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.
4
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0answers
60 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 ...
3
votes
2answers
45 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 ...
4
votes
1answer
74 views
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)....
10
votes
2answers
718 views
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.
...
5
votes
2answers
52 views
Fault tolerant quantum measurement: how is implemented the “majority vote”
As a fundamental component for a quantum computation, the measurement needs to be implemented in a fault tolerant way.
As indicated in Chuang and Nielsen Quantum Computation and Quantum Information, ...
7
votes
1answer
164 views
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 ...
6
votes
1answer
97 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 ...
8
votes
1answer
101 views
How does the size of a toric code torus affect its ability to protect qubits?
The Toric code Hamiltonian is:
$\sum_{x,y}\left( \prod_{i\in p(x,y)} Z_{ixy} + \prod_{i\in v(x,y)} X_{ixy} \right),$
where the $v$ and $p$ are defined according to this picture (courtesy of James ...
6
votes
2answers
92 views
Why or how is 'cat' state preparation via a C-not-not operation not fault tolerant?
On p490 of Nielsen and Chuang, 2010 the authors say that the preparation of the 'cat' state ($|000\ldots 0\rangle+|111\ldots 1\rangle$) is not Fault Tolerant. Below is my mock up of the diagram they ...
5
votes
1answer
177 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 ...
15
votes
5answers
298 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 ...
10
votes
1answer
268 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 ...
12
votes
1answer
117 views
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 ...
18
votes
3answers
318 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 ...
21
votes
2answers
557 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 operation of a QC to gain a result collapses the state into one of many possibilities.
But as the ...
