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Hot answers tagged stabilizer-state

10 votes
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• 3,042
5 votes

How to find the stabilizer generators for a post-measurement state?

Let $n$ be the observable you measured, and let $S$ be the set of stabilizer generators for the state before the measurement. Some of the old stabilizers generators anti-commute with the new ...
• 21.8k
4 votes
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Stabilizer state QFI lower limit query

The state $\psi$ (this is denoting the density matrix, even though it's a pure state) can be described as a sum of all the products of the stabilizers. We are promised that $X_i$ is not in the ...
• 46.2k
4 votes

Measuring entanglement entropy using a stabilizer circuit simulator

I think stim is the right tool for the job here, because it gives you access to the stabilizer generators and also it defines stim.PauliString which you can use to ...
• 21.8k
4 votes
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• 4,649
4 votes
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Quantum algorithm for hidden subgroup problems: question on cosets

Consider that if we enumerate the cosets of $H$ as $g_0+H,g_1+H,\dots, g_n+H$, then every $g\in G$ can be written as $g_i+h$ for some $i$ and some $h\in H$, and this correspondence is 1-to-1. This ...
• 1,571
3 votes
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Are there any packages that can calculate stabilizer tableau of a QECC

You can use stim for this, although you do have to write the stabilizer projection procedure for yourself. Write some methods to project a system into the +1 eigenstate of several stabilizers: ...
• 21.8k
3 votes
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Gottesman Knill theorem: why $O(n^2)$ classical operation to keep track of a Clifford gate

You can pretty easily prove by counting that specifying a stabilizer operation or a stabilizer state requires $\Omega(n^2)$ bits. If you're not tracking some of those bits, your simulator is ...
• 21.8k
3 votes
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How to get the stabilizer group for a given state?

You need to watch out when you say 'stabilizer' or 'stabilizers' because there is a little bit of ambiguity in that terminology$^{1}$. The stabilizer $\mathcal{S}$ of a state $|\psi \rangle$ is the ...
• 4,649
3 votes

Degenerate vs non-degenerate errors

As you say, non-degenerate codes have a lot of well-understood machinery that's brought in from the classical side. That helps us from a conceptual stance, and a mathematical one (making rigorous ...
• 46.2k
3 votes
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How to calculate the generators of a list of stabilizer?

The way that I'd do it is to write out the stabilizers in a $10\times 8$ matrix in this case (number of rows= number of stabilizers, number of columns is double the number of qubits). For each row, ...
• 46.2k
3 votes
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What is the stabilizer group of a $|W\rangle$ state?

To cite from my answer from over at physics.SE: The W state is not a stabilizer state - for a stabilizer state, the 1-site reduced density matrices must be maximally mixed or pure, which they aren't. ...
• 4,988
3 votes
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Constructing an eigenbasis of graph states for a set of stabilizers

If you start with one graph state, which is an eigenstate of stabilizer (each of which comprises an X tensored with a bunch of Zs), then the other eigenstates of those stabilizers are the original ...
• 46.2k
3 votes
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Computing expectation value of a Pauli string on stabilizer states

You can use stim.TableauSimulator.peek_observable_expectation to compute the expected value of Pauli product observables without affecting the simulator's state: <...
• 21.8k
3 votes

• 353
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Stabilizer for quantum error correction code

Here are a couple of observations which will hopefully clarify things. Only some states have Pauli stabilisers. You have correctly identified that not all states have Pauli stabilisers. An example ...
• 10.8k
2 votes

Stabilizer state verification and specification from state vector

Here's a necessary condition that might help recognise potential stabilizer states. I'll state it for qubits as that's what I'm used to thinking about, but I suspect it can be generalised: all the ...
• 46.2k

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