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)

Filter by
Sorted by
Tagged with
2
votes
1answer
29 views

What are the Main Classes of Quantum Error-Correcting Codes?

Classically, we have the Hamming Code, Turbo Code, Reed-Solomon Code, etc. I am interested in knowing the classes of quantum error-correcting codes. They don't have to be analogous to classical codes, ...
1
vote
1answer
77 views

How do I interpret the readout error for a quantum computer?

For example, the ibmqx2 computer has the most recent readout error of $4.40 \cdot 10^{-2}$. Does this mean per 1000 measurements, 44 faulty results exist?
1
vote
0answers
47 views

Job execution issue while using IBMQ Experience

I am trying to run QSVM algorithm on the IBMQ backend devices using the API_TOKEN. Below is the snippet of the code that I am running. The code fails the validation test and throws an exception after ...
2
votes
1answer
42 views

Questions about theorem and proof: “Quantum error correction condition”, Thm 10.1 Nielsen & Chuang

I have some basic questions around the theorem giving quantum error correction conditions that give necessary & sufficient conditions to have an error correcting operation. The theorem is stated ...
2
votes
0answers
27 views

Intuition about Knill-Laflamme QEC conditions

The Knill Laflamme QEC conditions are stated this way: We consider a code space $C$ and its associated projector $P_C$. We consider a noise acting on our system: $E(\rho)=\sum_a E_a \rho E_a^{\...
2
votes
1answer
33 views

Basics on CSS codes: manipulation of the ancillas to detect error

I am reading the very basics about CSS codes in the Nielsen & Chuang. On page 450 of this book is explained how the ancillas are used to detect a bit-flip error on the encoded data. We consider $...
4
votes
1answer
36 views

Knill-Laflamme condition and requirements for error correction

Suppose we have a stabilizer group $\mathcal{M}$, the Knill-Laflamme condition for error correction states An error with Kraus operators $\{E_k\}$ is correctable if either $$E^\dagger_kE_l\in\...
3
votes
1answer
79 views

Going from a circuit to the quantum state output of the circuit

I'm looking at the following lecture notes where we start with the circuit below for some state $\vert\psi\rangle_L$ that picks up an error to become $E\vert\psi\rangle_L$ It is later claimed in the ...
1
vote
1answer
201 views

All unitary errors are correctable

The Knill-Laflamme condition for a stabilizer $\mathcal{M}$ is An error with Kraus operators $\{E_k\}$ is correctable if either $$E^\dagger_kE_l\in\mathcal{M}\quad\forall\, k,l $$ or there exists $...
0
votes
0answers
19 views

Density Evolution to Optimize QLDPC code design

Density Evolution is a simulative tool that models the behaviour of SPA (sum-product) decoders. It is useful because it enables the optimization of code designs so that extensive simulations can be ...
2
votes
2answers
86 views

The merit of quantum error correction codes

We know that word error rate (WER) rather than qubit error rate (QER) is used to evaluate the performance of quantum Turbo codes and quantum LDPC codes. In classical coding theory, when we are ...
2
votes
0answers
47 views

I thought we had already passed this error and qubit threshold?

As outlined in Quantum Computing Progress and Prospects published this year, on page 169-171 there is the diagram showing that we are at the 10's of qubits mark. Looking into the diagram further there ...
2
votes
0answers
19 views

There seems to be a problem with the implementation of identity gates on Qiskit as compared to the circuit composer

I have been experimenting with slowing down the decay of qubits, and as a control, I implemented a circuit with just identity gates for comparison. However, when I implement such circuits in Qiskit, ...
2
votes
2answers
55 views

How do you implement a negative controlled gate using the regular controlled gate?

I have been reading a paper about perfect error correction codes, and when the circuit is described, the author uses some negative controlled gates, that is: The gate is applied if the control is $|0\...
3
votes
2answers
57 views

2 ways to do the three qubits bit-flip code

I'm trying to understand the three qubits bit-flip code. I use the book of Phillip Kaye An introduction to quantum computing. In this book he introduce the three qubits bit-flip code with this ...
5
votes
1answer
73 views

Get result measurement into a circuit with Qiskit

I'm trying to implement the three qubit bit flip code in Qiskit. Therefore, I need to get the result of a measure of two ancilla qubits, to deduce which gate I need to use do recover my logical qubit....
6
votes
1answer
92 views

What is the definition of Bell state on a n-qubit system?

Question 1: The bell state for a 2-qubit system has been defined in Neilsen and Chuang's book as the set of maximally entangled states spanned by $\{|00\rangle + |11\rangle, |00\rangle - |11\rangle, |...
6
votes
1answer
40 views

Error syndromes and recovery procedure in bit flip code

This question relates to exercise 10.4 in Nielsen and Chuang. For syndrome diagnosis, the textbook provides an example where one has four projectors, by which, you can identify where a one qubit ...
5
votes
1answer
93 views

How does measurement calibration work?

One of the possible ways to improve the results of an experiment on the IBM machine using the Qiskit language is to use the measurement calibration methods. This is the link to the documentation. I ...
7
votes
1answer
60 views

How to calculate the distance of stabilizer code?

How to calculate the distance of the stabilizer code [[n,k,d]]? It's better if you can make a 3-qubit example. And what's the relationship between d and Pauli group?
1
vote
1answer
44 views

Where (in the algorithm) is the logical qubit encoded in Q.E.C?

I have a basic question about the encoding of logical information into physical qubits. I only know the 3 qubit code (I have very limited knowledge in QEC). The 3 qubit code is usually presented as: ...
3
votes
2answers
80 views

Shor 9 qubit code — how are the observables measured and eigenvalues obtained during syndrome measurement?

Say we have the Shor 9 qubit code $$|\psi_L\rangle=\tfrac{1}{\sqrt{2^3}}((|000\rangle+|111\rangle)^{\otimes3}+(|000\rangle-|111\rangle)^{\otimes3}),$$ and we have a bit flip error. My lecture notes ...
22
votes
3answers
736 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 ...
3
votes
1answer
54 views

State of a system after the second qubit of a Bell state sent through a bit flip error channel

The second qubit of a two-qubit system in the Bell state $$|\beta_{01}\rangle= \frac{1}{\sqrt{2}}(|01\rangle+|10\rangle)$$ is sent through an error channel which introduces a bit flip error with ...
11
votes
1answer
303 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 ...
2
votes
2answers
94 views

What quantum volume is needed to represent a single logical qubit?

The quantum volume metric $V_Q$ is a proposed metric for quantifying and comparing the performance of quantum computers1. The quantum volume is defined as $$V_Q = \max_{n<N} \left(\min\left[n, d(n)...
8
votes
1answer
101 views

Are all $[[n, k, d]]$ quantum codes equivalent to additive self-orthogonal $GF(4)^n$ classical codes?

Theorem 2 of [1] states: Suppose $C$ is an additive self-orthogonal sub-code of $\textrm{GF}(4)^n$, containing $2^{n-k}$ vectors, such that there are no vectors of weight $<d$ in $C^\perp/C$. ...
5
votes
0answers
21 views

How is the decoherence rate connected to the error rate?

I'm reading about the threshold theorem, which states that "a quantum computer with a physical error rate below a certain threshold can, through the application of quantum error correction schemes, ...
2
votes
1answer
42 views

How does Steane code use the classical Hamming code for error correction?

I know what the Hamming code is. But I don't understand how could this idea be applied in quantum computation since it's required to cover the case of superposition and entanglement. How could you ...
4
votes
0answers
51 views

Is the quantum Singleton bound compatible with the Toric Code?

Note: Cross-posted on Physics SE. The quantum Singleton bound states that for an error-correcting code with $n$ physical qubits and $k$ encoded qubits, and some subsystem $R$ of $m$ qubits that can '...
3
votes
1answer
70 views

In error correction code why don't we imitate the Hamming code instead of the complicated Steane code?

Instead of the complicated Steane code, I don't understand why don't we use a much simpler and exact imitation of the classical Hamming code. So here is my idea: Let's have 7 qubits, and we will ...
1
vote
1answer
36 views

Is there an inherent difference in need for error correction between quantum annealing and gate based methods?

When I read about computing using gate based methods, I mainly read about the difficulties with error rates, circuit depth (and connectivity) and not enough qubits. With computing using quantum ...
3
votes
1answer
49 views

How does the actual measurement collapsing an error to an orthogonal basis look like?

An error can be written as a linear combination of $\Bbb I$, $X$, $Z$, $XZ$ Pauli matrices. So when measuring an errand state we aim at collapsing the error into one of these four possibilities. How ...
4
votes
0answers
82 views

In what situation are three rounds of syndrome measurement required for fault-tolerance in the surface code?

I have heard multiple times the claim that three rounds of syndrome measurement required for fault-tolerance in the surface code. I'm not sure what situation would require this, as I think less would ...
4
votes
1answer
132 views

How to deal with -LookupError: backend “ibmqx4” is not found?

I am using Jupyter notebook to write and running my qiskit codes (python 3.6) and every time I encounter the message: LookupError: backend "ibmqx4" is not found, right now the ibmqx4 computer is not ...
3
votes
1answer
68 views

Estimating the depolarizing probability of depolarizing channels

When considering quantum error correction over depolarizing channels, the depolarizing probability $p$ such that an error of the kind $X,Y,Z$ will happen is used as a priori information in order to ...
1
vote
1answer
56 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 ...
2
votes
1answer
49 views

Why does phase flip correction error? Why could any error be written as a linear combination of I, X, Z and ZX matrices?

I don't understand how it's being proven that error correction can be applied only to X, Z noises and this solves all errors? Does this have to be with this set being universal? (Z is exactly like ...
3
votes
2answers
94 views

A question on Eastin-Knill theorem

I am reading the paper Restrictions on Transversal Encoded Quantum Gate Sets, Bryan Eastin, Emanuel Knill. I am unable to understand the following lines in the proof. As the set of all unitary ...
2
votes
1answer
56 views

Decoherence in quantum systems always produces $\vert0\rangle$

I was recently asked two questions concerning error in quantum computing: Is it possible for quantum computers to exhibit behavior similar to flip errors in classical computers where a state $\vert0\...
2
votes
2answers
64 views

Why is it that the Pauli matrices and error correction operator act only on $|\psi\rangle\langle \psi|$ and not on state vector $|\psi\rangle$ itself?

I saw that the Pauli matrices really work, that's rotating a state by 180 degrees, only if you take the density matrix for example with X it only works if first we take X $|\psi\rangle$ and multiply ...
5
votes
1answer
103 views

Is the common depiction of a surface code to be taken literally as a real-space image of the actual hardware?

I'm currently reading the paper "Surface codes: Towards practical large scale quantum computing" and have a couple of very basic questions that if answered will help me contextualize and organize the ...
5
votes
0answers
109 views

Why can a point in anti-de Sitter space be modeled as a logical qutrit and how is its error correction done?

This isn't my area but the recent Quanta article How Space and Time Could Be a Quantum Error-Correcting Code struck me as interesting. They mention: In their paper[1] conjecturing that holographic ...
8
votes
0answers
69 views

Reference that explains how to read 3d topological diagrams for surface code computations

I like making diagrams to describe computations. For the surface code, an excellent tool is 3d topological diagrams. Here is an example diagram (made by me in SketchUp): The basic idea is that white ...
20
votes
5answers
666 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 ...
11
votes
3answers
936 views

What is the difference between “code space”, “code word” and “stabilizer code”?

I keep reading (e.g. Nielsen and Chuang, 2010; pg. 456 and 465) the following three phases; "code space", "code word" and "stabilizer code" - but am having a difficult time finding definitions of them ...
8
votes
1answer
285 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\...
3
votes
1answer
133 views

Confusion on the definition of the phase-damping channel

I am reading about the phase damping channel, and I have seen that some of the different references talking about such channel give different definitions of the Kraus operators that define the action ...
4
votes
1answer
55 views

How to find the fidelity between two state when one is an operator?

I am going through Nielsen and Chuang and am finding the chapter on error-correction particularly confusing. At the moment I am stuck on exercise 10.12 which states Show that the fidelity between the ...
15
votes
5answers
366 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 ...