# Questions tagged [quantum-error-correction]

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### $n$-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? ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 $R_y(\theta)$.
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 ...
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. ...
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 ...
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 ...
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 $\mathcal{E} = \sum_{i=1}^{n}E_i \rho E_i^*$ ...
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 ...
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 ...
1answer
321 views