Questions tagged [hadamard]
Single qubit Hadamard gate transforms standard basis states (zero and one states) to their superpositions (plus and minus states)
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How does this measurement in the Hadamard basis look like?
I am reading this paper by Mahadev. In going from (19) to (20) the author does a Hadamard measurement on two registers. I don't understand what exactly the Hadamard measurement does.
The (simplified) ...
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Hadamard Gate on Cluster States
In measurement based quantum computing, according to R. Raussendorf, Hadamard Gate can be realized by five qubit cluster state, where the first qubit is measured in X basis and the following three are ...
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How to explain the output as $|-\rangle$
I am a complete newbie to quantum computing and qiskit. I am trying to implement $H$ gate in Measurement-Based QC architecture based on a paper "Qiskit As a Simulation Platform for
Measurement-...
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Inner product in terms of Hadamard and controlled SWAP gates
On p. 7 of this paper (https://arxiv.org/abs/2112.04958) it is claimed that:
"For any two states $|φ\rangle$ and $|ψ\rangle$ with the same dimensions, the
fidelity $F(|φ\rangle, |ψ\rangle)$ can ...
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Easy way to look at matrix in computational and Hadamard bases?
Given a $2^n \times 2^n$ matrix $M$ of classical data (so, just a bunch of numbers), is there any way to query that matrix in both the computational basis (basically, $M$) and the Hadamard basis, i.e. ...
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How to apply CNOT on a three qubit system, with two qubits already entangled?
I am trying to understand the math behind the following applications of gates on three qubits:
You can view this via the Quirk simulator here:
https://algassert.com/quirk#circuit={%22cols%22:[[%22H%...
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How to eliminate the global phase of a state vector?
Say that I have a qubit that began in the $|0\rangle$ state and then the
Hadamard gate is applied, resulting in the following state:
$ \begin{bmatrix}
\frac{1}{\sqrt{2}} \\
\frac{1}{\sqrt{2}}
\end{...
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How to get rid of the indices of qubits at the side of a custom gate when visualizing a circuit (IBM Qiskit)
I have written a function that applies the Hadamard gate to all qubits in a circuit, and use the draw() function to visualize the circuit. However, there is this ...
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How to predict state vector of a quantum circuit in IBM qiskit
How to Predict the state vector output of the following quantum circuit?
...
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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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Is the plus state a magic state for the Hadamard gate?
Is the plus state $\left|+\right>:=\frac{\left| 0\right>+\left| 1\right>}{\sqrt{2}}$ a magic state for the Hadamard gate $H$? That is, given the ability to perform (controlled) Pauli ...
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How to get all unit vectors of 4 dimension with all entries $\pm 1/2$ using only Hadamard and SWAP transformations
We consider the group of unitary matrices, $G$ that generated by the Hadamard matrices $H_2$,$H_4$ and and SWAP matrix (i.e., permutation matrices that swap two qubit lines). Consider all unit vectors ...
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Decomposing Hadamard gate
I'm following a lesson, and it says that the Hadamard gate can be decomposed to three gates: RZ(pi/2), squared root Z, and RZ(pi/2). However, when I do matrix multiplication of these three matrices, I ...
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How do you write the Hadamard operator on two qubits in braket notation?
I understand how to write the Hadamard operator on one qubit in braket notation using $$\newcommand\bra[1]{\left\langle#1\right|}\newcommand\ket[1]{\left|#1\right\rangle} H=\sum_{i,j} \bra{w_{j}}H\ket{...
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Mathematical justification of postprocessing in QRNG
I have reading about Quantum Random Number Generators (QRNGs), and it seems that usually classical post processing is applied to the initial output of the quantum circuit to:
improve the quality of ...
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How to express Hadamard gate as a generic trigonometric functions of theta? [duplicate]
Hadamard gate is expressed as $H=R_x(\pi)*R_y(2\theta)$ where $\theta$ is $\pi/4$.
$$H=\begin{bmatrix}
0 & 1\\
1 & 0
\end{bmatrix} \begin{bmatrix}
\cos \theta & -\sin \theta\\
\sin \...
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Half-wave plate (HWP) Hadamard gate implementation
The transformation of a qubit encoded in the polarization state from $|H\rangle$ to the state $|+\rangle$ is theoretically achievable with an HWP@π/8. However, I rarely see this solution in ...
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Internal calculation of a quantum circuit
Upto the below point, i understand clearly..
But what happened after that, the phase value changes why? do not understand the internal calculations?
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In general, what is feasible quantum computation?
I don't really understand what is feasible quantum computation, in my book (Lipton and Regan's Quantum Algorithms via Linear Algebra) they said that:
A quantum computation $C$ on s qubits is feasible ...
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How do I construct the eigenvectors of the Hadamard gate using Quantum Gates?
How do I use quantum gates offered on IBM quantum to construct either eigenvector of the Hadamard gate?
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How to represent 2 Hadamard gates with Universal set of gates?
I was reading through Child's Paper on Universal Computation by Quantum Walks: https://arxiv.org/abs/0806.1972
When he discusses how his universal set of gates contains CNOT and the following 2 "...
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multiple Hadamard gates
query in when we apply multiple H gates in multiple qubits.
suppose, one circuit,
qreg_q = QuantumRegister(2, 'q')
creg_c = ClassicalRegister(2, 'c')
circuit = QuantumCircuit(qreg_q, creg_c)
circuit.h(...
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Why does a bitwise product show up in Simon’s algorithm?
I’m reading up on Simon’s problem from the Qiskit textbook, but don’t understand the second Hadamard transform of the first qubit register.
Mathematically, they are stating that a state that looks ...
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Help in understanding the algebra of hadamard test
I am new to quantum computing and was looking through the jupyter notebook of Variational Quantum Linear Solver by Qiskit. I came across the hadamard test and was not understanding how it works.
It is ...
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What is $HTHTH\left| 0 \right>$?
I'm currently going through Introduction to Classical and Quantum Computing, by Thomas Wong, and I'm struggling with exercise 2.33 (page 108):
Exercise 2.33. Answer the following:
(a) Calculate $...
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What is $H\left| \psi \right>$ with $\left| \psi \right> = \alpha\left| 0 \right> + \beta\left| 1 \right>$?
I'm currently going through Introduction to Classical and Quantum Computing, by Thomas Wong, and I'm struggling with exercise 2.29 (page 107):
Exercise 2.29. Say $\left| \psi \right> = \alpha\left|...
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how do i get the sequence of resulting data on the ibm quantum computers platform?
I have been working on the ibm quantum computer platform, but i have faced a problem with the output. My circuit contains Hadamard gates and entanglement gate between two qubits. I want to get the ...
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Circuit containing only Hadamard gate returns bad results
I am new to quantum computing. My circuit contains only one qubit, one Hadamard gate and an operation to measure the state of the qubit. So, as I understand, the qubit is in superposition state after ...
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Hadamard in surface code not understood
I am reading how Hadamard is performed in surface code at https://arxiv.org/pdf/1208.0928.pdf
At some point, they apply H on all data qubits, and they claim that it converts X to Z stabilizers and ...
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How does the Hadamard gate work?
I'm learning about the Quantum Fourier Transform (QFT) and from what I can see the Hadamard gate equation doesn't make sense from what I have learnt so far. Here's a link to the resource (Example 2). ...
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How do I get this FRQI equation? [duplicate]
I have been working with FRQI and there is this equation in a paper is given. Can anyone explain how they get that just by multiplying by $\mathcal{H}$ ?
$$\mathcal{H}\left(|0\rangle^{\otimes2n+1}\...
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Does the standard 3 qubit code scheme admit a transversal implementation of $H$?
The standard 3 code scheme encodes one qubit into 3 by applying 2 $CNOT$s targeted on auxiliary qubits set on ground state $|0\rangle$.
I am struggling to perform logical operations between two ...
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Implementation of quantum Hadamard gate using electron spins?
The Hadamard gate performs the following operation on an incoming electron spin:
What is a realistic laboratory way of implementing a Hadamard gate that will change a known electron spin into one ...
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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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Modeling light transfer through every path with superpositioning
So I asked a question about this topic earlier but since then, I did more digging into this problem.
Researchers at Berkeley experimented with a theory of photosynthesis happening using Quantum ...
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Seeking an explanation of the Hadamard transformation on a 2-qubit system
Edit Here is a link to the notes I referred to. The problem is on page 7.
https://www.eecs.ucf.edu/~dcm/Teaching/COT6600-Fall2010/Literature/CleveQuantumComplexityTheory.pdf
I am a beginner in this ...
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Is this state a superposition in the standard basis?
This is a very basic question, but I am wondering how does one determine if the state is in a superposition in the standard basis? What I know is a state is in superposition iff ⍺ and β are both ≠ 0, ...
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Cannot derive probability graph for Hadamard gate given in Qiskit textbook
I am reading the Qiskit textbook(beta) and they have explained Hadamard gate using an amplitude tree. To show how two H-gates on a qubit give the output as 0 everytime they said to consider that it ...
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Multiple Hadamard gates Transformation on N qbits
I am newbie to quantum computing and having a bit confusion regarding the action of Hadamard gate on multiple qbits which are already in superposed state (I well understand how it works for qbits ...
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Equivalence between quantum circuit: CNOT changes control and target qubit
It's know that the following two circuits are equal.
In fact, answers for this can be found on wikipedia, and on this website. However, I am looking for a more formal answer. I'd like to see the ...
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Where can I find runtime of ibm quantum gates?
I'm looking for the runtime of IBM quantum gates. For instance how long does it take to apply an Hadamard gate to a qubit ? and a CNOT gate to two qubits ?
I didn't find any answers in the ...
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How does a Hadamard gate impact the initial/previous values of a Qubit? [closed]
I've been studying Quantum Computing and one thing that intrigued me is:
given a qubit q1 with an initial value x, when I apply a Hadamard gate on it, then it goes to superposition, so the probability ...
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What's the deal with quantum random number generators?
Classical computers are usually incapable of generating true random numbers as they are based on deterministic algorithms. To overcome this challenge, one can either use pseudo-random number ...
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Exercise 2.33 in Nielsen & Chuang QCQI book - H tensor n
The question on the book is:
The Hadamard operator on one qubit may be written as
$$\frac{1}{\sqrt{2}}[(|0\rangle + |1\rangle)\langle0| + (|0\rangle - |1\rangle)\langle1|]$$
Show explicitly that the ...
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Hadamard gate in Grover algorithm
What is the need to apply the Hadamard gate as the first step while designing the diffuser circuit in the implementation of Grover's algorithm? I know what the gate does but I cannot understand what ...
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Constructing a pure state in Bloch sphere using 3 gates
We have the 3 following gates :
$$
H = \dfrac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\ 1 & -1 \end{bmatrix}
$$
$$
R(\varphi) = \begin{bmatrix}1 & 0 \\ 0 & e^{-i\varphi} \end{bmatrix}
$$
$$
...
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How to obtain the state $|0\rangle+|1\rangle$ from $|0\rangle$ via Pauli gates?
Could somebody explain in which way are we able to achieve superposition with Pauli $X$, $Y$, $Z$ matrices? In case of Hadamard gate $H$ we change coefficients to $1/\sqrt{2}$ directly, in case of $X$ ...
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Qiskit: bind parameters to sub-circuit
I am trying to implement a Hadamard test on a parametrized sub-circuit $V(\bf{a})$. I create an outer circuit and then append the parametrized $V(\bf{a})$ to it.
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In the Bernstein-Vazirani algorithm, what is the use of the second Hadamard gate?
In the Bernstein-Vazirani algorithm, what is the use of the second Hadamard gate? What happens if I remove it? Would the algorithm works fine? I read something about it closing the interference.
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