# Questions tagged [hadamard]

Single qubit Hadamard gate transforms standard basis states (zero and one states) to their superpositions (plus and minus states)

109 questions
Filter by
Sorted by
Tagged with
1 vote
37 views

### 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 ...
• 181
1 vote
41 views

### 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 ...
30 views

### 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 ...
65 views

### 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 ...
• 145
80 views

### 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 ...
• 1,599
69 views

### 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 ...
1 vote
62 views

### 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 ...
We have the 3 following gates : $$H = \dfrac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\ 1 & -1 \end{bmatrix}$$ $$R(\varphi) = \begin{bmatrix}1 & 0 \\ 0 & e^{-i\varphi} \end{bmatrix}$$ $$... • 107 1 vote 2 answers 137 views ### 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 ... 0 votes 1 answer 174 views ### 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. ... • 189 1 vote 1 answer 75 views ### 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. • 143 2 votes 1 answer 59 views ### Why does application of Hadamard gate on |0\rangle inverts the state on bloch sphere? I am trying to understand what is the affect of Hadamard gate on qubit. So far, I understand that applying H gate on qubit, puts the qubit into superposition state where the probability of the qubit ... 4 votes 3 answers 467 views ### How to represent the Hadamard gate as a rotations on the Bloch sphere? I am new to Quantum Computing, and I have decided to try and learn the quantum gates. I am trying to understand how to represent some basic gates as rotations on the Bloch Sphere. I was able to ... 1 vote 2 answers 122 views ### Creating an entangled state in Hadamard basis (Qiskit) I am familiar with building a quantum circuit of an entangled pair providing that they are in the computational basis: |ψ⟩ = 1/√2 (|00⟩ + |11⟩) This circuit works great. I am trying to build the ... 2 votes 2 answers 159 views ### Commutation rules between Pauli X and controlled-Hadamard Are there any known commutation rules between the X gate and the CH gate? 1 vote 1 answer 64 views ### Simon's Algorithm: Calculating the effects on the second Hadamard gate and the resulting amplitudes I am currently reading about Simon's algorithm in "An Introduction to Quantum Computing" and stumbled over Exercise 6.5.1, that ask the reader to show that: Let \textbf{x}, \textbf{y} \in \... 3 votes 1 answer 54 views ### Hadamard Test Circuit Missing Term I am trying to understand a specific Hadamard Test circuit used to calculate the direct product coefficient$$ B_{l,m} = \langle 0|V^{\dagger} A^{\dagger}_m A_l V |0\rangle $$where V is a ... • 107 3 votes 2 answers 454 views ### Does the X (NOT) gate affect superpositions at all? Does "NOT" gate have any effect on qubit in superposition state? After applying Hadamard gate on qubit seems like the "NOT" gate doesn't have any effect on it. Could somebody ... 2 votes 0 answers 60 views ### I can not extract the final statevector when using a binded Parametric Controlled gate I'm trying to implement a Parametric Hadamard Test. I have already my parametric evolution gate \exp(-i\theta H) where \theta is the parameter. When I defined the controlled-gate with Gate.control(... • 21 4 votes 1 answer 46 views ### Can you detect if the collapse of an entangled pair using a Hadamard gate? I'm trying to understand how the Hadamard gate works with entangled pairs. If I have two particles A and B which are entangled and have gone through a Hadamard gate to become super-positioned Qubits, ... 6 votes 1 answer 284 views ### Can we use Hadamard test to estimate phases? There have been some questions discussing the Hadamard test and quantum phase estimation (QPE), but I did not find the answer to the following question. Suppose we are given |\psi\rangle, which is ... • 830 2 votes 1 answer 106 views ### How to apply the Hadamard gate to a given qubit state? I have this qubit state:$$ H \left[ \frac{1}{\sqrt{2}} |0\rangle + \left( \sqrt{\frac{2}{7}}+\frac{1}{\sqrt{7}}i \right) |1\rangle \right] $$How to solve this given Hadamard gate on qubit? Hadamard ... 0 votes 1 answer 171 views ### Hadamard cascade Anyone of you can explain (with mathematical steps) me this circuit: I do not understand why the first qubit phase (as show on IBM composer) is influenced by the second. More precisely: In circuit ... 5 votes 2 answers 591 views ### Why isn't Ry(\pi/2) gate equivalent to Hadamard gate? I've been experimenting with quantum circuits and can't quite fathom how the difference between states comes together. Speaking in terms of simulations using qiskit,... • 147 2 votes 2 answers 82 views ### How does measurement change the effective transformation matrix? I have simulated three cases in Qiskit and tried doing some manual calculations to verify the simulated results. Case 1: The initial state is \psi_i = |00\rangle = \begin{Bmatrix}1 \\0 \\ 0 \\ 0\end{... 2 votes 1 answer 292 views ### Is the CNOT in the standard three-qubit circuit for the GHZ state necessary? This is a very basic question about the GHZ state. I know the standard construction: A Hadamard on one qubit, and then CNOT gates with targets on all the other ones. However, why can't I just have n... • 23 1 vote 1 answer 48 views ### why is H^{⊗2} used to denote the parallel action of two Hadamard gates? Why is the tensor product used here, what's its meaning? I learned tensor products as an operation between 2 matrices, and have an effect such as the follows: How does the tensor product above relate ... • 629 0 votes 1 answer 54 views ### Derivation of the effect of the Hadamard transform on a state |x⟩ in the Deutsch–Jozsa algorithm On pg. 35 of Nielsen and Chuang, there's the following paragraph: By checking the cases x=0 and x=1 separately we see that for a single qubit H|x\rangle=\sum_x (-1)^{xz}|z\rangle/\sqrt{2}. I'm ... 2 votes 2 answers 117 views ### Are composite gates within superconducting hardware implemented as a single pulse or as a series of pulses? If we have for example a gate U^{\otimes2}, then within superconducting hardware, is the U applied onto the first qubit and then the second or is a pulse corresponding to a composite gate (tensor ... • 161 0 votes 1 answer 75 views ### Applying Hadamard gate to \sqrt{3/4}|0\rangle + \sqrt{1/4}|1\rangle [I am just transferring this from Stack Overflow. It might need editing.] ———— [The reader can skip to “It all sounds fine…”, before the spreadsheet representation.] I am trying to figure out quantum ... 0 votes 1 answer 104 views ### Derivation for the result of performing the Hadamard transform on |0\rangle^{\otimes n} being 2^{-n/2}\sum_x|x\rangle It's said that the result of performing the Hadamard transform on n qubits initially in the all |0> state is$$ \frac{1}{\sqrt{2^n}}\sum_x|x\rangle where the sum is over all possible values of x.... • 629 1 vote 0 answers 143 views ### Represent the n-qubit 2^n\times2^n size Hadamard/quantum Fourier transform unitary square matrix as product of k two-level unitary matrices I wish to know if it is possible to express the n-qubit Hadamard unitary square matrix of size 2^n * 2^n as a product of 'k' two-level unitary square matrices where 'k' is of the order of polynomial ... 2 votes 1 answer 225 views ### How to derive the rotations caused by the H gate? In Nielsen and Chuang, there's the following paragraph: The Hadamard operation is just a rotation of the sphere about the ˆy axis by 90◦, followed by a rotation about the ˆx axis by 180◦. I am ... • 629 2 votes 1 answer 388 views ### Why is H gate called a ‘square-root of NOT’ gate? In Nielsen and Chuang, there's the following paragraph: I understand that \begin{align*} \sqrt{NOT} = \frac{1}{2}\left( {\begin{array}{*{20}{c}} \sqrt 2 e^{i\pi / 4}&\sqrt 2 e^{-i\pi / 4}\\ \sqrt ... • 629 2 votes 1 answer 218 views ### Initial state preparation for Hadamard test I thought I understood Hadamard test but it seems to be shaky. I understand that to get the expectation value \langle\psi\ | V^\dagger|{\bf Q}|V|\psi\rangle we need to have gate V (in blue) below ... • 889 0 votes 1 answer 85 views ### Doing |0\rangle then Hadamard gate then measurement I am starting to use quantum experience and following exactly first example from lecture. After initializing the qubit to |0\rangle, then applying a Hadamard gate, the probability for measuring |1\... 4 votes 1 answer 178 views ### How do you represent a Hadamard gate as a product of R_x and R_y gates? I'm looking for a representation of Hadamard gate that uses only R_x(x) and R_y(y) gates. The values x and y may be the same, but they don't necessarily need to be. 6 votes 2 answers 2k views ### How to visualize Hadamard gate as X-Z-X decomposition? In the book Quantum Computation and Quantum Information by Nielsen and Chuang, chapter 4, exercise 4.4 (pg. 175), the author has asked to express Hadamard gate as product of R_x, R_z rotations and ... 2 votes 2 answers 143 views ### How does a Hadamard discrete-time quantum walk result in a skewed distribution? I was reading this tutorial about discrete random walk and got confused by the following paragraph. After the succession of Hadamard applications (H), I wonder how do we get skewed distribution. I ... • 889 3 votes 1 answer 263 views ### What is the relation between Hadamard transformation and QFT? I am new to the field and I can't help having a feeling that Hadamard and Fourier Transform are somehow related, but it is not clear to me how. Any explanation on how these two are related would be ... • 889 2 votes 2 answers 563 views ### Is the tensor product of 2 Hadamard gates entangled? Assume that you have a system of two qubits in the state |11 \rangle. Apply H \otimes H, where H is the Hadamard matrix. Is the state (H \otimes H)|11\rangle entangled? I know if we take the ... • 177 0 votes 1 answer 41 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 ... • 177 0 votes 1 answer 182 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 ... • 13 0 votes 1 answer 64 views ### How do two H gates act on two entangled qubits? In this circuit, if the two qubits are initial in state 0, then after the oracle they are entangled and in state: 0.5 * (|00\rangle+|01\rangle+|10\rangle-|11\rangle) My question is how do the two H ... • 1 6 votes 2 answers 1k views ### How to generalize the relationship HXH = Z for higher dimensions Concerning the Hadamard gate and the Pauli X and Z gates for qubits, it is straightforward to show the following relationship via direct substitution: HXH = Z.\tag{1}$$And I would like to ... • 95 4 votes 1 answer 141 views ### Is it possible to tune the amplitude of superposition generated by Hadamard gates? I had a question earlier about generating the superposition of all the possible states: Here. In that case, we could apply H^{\otimes n} to the state |0\rangle^{\otimes n}, and each state has the ... • 2,238 1 vote 2 answers 394 views ### How to describe the state of a qubit passing through two Hadamard gates? [duplicate] Describe the state of the qubit at points A, B and C. How does this demonstrate that we need the “ket” (or the vector) representation of qubits, rather than just describing them in terms of ... 2 votes 1 answer 86 views ### What is a complexity of producing arbitrary equally distributed superposition? In the article An Optimized Quantum Maximum or Minimum Searching Algorithm and its Circuits I found statement (pg. 4): Preparing an initial state takes \log_2(N) steps. In this case the initial ... • 12.1k 2 votes 1 answer 49 views ### Is there an error on Qiskit.org textbook with the superdense coding section? The textbook on Qiskit.org has When the H-gate is applied to first qubit, it creates superposition and we get the state |0+\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |01\rangle) Shouldn't it be:$$|...
Find a $2 \times 2$ Hamiltonian $H_H$ such that $e^{iH_H}$ equals the Hadamard matrix and a $4 \times 4$ Hamiltonian $H_{CNOT}$ such that $e^{-iH_{CNOT}}$ equals the matrix of the CNOT gate. I have ...