# 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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### How to create the logical $|0_L\rangle$ state for the Steane's 7-qubit code?

I don't know how to prepare using Qiskit the following state in order to implement a Steane's 7-qubit code circuit (I omit the normalization factor): \begin{align*} |0_L\rangle =&|0000000\rangle+|...
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### Circuit for implementing Steane's code for Quantum Error Correction

I was reading about the Steane's code for QEC. However I could not find any implementation or circuit describing its creation. Can anyone share/explain how the Steane's code could be implemented. The ...
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### A question about quantum noise model

Now, I try to understand some concept of Quantum Noise Model and Quantum Channel. The Quantum Noise can be represented as a quantum operator with their own probability. As far as I concerned,(I dont ...
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### What is the pseudo threshold of a QECC using stabilizer formalism

Can someone explain what is the threshold and the pseudo threshold of a Quantum Error Correction Code , for instance the 9-qubit code, and how to calculate it using the stabilizer formalism simulation ...
206 views

### Find the Kraus operators of a combined amplitude and phase damping channel

I am going through the paper Surface code with decoherence: An analysis of three superconducting architectures and I have a doubt about how the authors get what they refer to as the combined channel ...
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### Question regarding part of the proof for the typical subspace theorem

Part three (going by N&C page 544) states that $$tr(S(n)\rho^{\otimes n})=tr(S(n)\rho^{\otimes n}P(n,\epsilon))+tr(S(n)\rho^{\otimes n}(I-P(n,\epsilon))).$$ Now I understand how the term on the ...
100 views

### Quantum Error Correcting Codes and Graphs

Couple of weeks ago I asked this question on theory CS but I didn't get an answer. So trying it here. I was reading combinatorial approach towards quantum correction. A lot of work in this is on ...
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### Qubit relaxation time dependencies

The qubit relaxation time $T_1$ is an important parameter in order to describe the coherence time that a qubit presents, that is, the time in which its coherence quantum state is not compromised by ...
266 views

### How to do error mitigation on the ibmq_16_melbourne?

I'm trying to make a calibration matrix using CompleteMeasFitter as in here on IBMQ Melbourne, but I need to use all 15 qubits, which mean it has to run 32768 calibration circuit, far exceeding the 75 ...
194 views

### Algorithm to find stabilizer states

I'm working on a project in which I have to find stabilizer states based on a few criteria, the main one being that it has to have a certain amount of coherence, I'm using the following equation to ...
52 views

### How to calculate destabilizer group of toric and other codes

Some papers use the "destabilizer group" for more efficient simulations; see for example (page 3): https://www.scottaaronson.com/showcase2/report/ted-yoder.pdf "In addition to ...
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### Smallest Distance-5 Quantum Error Correction Code?

Is it known/proven what the smallest quantum error correction code is that can correct arbitrary two-qubit Pauli errors? I can think of the nested/concatenated 5-qubit code or a 25-qubit version of ...
217 views

### Exponential Growth of Noise in Quantum Computers

I recently listened to a presentation for Introductory Quantum Computing. It was very general and meant to give the listeners an idea about the potential for Quantum Computing. The speaker ended the ...
220 views

### Physical Interpretation of Non-Trace Preserving Quantum Operations

In Chapter 8 of Nielsen and Chuang's Quantum Computation and Quantum Information, a mathematical framework is developed to describe the dynamics of open quantum systems. Suppose the initial state of ...
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