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

160 questions
Filter by
Sorted by
Tagged with
47 views

### 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 ...
• 3
1 vote
82 views

### 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 ...
• 681
370 views

• 520
27 views

### 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 ...
342 views

### 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. ...
• 247
136 views

### 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) ...
• 3,033
138 views

### 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 ...
1 vote
76 views

### 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-...
43 views

### 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 ...
• 121
55 views

### 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. ...
212 views

### 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%...
• 143
437 views

201 views

• 57
1 vote
31 views

### 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 ...
• 129
83 views

### 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 ...
• 125