Quantum Computing Stack Exchange
Quantum Computing Stack Exchange

Questions tagged [fault-tolerance]

For questions about achieving (almost) perfect logical operations with imperfect gates. The tag also applies to questions about the amount of tolerable noise in a quantum circuit, as well as designing circuits to prevent errors from spreading.

170 questions
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What are magic states?

I wonder what are magic states, and a magic state gadget. While I'm reading a paper, these terms frequently appear.
김동민
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Which quantum error correction code has the highest threshold (as proven at the time of writing this)?

Which quantum error correction code currently holds the record in terms of the highest threshold for fault-tolerance? I know that the surface code is pretty good ($\approx10^{-2}$?), but finding exact numbers is difficult. I also read about some…
M. Stern
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What level of "confidence" of the result from a quantum computer is possible?

At a very basic level, reading or measuring a qubit forces it to be in one state or the other, so the operation of a quantum computer to gain a result collapses the state into one of many possibilities. But as the state of each qubit is…
Rory Alsop
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How does approximating gates via universal gates scale with the length of the computation?

I understand that there is a constructive proof that arbitrary gates can be approximated by a finite universal gate set, which is the Solovay–Kitaev Theorem. However, the approximation introduces an error, which would spread and accumulate in a long…
M. Stern
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Why exactly are variational algorithms considered promising?

There is obviously a great deal of work happening at the moment on variational quantum algorithms. However, I'm struggling to understand why exactly are they considered promising? Looking through some papers and review articles (such as this one…
Nikita Nemkov
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Why do error correction protocols only work when the error rates are already significantly low to begin with?

Quantum error correction is a fundamental aspect of quantum computation, without which large-scale quantum computations are practically unfeasible. One aspect of fault-tolerant quantum computing that is often mentioned is that each error-correction…
glS
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Where do we put error correction code in quantum circuit?

First of all : I am a beginner in quantum computing. I would like to have a resource (or an answer if it is not complicated) explaining where we put the error correction codes in a quantum circuit. Indeed, I know we have different possible errors…
Marco Fellous-Asiani
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How are magic states defined in the context of quantum computation?

Quoting from this blog post by Earl T. Campbell: Magic states are a special ingredient, or resource, that allows quantum computers to run faster than traditional computers. One interesting example that is mentioned in that blog post is that, in…
glS
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What is the leading edge technology for creating a quantum computer with the fewest errors?

Which technological path seems most promising to produce a quantum processor with a greater quantum volume (preferring fewer errors per qubit over more qubits), than Majorana fermions? The preferred format for the answer would be similar to: "Group…
Rob
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Can you give an intuitive idea behind how the Minimum Weight Perfect Matching (MWPM) decoder work?

The Minimum Weight Perfect Matching (MWPM) decoder seems to be the most popular choice for decoding error syndromes in Surface Code quantum error correction. Can anyone give an intuitive idea of how it works, with an example?
Aubrey Sharansky
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Transversal logical gate for Stabilizer (or at least Steane code)

I know that for Steane code, we can implement transversally some gates like cNOT, Hadamard and Pauli. What I am looking for is a resource in which it is explained why implementing those gate give rise to the good logical operation. If this is a…
Marco Fellous-Asiani
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Good references to learn magic state distillation for fault tolerance

I need to learn magic state distillation procedure and their application to fault-tolerance. One of the original paper on this subject is the following: https://arxiv.org/pdf/quant-ph/0403025.pdf I am wondering if there are more recent and pedagogic…
Marco Fellous-Asiani
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CSS Code in disguise

Suppose I have a quantum error correcting code described by a set of stabilizers. Is there any easy way of checking whether or not it is equivalent to a code constructed using the CSS construction, using local Clifford transformations?
guest-20
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Magic State Distillation Understanding Check

I'm currently trying to understand the T magic state distillation algorithm described in "Universal Quantum Computation with Ideal Clifford Gates and Noisy Ancillas" [1] (Section V starting on Page 6). I need to understand the basics of magic state…
Malcolm Regan
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What exactly is a subsystem code?

I'm sure I'm just tripping up on terminology here. I'm new to the wonderful field of QEC, and so far am familiar with the stabiliser formalism and basic codes such as the generic surface code. I keep seeing references in the [vast] literature to…
user23402
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