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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