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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11
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1answer
891 views

Is Gil Kalai's argument against topological quantum computers sound?

In a lecture, recorded on Youtube, Gil Kalai presents a 'deduction' for why topological quantum computers will not work. The interesting part is that he claims this is a stronger argument than the ...
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1answer
295 views

What is the Helstrom measurement?

I have been reading the paper Belief propagation decoding of quantum channels by passing quantum messages by Joseph Renes for decoding Classical-Quantum channels and I have crossed with the concept of ...
11
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1answer
296 views

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 ...
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5answers
620 views

Is error correction necessary?

Why do you need error correction? My understanding is that error correction removes errors from noise, but noise should average itself out. To make clear what I'm asking, why can't you, instead of ...
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3answers
707 views

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 ...
15
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5answers
344 views

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 ...
7
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3answers
732 views

What is a Bacon-Shor code and what is its significance?

I'm at the AQC conference at NASA and everybody seems to suddenly be talking about the Bacon-Shor code but there is no Wikipedia page and the pdf that I gave a link to does not really explain what it ...
19
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3answers
346 views

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 ...
10
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1answer
127 views

Violation of the Quantum Hamming bound

The quantum Hamming bound for a non-degenerate $[[N,k,d]]$ quantum error correction code is defined as: \begin{equation} 2^{N-k}\geq\sum_{n=0}^{\lfloor d/2\rfloor}3^n\begin{pmatrix}N \\ n\end{...
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1answer
55 views

What does it mean to perform a measurement in correspondence with different projections?

In error correction, like the bit flip, you perform a measurement which corresponds to different projections so that the outcomes can teach you about the error. What does it mean? How do you actually ...
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2answers
1k views

Allowed CNOT gates for IBM Q 5 quantum computer

I trying to do some tests in the IBM Q5 computer of IBM quantm experience for some simple error correction protocols, but as I can see, some operations between the qubits are not allowed. For example,...
8
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1answer
273 views

Quantum Channel Models

The so called depolarizing channel is the channel model that is mostly used when constructing quantum error correction codes. The action of such channel over a quantum state $\rho$ is $\rho\...
7
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148 views

Intuition for Shor code failure probability

Consider the 9 qubit Shor code. This can detect and correct arbitrary single qubit errors, but if there are 2 or more single qubit errors before a correction round, the correction will fail. (In the ...
7
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1answer
205 views

Is the Pauli group for $n$-qubits a basis for $\mathbb{C}^{2^n\times 2^n}$?

The Pauli group for $n$-qubits is defined as $G_n=\{I,X,Y,Z \}^{\otimes n}$, that is as the group containing all the possible tensor products between $n$ Pauli matrices. It is clear that the Pauli ...
6
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1answer
103 views

Lower bound for Degenerate Codes?

According to (Macchiavello, Palma, Zeilinger, 2001; pg82) a lower bound of the encoding Hilbert space of a non degenerate code is given by the quantum version of the Hamming bound: $$2^k \sum_{i=0}^t ...