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1 vote
Accepted

Recognizing a CWS code in a specific case

Theorem 6 of https://arxiv.org/abs/0803.3232 states "All $((n, 2, d))$ CWS codes are additive." The $ ((11,2,3)) $ code described in the question is non-additive, which can be verified by ...
Ian Gershon Teixeira's user avatar
2 votes
Accepted

What is an example of a non-additive code that is not a CWS code?

A simple example of a non-additive code that is not a CWS code is the $ ((11,2,3)) $ code given in On the Structure of Additive Quantum Codes and the Existence of Nonadditive Codes . Theorem 6 of ...
Ian Gershon Teixeira's user avatar
0 votes

Moving pauli product rotations past measurements

Let $\sigma$ and $\tau$ be two tensor products of Paulis. Imagine you have a gate sequence $$ e^{i\theta\tau}\sqrt{\sigma}, $$ then you can always rewrite this as $$ e^{i\theta\tau}=\sqrt{\sigma}e^{i\...
DaftWullie's user avatar
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2 votes

Error while plotting the resulting distribution

Once you have the .qasm, you can also upload it to the Classiq platform https://platform.classiq.io/circuit, and then run it on a simulator. Here's how to do this step by step: Step 1: Create and save ...
Amir Naveh's user avatar
0 votes
Accepted

Confusion about lattice-surgery operation

According to https://arxiv.org/abs/1111.4022, to perform a logical CNOT using lattice surgery, three patches of surface codes are needed They show that three patches are sufficient, not that three ...
Craig Gidney's user avatar
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3 votes
Accepted

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

Why can't there be an error detecting code with fewer than 4 qubits?

Here's a proof using the Shadow inequalities, analogous to what @Adam Zalcman described using the Shadow for qubit systems: A $[\![3,1,2]\!]$ is a quantum maximum distance separable code (QMDS). QMDS ...
Felix Huber's user avatar
3 votes
Accepted

How does the surface code satisfy constraints of relativity?

TL;DR: Yes, you can apply logical $X$ gate by applying physical $X$ gate on qubits along one boundary, e.g. on the left, and you can measure logical $X$ by measuring physical $X$ on qubits along ...
Adam Zalcman's user avatar
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1 vote
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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
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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
3 votes

Definition of good quantum LDPC code

Regarding your second question, it does seem that if I have an $[[n, k, d]]$ code, then by putting $m$ of these codes next to each other, I appear to have an $[[nm, km, d]]$ code. As you can see, $n \...
rmehta's user avatar
  • 51
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
Accepted

Definition of good quantum LDPC code

Your definition is correct. Usually one talks about the rate of the code, i.e. k/n. Then, a good qLDPC is a code with linear distance, and also a constant rate when n goes to infinity (i.e. the number ...
David Dentelski's user avatar
2 votes
Accepted

Deformation rules for ZX "pipe" diagrams

I'm not sure what the equivalence rules are I gave a talk about this at one point. The slides are here, and define the flows of the lattice surgery constructions as well as the ZX analogues: since ...
Craig Gidney's user avatar
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0 votes
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Remove edges from PyMatching matching graph / Copy Matching object

Even if you manage to change the graph from the python API in the way you want, you will just trigger a complete internal recreation of the C++ data structures used for decoding. Pymatching is just ...
Craig Gidney's user avatar
  • 37.5k
1 vote

Transversal CNOTs on CSS codes with multiple logical qubits

Expanding on DaftWullie's answer: it is sufficient to prepare "selection states". Suppose you can prepare a "selection state" $|S_k\rangle$ where all the logical qubits are $|0\...
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

Transversal CNOTs on CSS codes with multiple logical qubits

As you say, when people talk about these transversal gates, they typically mean a physical transversal application, resulting in transversal logical application. Whether you can localise it to qubits ...
DaftWullie's user avatar
  • 58.7k
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
2 votes
Accepted

Fault-tolerant syndrome extraction

I highly recommend chapter 12 of Daniel Gottesman's book Surviving as a Quantum Computer in a Classical World Section 12.2 Shor Error Correction Section 12.3 Steane Error Correction and Measurement ...
qubitzer's user avatar
  • 127
1 vote

Transversal QLDPC Code Confusions

The Pauli operators of any stabilizer codes are transversal. By "transversal" I mean the logical operator can be written as a tensor product of single (physical) Pauli operators. This is a ...
Yunzhe's user avatar
  • 741
1 vote

Fault Tolerance of 2-transversal gates

I think you are right that such a 2-local gate would be fault tolerant with "fault-tolerant distance 3" as you say. I think the reason that you don't see this idea around is that it is more ...
Ian Gershon Teixeira's user avatar
2 votes
Accepted

In the QECC condition $\langle\psi|E_a^\dagger E_b|\phi\rangle=C_{ab}\langle\psi|\phi\rangle$, what is $C_{ab}$?

The concept of $C_{ab} $ in the context of the Quantum Error-Correcting Code (QECC) conditions as described in Theorem 2.7 can indeed be confusing due to the mathematical notation and the terminology ...
Bram's user avatar
  • 654
1 vote

In the QECC condition $\langle\psi|E_a^\dagger E_b|\phi\rangle=C_{ab}\langle\psi|\phi\rangle$, what is $C_{ab}$?

I imagine it's supposed to be a matrix $C$ with elements $C_{ab}$, i.e. $a$ indexes the row, and $b$ the column of $C$.
DaftWullie's user avatar
  • 58.7k
1 vote

Can we somehow relate quantum volume with the total number of gates present in a circuit which the machine can succesfully run without large errors

Quantum volume is a metric designed to quantify the performance and capabilities of a quantum computer. It encompasses various factors like gate fidelity, connectivity, coherence time, and others to ...
Shravan Patel's user avatar
3 votes

Fault-tolerant syndrome extraction

As far as I know, there is not a paper that details all these schemes and make comparisons(correct me if I'm wrong). The results are indeed scattered, especially assumptions on error models are ...
AndyLiuin's user avatar
  • 325
0 votes

Can we perform teleported-error-correction with noisy Bell pairs?

Yes. You just prepare, on one side, a logical Bell pair and teleport one half of it through the noisy bell pairs. When you run error correction on it, it effectively corrects the errors that were in ...
DaftWullie's user avatar
  • 58.7k
3 votes

Quantum error correction references

Here is a zoo for error correction codes. https://errorcorrectionzoo.org/ In particular it contains (what should be a near to all known) quantum references.
Turbo's user avatar
  • 181
0 votes

Is this quantum circuit design more prone to noise?

The reason why you are seeing inaccurate results on a real backend is because of the SWAP gates. In the current quantum computing hardware that IBM uses, the dominant source of noise is because of ...
Shravan Patel's user avatar
1 vote
Accepted

Quantum Error Correction Difficulties: "Measurements destroy quantum information" Intuition

Not really, this statement does not capture the intuition for the use of entanglement, as it is not due to the measurement problem. It is more akin to the idea of redundancy in classical error ...
Balint Pato's user avatar
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