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Daniel Knüttel 2020-03-20 09:59:55 +01:00
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20
thesis/chapters/conclusion.tex
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@ -82,10 +82,18 @@ and
CX_{2,1} (h_1 \otimes h_2) CX_{2,1} = h_1'' \otimes h_2'' CX_{2,1} (h_1 \otimes h_2) CX_{2,1} = h_1'' \otimes h_2''
\end{equation} \end{equation}
might be a good step to find new classes of states that can be simulated efficiently might be a good step to find new classes of states that can be simulated
using this method. This property has to be fulfilled by all elements of a group generated efficiently using this method. This property has to be fulfilled by all
by such hermitian matrices. elements of a group generated by such hermitian matrices. How computations and
How computations and measurements would work using this method measurements would work using this method is not clear at the moment as many
is not clear at the moment as many basic properties of the stabilizers are lost. basic properties of the stabilizers are lost. One important property is that the
stabilization: The simulated state is the $+1$ eigenstate of the stabilizers.
This is another property that will have to be fulfilled by the hermitians as it
is a key property used in \ref{ref:dynamics_stabilizer}. To ensure that the
state is well defined one will have to demand that the eigenvalues fulfill
$\lambda_1 = 1$ and $\lambda_2 < 1$.
One should also note that the sabilizer states do not form a Hilbert (sub)space.
Linear combinations of stabilizer states are (in general) no stabilizer states.
The superposition principle is quite essential to many quantum algorithms and
quantum physics which limits the use of the stabilizer formalism drastically.

1
thesis/chapters/stabilizer.tex
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@ -144,6 +144,7 @@ In the following discussions for $n$ qbits a set $S = \langle S^{(i)}
\subsubsection{Dynamics of Stabilizer States} \subsubsection{Dynamics of Stabilizer States}
\label{ref:dynamics_stabilizer}
Consider a $n$ qbit state $\ket{\psi}$ that is the $+1$ eigenstate of $S Consider a $n$ qbit state $\ket{\psi}$ that is the $+1$ eigenstate of $S
= \langle S^{(i)} \rangle_{i=1,...,n}$ and a unitary transformation $U$ that = \langle S^{(i)} \rangle_{i=1,...,n}$ and a unitary transformation $U$ that

10
thesis/main.bib
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@ -174,3 +174,13 @@
year=2020, year=2020,
note={https://docs.python.org/3.5/library/timeit.html} note={https://docs.python.org/3.5/library/timeit.html}
} }
@online{
openqasm,
url={https://github.com/QISKit/openqasm},
urldate={19.09.2019},
title={GitHub - Quiskit/openqasm},
author={Jay Gambetta at al.},
note={https://github.com/QISKit/openqasm},
year=2019
}