Questions tagged [quantum-error-correction]

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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 ...
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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 ...
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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 ...
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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 ...
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How does Teleportation based Error Correction (TEC) detect and correct loss/erasure errors?

I'm looking at papers like https://arxiv.org/pdf/1902.01692.pdf Page 10 and https://arxiv.org/pdf/1605.00527.pdf Page 3 and 4 and Figure 2. In all these, they mention that a QND measurement enables ...
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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 ...
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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 duplicateā€¦ :-| I am not really a physicist (I am actually a professional mathematician), but I have already read quite a ...
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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 $R_y(\theta)$.
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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 ...
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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. ...
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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 ...
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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 ...
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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 $\mathcal{E} = \sum_{i=1}^{n}E_i \rho E_i^*$ ...
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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 ...
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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 ...
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257 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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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 ...
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135 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?
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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&...
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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 ...
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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 ...
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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 ...