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Universal gate sets and conjugates of $SU(2)$

Let $G \subseteq SU(2)$ be a finite set, and let $E \in SU(2^k)$ be any entangling gate (so $k$ is some number strictly greater than 1). We often say $G$ is universal iff $\langle G \rangle$ is dense ...
trillianhaze's user avatar
2 votes
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Approximating the concatenation of two approximate circuits

Suppose I have two quantum circuits $A_n,B_n$ that I have already found to approximate the operations $U,V$ within some error $\epsilon_n$ and each with an overall circuit depth $\ell_n$ using $n$ ...
User71942's user avatar
1 vote
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Algorithm for finding the appropriate rotating frame Hamiltonian?

Context Consider an $N$-level Hamiltonian with energies $\omega_1...\omega_N$ with coupling drives at frequencies $f_{i,j}$ which couple the $i$ and $j$-th levels (not necessarily resonantly, so $f_{i,...
Dr. T. Q. Bit's user avatar
1 vote
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Improving operator norm bound on total variation distance

Let $U$ be an $n$-qubit unitary and $P_U(x) = |\langle x |U|0^n\rangle|$ the probability of measuring $x$ after acting $U$ on $|0^n\rangle$. For two $n$-qubit unitaries $U$ and $V$, one can prove that ...
trillianhaze's user avatar
1 vote
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Close in operator norm imply close in weak multiplicative sense?

Fix $\epsilon > 0$, and suppose $U$ and $S$ are $n$ qubit unitaries such that $\| U - S \| \leq \epsilon$ (operator norm). Furthermore, let $P_U(y \mid x) = |\langle y | U | x \rangle|^2$ be the ...
trillianhaze's user avatar
1 vote
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Error analysis on the approximation of an adiabatic evolution operator by a QAOA circuit

I would like to know what would be the approximation error of a QAOA circuit. Suppose we have time-dependent Hamiltonian $H(t) = (1 - s(t))H_{init} + s(t)H_{prob}$ where $H_{init}$ in an initial ...
MonteNero's user avatar
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