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1 vote
0 answers
60 views

Why does the quantum walk operator only have two eigenvectors?

In Child's paper on the relationship between discrete and continuous quantum walks, he makes the following claim. Although he provides a proof after this: I don't understand how the walk operator mu …
Loic Stoic's user avatar
0 votes
1 answer
192 views

How is the P function applied in QSVT for the case of Hamiltonian simulation if it only modi...

\end{bmatrix} $ However, on a following slide regarding Hamiltonian simulation, he brings this up: What is $P(H)$ here? …
Loic Stoic's user avatar
1 vote
0 answers
53 views

Proof of $cos(Ht) = \sum_\sigma cos(\sigma) \left | w_\sigma \right > \left < v_\sigma \righ...

I am reading the grand unification of quantum algorithms, and read over the hamiltonian simulation technique. However, I am a bit confused. … Then they use this fact to reduce the problem of hamiltonian simulation to finding $cos(Ht)$ and $sin(Ht)$, which is all well and good. …
Loic Stoic's user avatar
0 votes
1 answer
185 views

How to choose values of phi for Hamiltonian simulation with Quantum Singular Value Transform?

I am really trying to understand it behind the context of Hamiltonian Simulation, and have read many papers and watched a few videos outlining the methods. …
Loic Stoic's user avatar