Questions tagged [error-correction]
Quantum error correction (QEC) is a collection of techniques to protect quantum information from decoherence and other quantum noise, to realise fault-tolerant quantum computation. Quantum error correction is expected to be essential for practical quantum computation in the face of noise on stored quantum information, faulty quantum gates, faulty state preparations, and faulty measurements. (Wikipedia)
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Automated methodology / tool to find logical operators for QEC codes
Is there a standard tool or automated methodology to find logical operators for arbitrary stabilizer QEC codes (or specific families of codes?). I am aware that one could work through the math and ...
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Can QEC Handle Continuous Errors Like Rotation and Dephasing?
"I've recently started learning about Quantum Error Correction (QEC). I notice that many papers focus on discrete errors like bit-flips and phase-flips (Pauli errors), and I understand that ...
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Do logical operations map stabilizer group to itself?
Say we have a $n$-qubit stabilizer code $Q$ with stabilizer group $S$. If unitary $\bar{K}$ is a logical operation that preserves the codespace, what conclusion can we draw for $\bar{K}$ and $S$?
If $\...
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Lattice Surgery for Rectangular Surface Codes?
It has been shown that one can reduce the X or Z code distance for surface codes, when the noise is biased towards one type of fault. From my understanding, this is referred to as the rectangular ...
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What are textbook about quantum computing for graduate students?
I'm looking for an overview of quantum computing for graduate students. Does anyone know of a textbook that includes topics on surface codes and transmon qubits? Nielsen-Chuang is certainly a bible, ...
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Can stim calculate "circuit distance"
This paper (page 23) defines "circuit distance" through :
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Logical operator in cylindrical surface code
I'm trying to define a cylindrical surface code; that is, a surface code that has boundaries in 1 axis and that is periodic over the other. Let's assume it is periodic in the horizontal axis, and it ...
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How is $Rx(\pi/2)$ applied to a qubit via state injection?
In High threshold universal quantum computation on the surface code VI(C), Injecting $Rx(\pi/2)$ is claimed to be done with the following circuit
The paper says that if we want to do $Rx(\pi/2)$, we ...
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Repetition of syndrome measurements in the circuit-level noise
It is well known that in the presence of measurement errors, we need to repeat syndrome measurement about $d$ times, for example in surface codes. I know that it is true for the phenomenological noise,...
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Single-shot error correction in high dimensional topological codes and Knill or Steane gadget
I have heard that some high dimensional topological codes, such as 3D subsystem toric code and 3D gauge color code, allow single-shot error correction, i.e., we can extract syndrome fault-tolerantly ...
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Smallest distance-2 codes with non-trivial logical transversal $T$ gates
It has been shown that the $[[15, 1, 3]]$ code is the smallest distance-3 code with logical transversal $T$ gates (See arXiv:2210.14066). I say a code admits logical transversal $T$ gates if 1. The ...
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Counting the number of faults inside an exRec
Given a constructive proof of the threshold theorem based on exRecs, as in (AGP05), the most elementary definition of an exRec being bad for a code that corrects 1 error, in the context of independent ...
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How is stim validated
A lot of papers I see use stim to get performance of QECC with "circuit noise".
I'm sure stim is a decent tool, but can it really be treated as a golden reference?
How would you know that ...
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Threshold theorem for general markovian noise
The threshold theorem stated in (AGP05) has an elegant and reasonably simple proof in the case of independent stochastic noise. After presenting that, they prove the threshold theorem in the case of ...
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Full QEC circuit simulation in stim
Here is a question that appears in Stim/Issues,I think it is really worthwhile to discuss about it or at least recommend other similar questions with correct answers to it:
"I want to efficiently ...
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