All Questions
Tagged with textbook-and-exercises error-correction
25
questions
1
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2
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59
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In the QECC condition $\langle\psi|E_a^\dagger E_b|\phi\rangle=C_{ab}\langle\psi|\phi\rangle$, what is $C_{ab}$?
In this book, Theorem 2.7 has the QECC conditions. I attach a snippet here
Theorem 2.7 (QECC Conditions). $(Q, \mathcal{E})$ is a $Q E C C$ iff $\forall|\psi\rangle,|\phi\rangle \in Q, \forall E_a, ...
- 13
0
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1
answer
41
views
Understanding the error operator representation $E = i^{\lambda}X(a)Z(b)$
Question regarding exercise $27.3.2$ in "Concise Encyclopedia of Coding Theory".
The exercise states:
We write $E = X((0,1))Z((0,0))$ and $E' = iX((0,1))Z((1,1))$. We
choose the ordering $(...
- 631
1
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2
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98
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Why $\sqrt{\rho} = P \sqrt{\rho}$ in the proof of quantum error correction conditions in Nielsen & Chuang?
I have trouble understanding a proof in Nielsen & Chuang, specifically the identity in (10.20), which reads $$ U_k^\dagger P_k F_l \sqrt{\rho} = U_k^\dagger P_k^\dagger F_l P \sqrt{\rho}.$$
By ...
- 23
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1
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72
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In quantum error correction, what does an "arbitrary error that yields an un-normalized state" mean?
This is from page 434 of Nielsen and Chuang:
. Supposing the state of the encoded qubit is |ψ⟩
before the noise acts, then after the noise has acted the state is
E(|ψ⟩⟨ψ|). To analyze the effects of
...
- 146
0
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1
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146
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Definition of fault-tolerant measurement in QCQI
In the book "Quantum Computation and Quantum Information," one of the definitions for fault-tolerant measurement is mentioned as "any single component in the procedure results in an ...
- 61
3
votes
2
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209
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How are quantum error-correction conditions in Nielsen and Chuang implemented in practice?
Quantum error-correction conditions in Nielsen and Chuang, 10th-anniversary edition (Theorem 10.1) state that the error operation $\mathcal{E}$ with operation elements $\{E_i\}$ is correctable if and ...
- 177
1
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2
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240
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Errors while encoding (3 qubit code)
I am relatively new to quantum error correction, so apologies if this question appears is naive.
In the three qubit code, there seems to always be the assumption that errors occur after encoding the ...
- 797
0
votes
1
answer
198
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Bit flip error correction syndrome measurements
I'm coming across some confusion in chapter 10.1.1 of Nielsen and Chaung. In terms of the 'recovery' procedure, how can the result of the syndrome measurement be 0, 2 or 3?
I am assuming that, for ...
- 797
5
votes
1
answer
361
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Regarding the inductive proof that any Clifford gate can be made of Hadamard, phase and c-not
In Exercise 10.40 of Nielsen and Chunang's textbook, the reader is supposed to construct an inductive proof of Theorem 10.6 that any Clifford gate can be made of Hadamard, phase and c-not. There it is ...
- 51
3
votes
1
answer
135
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When discussing error correction, what are the objects in the expression $PE_i^\dagger E_j P=\alpha_{ij} P$?
I've started reading the book "Quantum Computation and Quantum Information" by Michael A. Nielsen and Issac L. Chuang, specifically chapter 10 (about quantum error correction), and I'm ...
- 51
0
votes
1
answer
115
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Knill Laflamme conditon
In Preskill's notes on quantum error correcting codes in Section 7.2, there seems to be no condition on the environment part of the state, i.e. $|0\rangle_E$ in $|\psi\rangle \otimes |0\rangle_E$.
...
- 109
2
votes
1
answer
191
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Qiskit noise model question (from textbook)
I'm reading the chapter Introduction to Quantum Error Correction using Repetition Codes and a code example demonstrates how to add depolarizing and pauli error. I have several questions.
Is it not ...
- 41
3
votes
1
answer
423
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What does measurement mean in quantum error correction(syndrome diagnosis)?
In the case of the simple three-qubit repetition code, the encoding consists of the mappings $|0\rangle \rightarrow\left|0_{\mathrm{L}}\right\rangle \equiv|000\rangle$ and $|1\rangle \rightarrow\left|...
- 3,009
3
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1
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188
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Knill-Laflamme condition derivation in Nielsen&Chuang: issue to understand a part of the proof
I have some trouble to understand the proof in Nielsen&Chuang about Knill-Laflamme conditions.
The conditions:
Let $C$ be a quantum code and $P$ the projector onto $C$. Suppose
$\mathcal{E}$ is a ...
- 1,796
2
votes
1
answer
122
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5 qubit codewords definition in terms of operators: Mermin
Book: Quantum computer science by David Mermin
Chapter:5
Page-118
The 5-Qbit codewords are most clearly and usefully defined in terms of
the $M_{i}$ (rather than writing out their lengthy explicit ...
- 975