Questions tagged [quantum-error-correction]
The quantum-error-correction tag has no usage guidance.
22
questions
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1answer
92 views
$n$-fold degeneracy, ground state, toric code [closed]
I'm having a hard time understanding the degeneracy of the Kitaev toric code. Can anyone explain to me with details the following:
How do we find the ground states of the toric code and its gape?
...
0
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0answers
37 views
Transversal Hadamard gates for self-dual CSS quantum codes
I have come across a statement saying that a self-dual CSS quantum code has a transversal Hadamard gate. Initially I thought that there was a fairly elegant reasoning for this by considering only that ...
2
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0answers
41 views
Deducing fusion rules of non-abelian fluxons
I have been reading about non-abelian fluxons in John Preskill's lectures notes on topological quantum computing and I do not understand how he deduced the fusion rules for fluxons in the example he ...
2
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2answers
146 views
How to check if a qubit in a circuit is equal to another qubit?
If we have a set of qubits q1 ,q2 and q3 for example,
$$
\vert{q_1}\rangle = a \vert{0}\rangle +b \vert{1}\rangle\\
\vert{q_2}\rangle=\vert{0}\rangle\\
\vert{q_3}\rangle=\vert{0}\rangle
$$
the state ...
3
votes
0answers
80 views
Smallest Distance-5 Quantum Error Correction Code? [closed]
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 ...
1
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0answers
28 views
Understanding surface code diagrams
I'm trying to understand the diagrams used in the following paper. I'm new to the area so I don't have experience with the stabilizer formalism, but I'm trying to figure out what's going on in the ...
5
votes
2answers
145 views
Can a Hadamard gate be realized with perfect precision?
This is my first question on the Physics Stack Exchange; I hope it is not be a duplicate… :-|
I am not really a physicist (I am actually a professional mathematician), but I have already read quite a ...
0
votes
1answer
38 views
Is there a theoretical limit on the smallest angle that can be used in a quantum rotation gate?
Assuming ideal conditions and no error, what is the smallest $\theta>0$ that can be used in $R_x(\theta)$ or $R_y(\theta)$.
1
vote
2answers
99 views
Why doesn't using quantum error-correction increase the production of entropy and decohrence?
Error-correction in quantum computing is designed to get around the decoherence "washing out" the answer to a computation. But wouldn't the introduction of error-correction procedures or apparatus ...
4
votes
2answers
314 views
Is HaPPY code a certain type of MERA?
Pastawski, Yoshida, Harlow, and Preskill introduced the HaPPY code in their (now famous) paper, arXiv:1503.06237, as a way to model the AdS/CFT correspondence as a quantum error-correcting code. ...
1
vote
1answer
64 views
Can we restore a state of a whole system from its subsystem?
I am thinking about the deletion error correcting codes for quantum information.
In classical information theory, there exist some deletion error correcting codes. An easy example is the following ...
1
vote
1answer
38 views
What happens to physical qubits when they decohere during quantum error correction?
Say you have a scaled up system with 98% fidelity so 2% decoheres. These are physical qubits doing error correction on information encoded on logical qubits. 98% of these entangled qubits will be ...
1
vote
2answers
113 views
Showing that a set of errors is correctable (Knill-Laflamme conditions)?
I am confused about how to apply the Knill-Laflamme Quantum Error-correction conditions, which are the following:
A code $C \leq H$ is correctable for $\mathcal{E} = \sum_{i=1}^{n}E_i \rho E_i^*$ ...
4
votes
1answer
228 views
Why are only unitary operations allowed in quantum information theory?
In the quantum information theory, any operations for a quantum state have to be unitary operations. Why is this restriction needed? Can't we make a non-unitary operation to a state? I know that a ...
3
votes
1answer
138 views
Is the Quantum Singleton Bound Compatible with the Toric Code?
The Quantum Singleton Bound states that for an error-correcting code with $n$ physical qubits and $k$ encoded qudits, and some subsystem $R$ of $m$ qudits that can 'access the entire quantum code', it ...
0
votes
1answer
321 views
How can I prove that the partial trace is well-defined?
When I define the partial trace as below, how can I prove it well-defined?
I understand that I have to indicate $Tr_k(\rho)$ does not depend on how to take the ONB of $\mathbb{C}^2$
$$n\in \mathbb{Z}_{...
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0answers
40 views
Does the measuring instrument which counts the number of quantum particles exist?
I have recently been thinking about the quantum deletion error correcting codes, but the primary problem is whether the receiver can detect the loss of quantum particles or not. So my question is that ...
2
votes
2answers
149 views
Can quantum deletion error-correcting codes be constructed?
I'm wondering whether or not we can construct quantum deletion error-correcting codes. The quantum deletion error is defined by the partial trace. If we can, could anyone give an example?
2
votes
1answer
125 views
Uniquness of stabilizer generators of a state $\left| \psi \right>$?
Let $G_n$ be the $n$-qubit Pauli group and $S$ an abelian subgroup which does not contain the element ($-I$). I know that if $S$ has $n$ generators then it specifies a single state $\left| \psi \right&...
asked Mar 14 '18 at 20:00
Quantum spaghettification
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2
votes
0answers
36 views
On the optimality of Stabilizer codes
I have been studying about quantum error correction codes, specifically aobut the so-called stabilzer codes, and I wonder if are this class of quantum codes the best codes known (in terms of capacity ...
9
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0answers
155 views
Topological quantum error correcting codes which are not CSS codes
The most promising-seeming quantum error correction codes for the medium-to-long term are the topological codes, of which the toric code (and variants such as planar surface codes) and colour codes ...
5
votes
1answer
200 views
What are the quiescent states of the surface code?
Notation
$$X \equiv \sigma_x \qquad Z \equiv \sigma_z$$
Introduction
The surface code is a quantum error correction code.
In the surface code, we have a two-dimensional grid of qubits each coupled ...
