From b4be315a015397e3c4d745016b4c68b743abdda5 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Daniel=20Kn=C3=BCttel?= Date: Fri, 20 Mar 2020 09:59:55 +0100 Subject: [PATCH] some work --- thesis/chapters/conclusion.tex | 20 ++++++++++++++------ thesis/chapters/stabilizer.tex | 1 + thesis/main.bib | 10 ++++++++++ 3 files changed, 25 insertions(+), 6 deletions(-) diff --git a/thesis/chapters/conclusion.tex b/thesis/chapters/conclusion.tex index f174cc4..3b1580d 100644 --- a/thesis/chapters/conclusion.tex +++ b/thesis/chapters/conclusion.tex @@ -82,10 +82,18 @@ and CX_{2,1} (h_1 \otimes h_2) CX_{2,1} = h_1'' \otimes h_2'' \end{equation} -might be a good step to find new classes of states that can be simulated efficiently -using this method. This property has to be fulfilled by all elements of a group generated -by such hermitian matrices. -How computations and measurements would work using this method -is not clear at the moment as many basic properties of the stabilizers are lost. - +might be a good step to find new classes of states that can be simulated +efficiently using this method. This property has to be fulfilled by all +elements of a group generated by such hermitian matrices. How computations and +measurements would work using this method is not clear at the moment as many +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. diff --git a/thesis/chapters/stabilizer.tex b/thesis/chapters/stabilizer.tex index abb28db..8e94b5d 100644 --- a/thesis/chapters/stabilizer.tex +++ b/thesis/chapters/stabilizer.tex @@ -144,6 +144,7 @@ In the following discussions for $n$ qbits a set $S = \langle S^{(i)} \subsubsection{Dynamics of Stabilizer States} +\label{ref:dynamics_stabilizer} 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 diff --git a/thesis/main.bib b/thesis/main.bib index d2d0eb8..16382fd 100644 --- a/thesis/main.bib +++ b/thesis/main.bib @@ -174,3 +174,13 @@ year=2020, 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 +}