Questions tagged [pauli-group]
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What does Pauli's $Y$ matrix represent?
It is easy to see that Pauli's $X$ matrix represents the bit flip operation, i.e. $X \lvert 0 \rangle = \lvert 1 \rangle$ and $X \lvert 1 \rangle = \lvert 0 \rangle$.
Similarly, Pauli's $Z$ matrix ...
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Minimum-weight presentation for stabilizer group $S$ and logical Pauli group $N(S)/S$
Given some stabilizer group $S$ with presentation $\langle s_1, \dots, s_r \rangle$, what is known about finding a minimal-weight presentation for it? By this, I mean a new presentation $\langle s_1', ...
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Simulating stabilizer groups
Can any existing software be used (either directly or with a bit of persuading) to work with general stabilizer groups? From what I can see, tableau-based options like Stim and Qiskit can be used to ...
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Efficiently finding an explicit presentation for $N(S)/S$, for any stabilizer group $S$
Let $P_n$ denote the $n$-qubit Pauli group. This has presentation $P_n = \langle iI, X_1, \ldots, X_n, Z_1, \ldots, Z_n \rangle$. Suppose we have a stabilizer group $S = \langle s_1, \ldots, s_k \...
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How grouping of Pauli strings is handled in Qiskit when running VQE?
When performing a VQE algorithm, the electronic problem Hamiltonian of the physical system under study needs to be mapped to a qubit Hamiltonian written as a sum of tensor products of Pauli operators (...
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Applying a single-qubit Pauli measurement to 3 or more pure non-orthogonal $n$-qubit stabilizer states
If we have 3 or more pure non-orthogonal $n$-qubit stabilizer states, where $n \ge 2$, is it true that there always exists a single-qubit Pauli measurement that will map these states to a set of post-...
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Clifford gates constructed from CNOT, H and S gates
Trying to prove that all Clifford gates can be constructed with CNOT, H and S gates, I'm following the classical path by induction (Nielsen and Chuang, Quantum Computation and Quantum Information -- ...
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Tensor product of Pauli strings?
We define
\begin{equation}
\sum_{i=1}^{4^l} P_i \otimes P_i,
\sum_{i=1}^{4^m} Q_i \otimes Q_i,
\end{equation}
where $P_l$ is the $n$ qubit Pauli string and $Q_m$ is the $m$ qubit Pauli string.
Does ...
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What are the elements of quotienting the Pauli group $\mathcal{P}_n := \widetilde{\mathcal{P}}_n / N$, and how to do calculations with it?
Let $\widetilde{\mathcal{P}}_n = \langle X_1,X_2,\dots,X_n,Z_1,\dots,Z_n\rangle$ together with all the phases $\{\pm 1, \pm i\}$ the regular Pauli group, and $N = \langle \pm i I\rangle $. I would ...
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