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3 votes

Measuring stabilizers for qutrit stabilizer code

$\def\braket#1#2{\langle#1|#2\rangle}\def\bra#1{\langle#1|}\def\ket#1{|#1\rangle}$ I think your confusion lies with measuring qudit Pauli operators. It is true that operators like $X$ and $Z$ are not ...
user173611's user avatar
0 votes

Efficiently Generating Expectation Values of Operators Using Stim

You can use the flip simulator to efficiently sample how often the current error set anticommutes with each observable. That tells you how often they're flipped. Then the tableau simulator can be used,...
Craig Gidney's user avatar
  • 37.5k
1 vote
Accepted

Kraus decomposition of merging in lattice surgery

CP maps for lattice surgery merge with post-selection Post-selecting on $M_{ZZ}=0$, lattice surgery merge is described by the completely positive linear map with Kraus representation \begin{align} \...
Adam Zalcman's user avatar
  • 22.9k
3 votes
Accepted

Does a 3 qudit code always exist? (except for qubits)

The answer is yes. One can show that a $[\![3,1,2]\!]_q$ can be purified to a $[\![4,0,3]\!]_q$ with a reference system; or reversely, the $[\![4,0,3]\!]_q$ "punctured" to a $[\![3,1,2]\!]_q$...
Felix Huber's user avatar
2 votes

Kraus decomposition of merging in lattice surgery

Lattice merge isn't faithfully captured by a CPTP map description (and therefore a Kraus representation). Tracking $M$, the measurement outcome, conditions what logical correction operation you will ...
rmehta's user avatar
  • 51
2 votes

how to go from a stabilizer state to a graph

You can use Stim to turn a stabilizer state into a graph state. Internally what it does is to decompose the stabilizer state into any circuit (it happens to do this by Gaussian elimination of the ...
Craig Gidney's user avatar
  • 37.5k
2 votes
Accepted

Stabilizers of the [[12, 2, 4]] "Carbon" code

TLDR: I find the construction of the code, which can be understood as a special type a 3D color code based on a hexagon nut. Special thanks to @DaftWullie for providing information about the condition ...
Yunzhe's user avatar
  • 741
2 votes

Stabilizers of the [[12, 2, 4]] "Carbon" code

I tried to answer this (quickly) but failed. A probable reason is listed at the end of the answer. However, I thought I'd record the attempt in case it assists someone else: Since the code is self-...
DaftWullie's user avatar
  • 58.7k
1 vote

Can we find a product of single-qubit states that is orthogonal to a stabilizer codespace?

TL;DR: I prove that, under certain additional assumptions, if $\mathrm{tr}(P_C\rho)=0$ for any $\rho(x,y,z)$ with $xyz\ne 0$, then $C$ fails to correct single-qubit errors. The additional assumptions ...
Adam Zalcman's user avatar
  • 22.9k

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