All Questions
Tagged with error-correction entanglement
24
questions
1
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0
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36
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Are transversal entangling gates possible for stabilizer codes other than CSS?
It is well known that CSS codes can have lots of transversal entangling gates. For example, $ CNOT $ is exactly transversal on 2 blocks of any $ [[n,1,d]] $ CSS code. And https://arxiv.org/abs/1304....
- 4,490
2
votes
1
answer
49
views
Can we perform teleported-error-correction with noisy Bell pairs?
It is well-known that in https://arxiv.org/abs/quant-ph/0312190 that error correction can be performed by teleportation on the logical level, so prepare one logical Bell pair and (logical?) Bell ...
- 386
2
votes
0
answers
31
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Recent references establishing connections between stabilizer error correction and entanglement distillation procedures
I know some concrete entanglement distillation protocols (from this review).
I also know there are connections between error-correction codes and entanglement distillation (again this review but also ...
- 1,796
3
votes
1
answer
182
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Understanding entanglement distillation via stabilizer codes?
I am having some trouble understanding the distillation of EPR pairs using a stabilizer code. This idea goes back to the paper by Bennet, DiVincenzo, Smolin, and Wooters.
The idea (I think) is that $k$...
- 2,111
1
vote
0
answers
81
views
Equivalence between entanglement purification and quantum error correction
I've recently been reading the seminal paper recently (BDSW 1996), where they established the equivalence between 1-EPP (one-way classical communication) and error correction through explicit ...
- 386
2
votes
1
answer
253
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Is there a way to perform a defect-free logical CNOT on the toric code?
I was curious to whether the two logical qubits on the toric code can be entangled through, for instance, a logical CNOT operation. However, I cannot find any information on this, only how you can do ...
- 99
0
votes
1
answer
710
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How are logical operators performed and measured on the surface code, in a defect-free way?
I am reading about the surface code and I am still not sure how to perform and measure logical operators, such as $X_L$ or $Z_L$, without creating defects. Suppose I stabilise my qubit array into a ...
- 99
2
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0
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102
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How do Hashing bound, entanglement purification, and QECC, relate to each other?
Could anyone elaborate on how these three concepts relate to each other? According to Charlie Bennett's original paper BDSW96, EPP is equivalent to QEC in the sense that both have the hashing bound as ...
- 386
1
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0
answers
45
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Computation for threshold of CNOT gate
I'm trying to reproduce some threshold results using 7-qubit Steane code in those legacy papers. I managed to obtain the graph for circuit noise and single qubit gate
e.g. the pseudocode for computing ...
- 386
2
votes
1
answer
455
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Why doesn't reading the ancilla qubit in Quantum Error Correction kill entanglement?
In Quantum Error Correction we have ancilla qubits (in gray) that will be entangled with the pair of bits we want to check.
Because we don't want to directly measure the "main" qubits (in ...
- 209
2
votes
1
answer
85
views
Kind of errors on entangled states
I see on this chapter that, when noise applies to an even number of entangled qubits, such noise can be considered as operating only on half of those qubits. This is interesting, but I'm not sure if I'...
- 1,998
4
votes
1
answer
1k
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What are the typical gate times for single-qubit and 2-qubit gates for ion trap, superconducting, neutral atom, photonic, spin QC?
What are the typical gate times for single-qubit and 2-qubit gates for
-- ion trap,
-- superconducting,
-- neutral atom,
-- photonic,
-- spin
quantum computers based on today's technologies?
- 365
2
votes
1
answer
332
views
How many physical qubits are needed to encode a logical qubit on ion trap, superconducting, neutral atom, photonic QC?
How many physical qubits are needed to encode a logical qubit on an
-- ion trap,
-- superconducting,
-- neutral atom,
-- photonic,
-- spin
quantum computer based on today's technologies?
- 365
4
votes
1
answer
409
views
How to limit the error probability in large scale quantum computers
I am quite stumped by the fact that the roadmaps for quantum computers as given by IBM, Google, IonQ, etc. seem to imply a linear/exponential growth in the size of their quantum computers.
Naively, I ...
- 220
0
votes
1
answer
94
views
Pauli Matrix tolerant and encoding
I'm stumped by these questions in Chuang's book.
If I have a state $|ψ\rangle=1/2\sqrt2(1+M_0)(1+M_1)(1+M_2)|0\rangle_7$, where
$$M_0=X_0X_4X_5X_6; M_1=X_1X_3X_5X_6; M_2=X_2X_3X_4X_6$$
I rewrite its ...
- 11
0
votes
1
answer
145
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Is there a way to entangle to a dirty qubit?
Let's say I do something to a qubit, and I want to entangle it to a 2nd one, like this:
...
- 584
1
vote
1
answer
372
views
Is there any difference between a quantum- and classically-controlled gate if I know my basis?
Consider an unrealistic 2-qubit plus 1 ancilla bit-flip error correction code (images generated by quirk), where I know by some means or other that an error may have happen on qubit0 (represented by ...
- 181
3
votes
3
answers
261
views
In the three-qubit bit flip code, why can the first bit flip without impacting the entanglement with the other qubits?
The principle of the three-qubit Bit Flip Code is straight forward at first sight. Using CNOT you basically encode
$$a|0\rangle + b|1\rangle $$
to
$$ a|000\rangle + b|111\rangle$$
using ...
- 151
3
votes
0
answers
161
views
How does Teleportation based Error Correction (TEC) detect and correct loss/erasure errors?
I'm looking at papers like Demonstration of teleportation-based error correction in the IBM quantum computer (page) 10 and Role of syndrome information on a one-way quantum repeater using ...
2
votes
2
answers
104
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The behaviour of ebits in Entanglement-assisted Quantum Error Correction Codes?
I am reading about Entanglement-assisted Quantum Error Correction Codes from Quantum Information Processing and Quantum Error Correction: An Engineering Approach (Chapter 9) . It is a scheme that ...
- 822
2
votes
1
answer
176
views
Repetition code encoder circuit
The repetition code encodes $\vert \psi \rangle = \alpha \vert 0 \rangle + \beta \vert 1 \rangle \rightarrow \vert \psi \rangle = \alpha \vert 000 \rangle + \beta \vert 111 \rangle$ using the ...
- 822
10
votes
0
answers
102
views
Entanglement-assisted hashing bound for asymmetric depolarizing channels
I reading the paper EXIT-Chart Aided Quantum Code Design
Improves the Normalised Throughput
of Realistic Quantum Devices, which proposes the use of QTCs in order to do quantum error correction for ...
8
votes
1
answer
1k
views
What is the definition of Bell state on a n-qubit system?
Question 1: The bell state for a 2-qubit system has been defined in Neilsen and Chuang's book as the set of maximally entangled states spanned by $\{|00\rangle + |11\rangle, |00\rangle - |11\rangle, |...
- 81
11
votes
5
answers
938
views
What is quantum entanglement, and what role does it play in quantum error correction?
I want to understand what quantum entanglement is and what role does it play in quantum error correction.
NOTE:
As per the suggestions of @JamesWootton and @NielDeBeaudrap, I have asked a separate ...
- 251