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]
124 questions
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What is a stabilizer state?
I am reading through the paper "Direct Fidelity Estimation from Few Pauli Measurements" (arXiv:1104.4695) and it mentions 'stabilizer state'.
"The number of repetitions depends on the desired
state $\rho$. In the worst case, it is $O(d)$, but in…
Quantum Guy 123
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Quantum advantage with only Clifford gates (Gottesman Knill theorem)
Let's say I want to solve a computational task which input can be encoded in $n$ bits of information.
The look for a quantum advantage is (usually) asking to find a quantum algorithm in which there are exponentially fewer gates and qubits required…
Marco Fellous-Asiani
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How to verify whether a state is a stabilizer state?
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 the state is a stabilizer state (i.e. can be…
SLesslyTall
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What is the stabilizer rank of the W state?
The $ n $ qubit $ W $ state is defined here https://en.wikipedia.org/wiki/W_state
The stabilizer rank of a quantum state $|\psi\rangle$ is the minimal
$r$ such that \begin{equation} |{\psi}\rangle = \sum_{j=1}^{r} c_j
|φ_{j}\rangle. \end{equation}…
Ian Gershon Teixeira
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How to find the stabilizer generators for a post-measurement state?
My question is closely related to this one.
A bit of vocabulary and a reminder of basic properties:
I consider the total Hilbert space of the problem has dimension $2^n$.
I call a "well defined family of generators" a family of $n$-Pauli matrices…
Marco Fellous-Asiani
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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 expression of $|\psi\rangle$), either give a set of…
Marco Fellous-Asiani
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Fidelity concentration bound for random stabilizer states
Let $|\Phi\rangle$ be a normalized vector in $\mathbb{C}^d$ and let $|\psi\rangle$ be a random stabilizer state. I am trying to compute the quantity
$$\mathsf{Pr}\big[|\langle \Phi|\psi \rangle|^2 \geq \epsilon \big].$$
Note that if $|\psi\rangle$…
BlackHat18
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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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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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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 $2_+^{1+2n}$ denotes an extraspecial 2 group of $+$ type,…
Martin Seysen
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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:
An $N$-qubit stabilizer state $\lvert\psi\rangle_N$…
glS
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Finding all small stabilizer codes
Given some choice of parameters $ [[n,k,d]] $ with $ n $ small, is there any computationally easy way to find all of (or at least many of) the stabilizer codes with those parameters?
For certain parameters this is easy, for example it is known that…
Ian Gershon Teixeira
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5
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how to go from a stabilizer state to a graph
A comment (by Marcus Heinrich) in a
previous post says :
"any stabiliser state is locally Clifford equivalent to a graph state and vice versa".
I can go from a graph (defined by its adjacency matrix) to a set of stabilizers and the corresponding…
unknown
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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 work with stabilizer groups over $n$ qubits with…
Alex Townsend-Teague
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Does Gottesman-Knill theorem apply with any computational basis input?
On Wikipedia, the Gottesman-Knill theorem is said to state the following:
A quantum circuit using only the following elements can be simulated efficiently on a classical computer.
Preparation of qubits in computational basis states,
Clifford…
trillianhaze
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