Questions tagged [quantum-gate]
For questions regarding usage, performance, implementation, application or theory related to quantum gates.
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Exercise 4.16 in the Nielsen & Chuang book
In the 4.16 exercice in the Quantum Computation and Quantum Information (Michael A. Nielsen & Isaac L. Chuang), I don't understand why the correct answer is not this matrix :
$$
\left[ {\begin{...
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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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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 ...
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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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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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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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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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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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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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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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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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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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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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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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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:
$$CNOT \space \space (H \otimes I) \space CNOT = ( X \otimes X + Z \otimes I ) \frac{1}{\sqrt{...
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Computing the evolution of expectation values of the Pauli observable
I have a quantum state described by $N$ qubits, and I don't know anything about this quantum state except the expectation value of the single-qubit Pauli observables of the $i$-th qubit ($\langle X_i \...
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CNOT and quantum entanglement
I have the following problem:
"Consider two parties: Alice in possession of the one-qubit state |ψ⟩ = α|0⟩ + β|1⟩, and Bob who starts with a qubit in the state |0⟩
Show that Alice can teleport ...
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Conditional quantum circuits
Let's suppose that we have the following $\text{GHZ}$-state
$$|\psi\rangle = \frac{1}{\sqrt{2}}|a_1a_2a_3a_4\rangle + \frac{1}{\sqrt{2}}|b_1b_2b_3b_4\rangle$$
By using quantum gates, can we evaluate $...
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CNOT gate effect on 2 qubits
If the CNOT gate applies a NOT on the target qubit if the control qubit is a 1 and the control qubit was in superposition (for example in the $|+\rangle$ state), wouldn't this break the superposition ...
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How to alter the result of (somewhat) randomly generated circuits?
I create randomly generated circuits by iterating through a list of the gate set (in my case [$CX,SX,RZ,X$]) and adding the gate to the circuit. (In the case of the $CX$ gate we look at the topology ...
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Application of transformation $U_d$ that maps any qudit state to $|d-1\rangle$
When giving examples of universal gate sets in the paper Qudits and High-Dimensional Quantum Computing, the authors first define the transformation that maps any given qudit state to $|d-1\rangle$:
$$
...
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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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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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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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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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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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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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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.
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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 ...
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RY rotation on a qubit
The classical representation of a state on the Bloch sphere is given by
$|\psi\rangle = \cos \frac{\theta}{2} + e^{i \varphi} \sin \frac{\theta}{2}$.
If I want to apply a rotation around the $Y$-axis, ...
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Are equiprobable state same as superposition state
How
qc.h(0)
qc.h(1)
helps quantum circuit
qc=QuantumCircuit(2)
to put the given qubits in a equiprobable states?
Are ...
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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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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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Superposition of circuits (d-level case)
In this post: Superposition of quantum circuits, the two states are qubits. Is it possible to generalize this question to two qudit case? ie, given quantum circuits $C_1$ and $C_2$ that generates $\...
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Exact synthesis of Toffoli gate from CNOT and rational single-qubit gates?
Is it possible to implement a Toffoli gate exactly using just CNOT gates and single qubit complex rational gates (i.e. with entries in $\mathbb{Q}(i)$), possibly with ancillas?
I know this works with ...
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How to go from matrix to bra-ket representation of the CNOT?
I have the following definition for CNOT gate form my notes:
I am trying to derive the bracket notation form the matrix version, can someone help me to see where I am going wrong:
$$U ̂_{CNOT} ...
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How to add a value of -1/2 on the amplitude of a quantum state?
I have a quantum state which is in
$ \cos(c*f(x) + \pi/4) |0\rangle + \sin(c*f(x) + \pi/4) |1\rangle$
by using bunch of RY gates. Now I want to measure the probability of getting the state at $|1\...
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Quantum Computer Basics [closed]
I am a newbie to Quantum Computing world. My collage professor asked me to do presentation on quantum computing. I have read many articles online but still I think I am not satisfied with what I found....
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Existence of Hamiltonians such that the time evolution unitary becomes identity
Can we always find a set of coefficients ${k_i}$ (where not every $k_i = 0$) for a given Hamiltonian $H = \sum k_i H_i$, such that the unitary operator becomes the identity operation: $e^{-iH} = e^{i\...
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A question on the structure of the Clifford group
Let $P_n$ be the Pauli group on $n$ qubits defined by $P_n=\{i^k \sigma_1...\sigma_n: k=0, 1, 2 \; \mathrm{or}\;3, \sigma_j\in \{I, X, Y, Z\}\}$, where $I, X, Y, Z$ are Pauli matrices. The Clifford ...
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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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What are the theoretical minimum times for quantum and classical logic gates?
I'm interested in better understanding the ultimate limits on how fast quantum and classical logic gates can be performed. Based on principles like the time-energy uncertainty relationship, there ...
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Can every unitary be approximated by gates from the Clifford Hierarchy?
For $k > 1$, we recursively define $\mathcal C^{(k)}$ as
$$
\mathcal C^{(k)} = \Bigl\{ U \in \mathbf U(2^n)
\mathrel{\Big\vert} \forall P \in \mathcal C^{(1)} : U P U^\dagger
\in \mathcal C^{...
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How to get resultant statevector after applying parameterized gates in qiskit?
I want to check the expressibility of my ansatz and calculate the resultant statevector on paper seems difficult. Is there a way I can do this in qiskit? I have the circuit for the ansatz which has ...
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On unitary matrix form suggested in the Elementary gates paper
In the Elementary gates for quantum computation paper by Barenco et al authors start their proofs by defining a generic form of 2x2 unitary matrix of $\mathbb{C}$ as follows:
Can you help me with the ...
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Implementation of two qubit gate decomposition in local operations
My questions is regards to this paper: https://arxiv.org/abs/1909.07534
The above is the decomposition of a two qubit gate into local operations. Please note they are using a Super Operator formalism....
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What is Gate time of single and multi qubit?
How much quantum gate need time do computation in superconducting quantum computer. For all types of single and multi qubit gate.
