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.
38
questions
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1answer
42 views
Pros/cons of the different schemes to have complete fault-tolerant gatesets
I am interested to have references and comment about pro/cons of the various methods that are used to implement complete gateset in a fault tolerant manner.
Usually the Clifford operations have a ...
4
votes
1answer
67 views
Definition of magic $T$ and $H$ states: are there different definitions for them?
I am a bit confused by the definition of magic $T$ and $H$ states and I would like to check if their name is actually not uniformously spread in the litterature (or if I am not understanding something)...
4
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1answer
60 views
Good references to learn magic state distillation for fault tolerance
I need to learn magic state distillation procedure and their application to fault-tolerance.
One of the original paper on this subject is the following: https://arxiv.org/pdf/quant-ph/0403025.pdf
I am ...
9
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1answer
203 views
Why exactly are variational algorithms considered promising?
There is obviously a great deal of work happening at the moment on variational quantum algorithms. However, I'm struggling to understand why exactly are they considered promising? Looking through some ...
2
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2answers
81 views
Accuracy threshold theorem: what is the physical probability of failure exactly
In this famous paper is derived the quantum accuracy threshold theorem for concatenated codes.
I have questions for the case errors are assumed to be local and Markovian.
In the so called level-1 ...
1
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1answer
29 views
Can one easily compute the weight enumerator of a CSS code constructed from two binary codes $M_1,M_2$?
Consider a CSS code, which is constructed from two binary codes $M_1$ and $M_2$, so its symplectic matrix is of the form:
$$ \begin{pmatrix} M_1 & 0 \\ 0 & M_2 \end{pmatrix}.$$
Suppose one ...
2
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0answers
33 views
How to do the counting when computing the fault tolerant threshold of quantum codes?
Here, I want to ask a basic question about how to compute the fault tolerance threshold of quantum codes. As I know, maybe, the most usual way is to do some simulations. Howvever, I am more intersted ...
5
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3answers
232 views
CSS Code in disguise
Suppose I have a quantum error correcting code described by a set of stabilizers. Is there any easy way of checking whether or not it is equivalent to a code constructed using the CSS construction, ...
1
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1answer
46 views
What are the simplest examples of codes with transversal non-Clifford gates?
There are certain codes which have transversal non-Clifford gates. My question is, what are the simplest examples of such codes and how does one check for a non-Clifford gate? Is it a computationally ...
2
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1answer
90 views
Understanding transversal gates for the 7 qubit steane code
How can one derive the complete list of transversal operators for the 7-qubit Steane code? I can derive the Clifford operators that are transversal, but I do not understand an easy way to check for ...
3
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1answer
290 views
Transversal logical gate for Stabilizer (or at least Steane code)
I know that for Steane code, we can implement transversally some gates like cNOT, Hadamard and Pauli.
What I am looking for is a resource in which it is explained why implementing those gate give rise ...
2
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0answers
39 views
Fault-tolerant qudit computation: advantage? [closed]
What are advantages of a fault-tolerant qudit computation compared with fault-tolerant quantum computation for qubits?
2
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1answer
90 views
CSS Code and Fault-tolerant Problem in Nielsen and Isaac Chuang‘s book
Could someone help me with $Problem-10.52$ in Nielsen and Isaac Chuang‘s book?
The screenshot is shown below. I have no idea about that.
Hope someone can give me some suggestions.
By the way, if I ...
5
votes
1answer
123 views
(Why) does every CSS code allow for transversal measurement?
I recently encountered the statement that
any CSS code [that encodes single-qubit logical states] has a property that measurements can be performed qubit-wise, but the measurement outcome of every ...
0
votes
1answer
37 views
Where do errors occur during error syndrome and recovery?
I'm studying quantum error correction on Nielsen's Quantum Computation and Quantum Information, but I don't understand how it identifies the number of places where an error may occur.
It uses ...
17
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3answers
2k views
What are magic states?
I wonder what are magic states, and a magic state gadget. While I'm reading a paper, these terms frequently appear.
2
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1answer
58 views
Circuit of quantum error correction code
I read an interesting paper of QEC with only two extra qubits.
In the paper, there is a circuit. Note that .
Here are some contexts of the paper:
"The stablizer is $XZZXI$. If the second gate ...
2
votes
2answers
146 views
How is it not a contradiction that it is possible to build fault tolerant circuits with strictly contractive (e.g.: depolarizing noise) channels?
This paper discusses strictly contractive channels, i.e. channels that strictly decrease the trace distance between any two input quantum states.
It is shown that if a quantum circuit is composed of ...
3
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2answers
222 views
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 ...
0
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1answer
75 views
Quantum error correction - approximate vs exact
When one has a noisy quantum channel over which one wishes to send some quantum state, one usually comes up with an encoder and decoder. Then, the error between the input state and the output state is ...
5
votes
2answers
143 views
Why does quantum error correction work?
I read about some QEC codes such as Shor code. It encodes a logical qubit to 9 physical qubits, to correct the bit-flip and phase-flip error. To do this, it needs multiple $\mathrm{CNOT}$ and $\mathrm{...
4
votes
0answers
76 views
How's quantum noise and fault-tolerance related to symplectic geometry and geometric quantization?
Gil Kalai often speaks of the apparent connection between symplectic geometry, geometric quantization, and quantum noise. He is known to describe one of his focus areas as:
(...) properties and ...
4
votes
2answers
94 views
Where does error correction go in a quantum algorithm?
Where does QEC fit in the larger picture of the execution of a fault tolerant quantum algorithm?
For QEC, there is an initial preparation of the qubit state and the ancillary qubits; then a "noisy ...
6
votes
0answers
112 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
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2answers
256 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
224 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)....
11
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2answers
867 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
151 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, ...
11
votes
1answer
892 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 ...
8
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2answers
430 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 ...
9
votes
2answers
280 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 ...
7
votes
2answers
200 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
206 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
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5answers
541 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 ...
12
votes
1answer
452 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 ...
14
votes
1answer
272 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 ...
21
votes
3answers
637 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 ...
23
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3answers
1k 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 ...
