Stabilizer states are quantum states that can be efficiently represented by some set of Pauli operators of which the state is a +1 eigenstate. Stabilizer states are used commonly in many areas of quantum computation, such as error correction, teleportation and state verification.
Questions tagged [stabilizer-state]
83 questions
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How many N-qubit stabilizer states are there?
An N-qubit stabilizer state is a state that can be produced by starting from the $|0\rangle^{\otimes N}$ state and applying only H, CNOT, and S gates. How many N-qubit stabilizer states are there?
Because every stabilizer state can be represented as…
Craig Gidney
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How to generate all stabilizer states numerically?
I would like to obtain a list of all stabilizer states in the given dimension (not necessarily qubit systems). What is an efficient way of generating this list numerically?
Ver
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Inner Product of Stabilizer States
The end of Section III in the paper Improved Simulation of Stabilizer Circuits by Aaronson and Gottesman shows how to compute the inner product of stabilizer states $|\psi\rangle$ and $|\varphi\rangle$ represented by sets of generators of their…
Peter
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How to write the state associated to a family of stabilizers
The answer is probably obvious but I am missing something.
Let's say I have a quantum state $|\psi \rangle$ on $n$ qubits stabilized by $n$ Pauli operators $\{g_1,...,g_n\}$.
My question is: How can I express this quantum state as a function of the…
Marco Fellous-Asiani
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Do stabilizer operations map stabilizer states to stabilizer states?
Stabilizer operations comprised of stabiliser state preparations, Clifford gates, Pauli measurements, classical randomness and conditioning. Does stabilizer operations map stabilizer states to stabilizer states and why?
Michael.Andy
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Why are global phases neglected in the check matrix representation of stabilizers?
In the check matrix representation of stabilizers, one does not care about the global phase. Now why is that?
As far as I understand if I have a quantum computation, it can be computationally more efficient to keep track of how the stabilizers…
Lagrange
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Why does the Stinespring dilation of stabilizer operations have the form $\mathcal{E}(\rho) = tr_E(U \rho \otimes \rho_E U^\dagger)$?
Why does the Stinespring dilation of a stabilizer operation have the form
$\mathcal{E}(\rho) = tr_E(U \rho \otimes \rho_E U^\dagger)$
where $U$ is a Clifford unitary and $\rho_E$ is a stabilizer state?
Also, why does tracing out only take stabilizer…
Si Chen
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