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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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Why do we need to put the control qubit in superposition in Bell State?

I'm new to quantum computing, so I hope you don't find this question tedious. However, after watching many hours of lectures and reading online, I still don't 100% understand why we need to initialize ...
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An equivalent classical circuit for Hadamard gate

In principle, we can simulate any Quantum circuit via a classical circuit. However, this simulation could be inefficient. (Church-Turing thesis) Together, Hadamard and Toffolli are universal gate sets ...
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Represent Hadamard gate in terms of rotations and reflections in Bloch sphere

I read in a book that any single qubit operation can be decomposed as $$ \bf{U} =e^{i\gamma}\begin{pmatrix}e^{-i\phi/2}&0\\ 0&e^{i\phi/2}\end{pmatrix}\begin{pmatrix}\cos{\theta/2}&-\sin{\...
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What's the result of applying a CNOT gate followed by a Hadamard?

Say I have the following circuit And the input is $|\psi\rangle=\frac12(|00\rangle+|11\rangle+|01\rangle+|10\rangle)$. To find the output sate, I would first apply the CNOT to the second bit, ...
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Where does this upper bound relating the $T$ count and $H$ count come from?

I am reading this paper on optimisation of the Hadamard gate count (Optimal Hadamard Gate count for Clifford + $T$ synthesis of Pauli rotations sequences). The idea of the paper is to optimise the ...
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Strange non-normal distribution histogram when applying Hadamard gate in a loop

Recently I have explored Q# quantum programming language. My basic test was this,- for 10000 times in a loop reset qubit to ...
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Show that conjugating $\text{CNOT}$ by $H\otimes H$ exchanges control and target qubits

I have gotten so far to show that $$(H⊗H)\text{CNOT}(H⊗H) = (H⊗I)CZ(H⊗I)\,.$$ How do I proceed from here in first proving the identity and then using the identity to show that on the dual basis, when $...
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Converting $H$ gate to $R_x$ and $R_z$

EDIT: My solution is supposed to work for $|1\rangle$ state too. See https://imgur.com/a/7F1cHu4 Right of the bat the answer is $$H=R_z(\pi/2)R_x(\pi/2)R_z(\pi/2)\,.$$ My question is, I cannot reach ...
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Diffuser's hadamard logic in equal superposition with negative phases

This is with reference to the question here: How to understand intuitively the Grover diffusion operator? Overall it makes sense on how H^n of the diffuser logic creates the |000..0> from an equal ...
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Is there a fast sparse Hadamard transform?

Suppose I give you an $n$-qubit state vector as a classical list of numbers (or as an oracle that can query the amplitudes). I tell you this state vector will contain exactly $k$ non-zero amplitudes, ...
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Hadamard transform on state

I'm reading this paper and have a question about the computation to go from (3) to (4). Define the state $\vert\psi\rangle = \sum_b\alpha_b\vert b\rangle$. In (3), we have the state $$\sum_{b \in\{0,1\...
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How does a local Hadamard gate change the cluster state?

I was reading a paper on a fault-tolerant quantum computation protocol based on tree cluster states. The author said that by applying a local Hadamard gate to two of the qubits in a 4 GHZ state, we ...
physics22's user avatar
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What is the intuition behind uniform Hadamard superposition?

I noticed that in many quantum algorithms, you apply a layer of uniform Hadamard transformation before and after the operations in between. For example, Deutsch-Josza, Simon's, and Grover's search. ...
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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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How to predict output counts in ibm qiskit

In the given circuit below : ...
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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 ...
Khilesh Chauhan's user avatar
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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 ...
Milo Moses's user avatar
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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 ...
Dai Chi DO's user avatar
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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 ...
Martin Hurtado's user avatar
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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 ...
Francesco Sisini's user avatar
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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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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 ...
TwentyCents's user avatar
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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 ...
Vaishnav's user avatar
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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 $...
Maxime Desalle's user avatar
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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|...
Maxime Desalle's user avatar
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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). ...
WhiteWolfDev's user avatar
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1 answer
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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}\...
Rayhan's user avatar
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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 ...
Daniele Cuomo's user avatar
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1 answer
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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 ...
Levent Ozbek's user avatar
2 votes
1 answer
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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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