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
0answers
44 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
14 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
48 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
37 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
56 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
88 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, |...
5
votes
1answer
31 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
73 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
50 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
41 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
66 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
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 ...
3
votes
1answer
48 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
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 ...
2
votes
2answers
90 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
97 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
18 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
41 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
49 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
35 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
77 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
123 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
59 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
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 ...
2
votes
1answer
45 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
80 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
49 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
61 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
102 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
107 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
66 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
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 ...
11
votes
3answers
872 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
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\...
3
votes
1answer
103 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
53 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
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 ...
5
votes
1answer
182 views

What set of quantum logical operations can one use to benchmark spin Hamiltonians?

Chemistry background: In magnetic molecules, it is sometimes the case that one can adjust the time-independent Hamiltonian by chemical design. This means there is freedom to adjust parameters in the ...
8
votes
2answers
362 views

How could Majorana particles be used to improve quantum computers?

This recent press release claiming that Improved measurements bring final proof of Majorana particles closer than ever, which summarizes the results of a recent paper in Nature simply entitled "...
16
votes
1answer
207 views

How does magic state distillation overhead scale compare to quantum advantages?

I'm interested in the model of quantum computation by magic state injection, that is where we have access to the Clifford gates, a cheap supply of ancilla qubits in the computational basis, and a few ...
9
votes
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,...
2
votes
1answer
76 views

Measuring order ancilla qubits in surface code

Recently I have been reading about surface codes a little and one thing I came acros was a specific order in which gates should be applied before the ancilla is measured. See for instance figure 2 in ...
4
votes
2answers
242 views

Computing with Logical Qunits

What exactly is a logical (non-physical? error corrected?) qunit? Can quantum systems be built exclusively w/ logical qunits?
7
votes
2answers
279 views

Practical Implementations of QECCs in IBM Q Experience

I am learning how to program the IBM Q Experience quantum computers in order to learn more about how does it work and in order to perform some experiments in it. By doing so I was wondering what are ...
6
votes
1answer
117 views

Reference on MITxPRO Applications of Quantum Computing Professional Certificate Program

Recently I found out the Applications of Quantum Computing Professional Certificate Program that MITxPRO is offering for people interested in quantum computing. I saw that it is consisted of four ...
19
votes
2answers
2k views

What is 'Surface Code'? (Quantum Error Correction)

I am studying Quantum Computing and Information. I have crossed with the 'Surface Code' phrase but I can't find a brief explanation of what it is and how it works. Hopefully you guys can help me with ...
11
votes
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 ...
19
votes
4answers
2k views

Why can't there be an error correcting code with fewer than 5 qubits?

I read about 9-qubit, 7-qubit and 5-qubit error correcting codes lately. But why can there not be a quantum error correcting code with fewer than 5 qubits?