices ...
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CNOT and quantum entanglement
I have the following problem:
"Consider two parties: Alice in possession of the one-qubit state |ψ⟩ = α|0⟩ + β|1⟩, and Bob who starts with a qubit in the state |0⟩
Show that Alice can teleport ...
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Why can we simulate any measurement involving $U=R+iQ$ using $U'=R\otimes I+Q\otimes R_x(2\pi)$ instead?
In a book named "INTRODUCTION TO QUANTUM ALGORITHMS VIA LINEAR ALGEBRA", the authors say:
For any complex $N×N$ matrix $U$, we can uniquely write $$U = R + iQ$$
Assume we have $$ U' = R \...
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What are the possible non-entangling two-qubit gates?
The non-entangling gates in $ SU_4 $ contains the entire group of gates of the form
$$
SU_2 \otimes SU_2.
$$
It also contains
$$
\zeta_8 SWAP= \zeta_8 \begin{bmatrix}
1 & 0 & 0 & 0 \\
0 &...
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Does there exist an efficient gate that swaps values of different superposition kets?
Is there an efficient gate that swaps values of different superposition kets?
Let $ \alpha_i, \beta_i $ be string in $ \{0,1\}^n$. I'm wondering if there are known results about the existence of a ...
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CNOT gate effect on 2 qubits
If the CNOT gate applies a NOT on the target qubit if the control qubit is a 1 and the control qubit was in superposition (for example in the $|+\rangle$ state), wouldn't this break the superposition ...
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How to alter the result of (somewhat) randomly generated circuits?
I create randomly generated circuits by iterating through a list of the gate set (in my case [$CX,SX,RZ,X$]) and adding the gate to the circuit. (In the case of the $CX$ gate we look at the topology ...
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Quantum Crosstalk in gate scheduling with different gates
I am working on quantum crosstalk, specifically on CNOT and SWAP gate operations that lead to crosstalk. I have encountered works that decompose CNOT and SWAP with iSWAP and CZ gates. I would like to ...
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Apply Hadamard on a qubit in a register
I want to implement a Hadamard gate on a single qubit in a register.
Given two qubits
q0 := $|0\rangle$ and
q1 := $|+\rangle$
I would like to use a Hadamard gate on the first qubit (q0).
My intuition ...
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Functional form of the drive of IBMQ machines
I am trying to apply some ML techniques to try and find out pulse sequences to implement different kinds of gates using Qiskit Pulse. For the ML part, it is necessary for me to know the Hamiltonian of ...
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How to apply error-correction to the swap test circuit?
Swap test is a simple quantum circuit to measure the inner product of two quantum states [Wiki: swap test], it only contains three quantum gates. However, due to the error in the real quantum computer ...
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What is the mathematical intuition behind deferred measurement? [duplicate]
Please give a complete proof of the principle of Deferred Measurement Principle, including careful notation (preferably explaining the meaning of each symbol) and rigorous mathematical reasoning (...
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How many single and double qubit gates are required to create a uniform superposition of vertices of a Johnson Graph J(n,r)?
Can I in $\tilde{O}(r)$ number of gates (single and double qubit) create a uniform superposition of vertices of Johnson Graph $J(n,r)$? I would like to create a state $|\psi\rangle = \frac{1}{\sqrt{n \...
CommunityBot
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Obtaining the unitary matrix of a gate in analytic form in qiskit
Is there any way to obtain the unitary matrix of single way in analytic form?
In numerical form, I could use a workaround like this (i.e. for an X Gate):
...
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What are the transversal gates of the $[[5,1,3]]$ code?
What are the transversal gates of the perfect 5-qubit code ( [[5,1,3]] code) ?
Since this is a stabilizer code we have transversal Pauli gates.
Are there any others?
I am primarily interested in ...
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Amplitude amplification in Grover algorithm
In "Quantum Computation and Quantum Information", they talk about Grover search. One part of the Grover search is Amplitude amplification:
But i think the red line is not true. Because i do ...
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General parametrisation of an arbitrary $2 \times 2$ unitary matrix
From Nielsen & Chuang's Quantum Computation and Quantum Information (QCQI):
Since $U$ is unitary, the rows and columns of $U$ are orthonormal, form which it follows that there exist real numbers $...
glS♦
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New mode of Quantum and - or gate
I’m Aurelio, a computer engeneering student and I would propose a new quantum gate that maybe could be interesting to implement and use. I don’t know if such idea is already known but I have not found ...
glS♦
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Can any Qiskit circuit be converted to a gate?
I am trying to convert the following qiskit QuantumCircuit to a gate using to_gate() method.
...
