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Questions tagged [stabilizer-state]

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.

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Efficient implementation of the Clifford group for $n$ qubits

I'm looking for an efficient implementation of the Clifford group $\mathcal{C}_n$ of $n$ qubits. The Clifford group $\mathcal{C}_n$ has stucture $(2_+^{1+2n} \circ C_8).Sp(2,n)$, where $2_+^{1+2n}$ ...
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Stabilizer for quantum error correction code

I have some very basic questions about stabilizers. What I understood: To describe a state $|\psi \rangle$ that lives in an $n$-qubit Hilbert space, we can either give the wavefunction (so the ...
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Why is the $N$-qubit stabilizer group abelian?

In Devitt et al. 2013's introduction to quantum error correction, the authors mention (bottom of page 12) how the stabilizer group for $N$ qubits is abelian. More specifically, here is the quote: ...
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Stabilizer state verification and specification from state vector

Given an arbitrary $n$-qudit state vector $|\psi\rangle =\sum_i c_i| i \rangle \in \mathbb{C}_d^n$ for some orthonormal basis $\{|i\rangle\}$, what is the most efficient way one can: Verify whether ...