Questions tagged [error-correction]

Quantum error correction (QEC) is a collection of techniques to protect quantum information from decoherence and other quantum noise, to realise fault-tolerant quantum computation. Quantum error correction is expected to be essential for practical quantum computation in the face of noise on stored quantum information, faulty quantum gates, faulty state preparations, and faulty measurements. (Wikipedia)

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Keep receiving Error - AttributeError: 'QuantumCircuit' object has no attribute 'save_statevector'

I am attempting to code a feed-forward simulation of a QECC in Qiskit. Qiskit (to my knowledge) does not directly support feed-forward simulation, so I attempted a work-around. I call the simulator ...
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73 views

Why is the quantum volume vastly greater than the number of qubits squared?

According to Wikipedia, the Honeywell computer has quantum volume ("QV") equal to 1024 and has 10 qubits. QV should not be more than $n^2$ squared, i.e. 100. Is this any math error? Are the ...
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Simplifying equation for two qubit syndrome extraction code

In the paper Quantum Error Correction: An Introductory Guide, the author gives the following formula for a simple two qubit code (eq. 19 on the paper). $$ E|\psi\rangle_L|0\rangle_A \xrightarrow{\text{...
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Error correction on $n$ qubits all in same state except for a few

This might be a straightforward problem for you guys; it would be helpful if you can explain it in simple language. I have $n$-qubits given as $$\frac{1}{\sqrt{2}} \left(|0\rangle+ e^{\iota\theta_{1}}|...
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Circuit for fault tolerant syndrome measurements Steane Code

I was exploring this paper: https://arxiv.org/pdf/1505.07390.pdf The paper describes the syndrome measurement for the [7,1,3] code. I was looking a fault-tolerant syndrome measurement and found this ...
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How to do error correction after encoded Bell measurement?

Need some help with the concepts of encoded/logical bell measurement. Please visualize the picture in your mind. Suppose I have a node with 7+7 qubits side by side, left 7 is $|0_{L}\rangle$ and right ...
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Are there any packages that can calculate stabilizer tableau of a QECC

I'm experimenting with some small quantum error correcting codes (QECC). For example $[[5,1,3]]$, $[[8,3,3]]$ or toric codes $[[2d^2,2,d]]$ ($d=2,3,\cdots$). The last one being defined by redundant ...
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What do Z logical errors look like in 3d color codes?

I am trying to better understand (standard, not gauge) 3d color codes. In particular, I am working with the lattice proposed in 1. I understand how X error works, forming strings of the kind Vertex -&...
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What is the effect of measuring a node in a cluster state?

I'm still quite confused about the post-measurement state when a node of a cluster state is measured. As far as I'm aware, for a cluster state, a given node $j$ will have a stabilizer $$X_j\bigotimes_{...
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Construction of arbitrary Normalizer Gates using H, S and CNOT Gates

This question is in reference to Exercise 10.40 of Nielsen and Chuang's textbook, which is an attempt to prove the theorem that any $n$ qubit Normalizer gate can be built out of $H$, $S$, and $CNOT$ ...
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Stabilizer codes: why is $N(S)/S$ homomorphic to the Pauli group on $k$ qubits

Given an abelian subgroup $S$ of the Pauli group on $n$ qubits with $r$ independent generators we obtain an $2^{n-r}$-dimensional subspace stabilized by $S$. By picking a basis for this space, it is ...
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Degenerate vs non-degenerate errors

One of the key features of quantum error correction that makes it different from classical error correction. When code is non-degenerate, an error $E$ takes codewords to different words. codewords. ...
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QPE Circuit test on Quantum Computer ('ibmq_16_melbourne')

After several atempts, I cannot mitigate the error when running the code on a NISQ, via the qiskit library (more specifically on the 'ibmq_16_melbourne'). I've already mapped the connected qubits and ...
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translating between measurement based and circuit based quantum computation

I think I understand circuit based QC (CBQC) well enough; I know very little about MBQC. From what I read it seems that they are somehow "equivalent". I'd like to check this with a concrete ...
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Calculating symplectic dual of a code

Stabilizer codes can be treated as symplectic codes over $\mathbb{F}_2$ (or over $\mathbb{F}_p$ when taking about q-dits). While treating error class, symplectic dual of the code plays a crucial part (...
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Accuracy threshold theorem: what is the physical probability of failure exactly

In this famous paper is derived the quantum accuracy threshold theorem for concatenated codes. I have questions for the case errors are assumed to be local and Markovian. In the so called level-1 ...
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How do the extra energy levels of a transmon qubit affect computation/fidelity?

I was reading about transmon qubits, and I know that they are not true two-level systems. Are there any math/papers which talk about how those extra energy levels affect the computation? I'm assuming ...
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Proof that encoder for a stabilizer code is in the Clifford group

Given a stabilizer code on $n$ qubits defined by a set of stabilizers $S_1,\cdots S_m$; The encoder $E$ is a matrix in $U(2^n)$ (unitary group) such that $S_i E v = E v$. I'm pretty sure that $E$ is ...
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How to calculate the generators of a list of stabilizer?

Let's say we have a list of stabilizers: {'YZY*', 'XYY*', 'YZYZ', 'Z*Z*', '*XZ*', 'XZX*', 'ZX*Z', 'XZXZ', 'YYX*', 'Z*ZZ'}. Is there any existed formula or function (eg. in qiskit) that can calculate ...
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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|...
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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 ...
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Clean definition and interpretation of “error” in quantum error correction

Let us consider a noise channel $\mathcal{E}(\rho)=\sum_i E_i \rho E_i^{\dagger}$, where $\{E_i\}$ are one choice of Kraus operators associated to it. I assume I will perform error correction and that ...
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Who is responsible for implementing quantum error correction?

There are various options for error correction. For example, the Shore code or a whole class of surface codes. But I don't really understand at what level they should be implemented. For example, I ...
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Calculating length of code words in quantum information(compression)

I was studying this article by Boestrom and Felbinger. We define the significant length of the codewords in the preparation of the communication protocol : $$L_c(w_i) = \lceil log_k(i) \rceil$$ We ...
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Why is a 15-qubit IBM quantum computer not working correctly?

I just wanted to implement an algorithm for adding two 2-bit binary numbers. And it works, but only on an IBM 32-qubit simulator. And on a real 15-qubit computer, ibmq_16_melbourne, it produces very ...
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Characteristics of the IBM quantum computer

On the IBM Quantum Composer website, there are characteristics of qubit computers. For example, ibmq_16_melbourne. But there is no description anywhere of what: ...
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'Best practices' for making Stim run as fast as possible?

I'm currently testing out an error-correction surface code circuit in Stim. I've tried a 19x19 surface code over 10k rounds of syndrome extraction sampled 256 times, and this takes about 165 seconds. ...
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Error syndrome on logical operators

The stabilizers and logical operators (for five qubit-codes) are given by $$ \hat{S}_1= \hat{X}_1\hat{Z}_2\hat{Z}_3\hat{X}_4 \\ \hat{S}_2= \hat{X}_2\hat{Z}_3\hat{Z}_4\hat{X}_5 \\ \hat{S}_3= \hat{X}_1\...
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Understanding the (2,3) threshold quantum secret sharing scheme in Cleve et al. 1999

In the paper "How to share quantum secret" by R.Cleve et al (arxiv). There is an example of secret sharing using qutrit in a (2,3) threshold scheme. $$\alpha\vert0\rangle+\beta\vert1\rangle+\...
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In Shor’s 9-qubit code, is the error syndrome for qubit 5 phase-flip the same as that for qubit 6 phase-flip?

The Shor’s 9-qubit code has the following stabilizers $\hat{S}_1= \hat{Z}_1\hat{Z}_2$ , $\hat{S}_2= \hat{Z}_2\hat{Z}_3$, $\hat{S}_3= \hat{Z}_4\hat{Z}_5$ $\hat{S}_4= \hat{Z}_5\hat{Z}_6$, $\hat{S}_5= \...
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Why is this topological gate mentioned in Raussendorf et al. 2007 a CNOT?

I read a Paper about quantum error corrections. I don't know why this is a CNOT gate. How to calculate this kind of CNOT gate as a topology form?
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Can quantum error correction work on any type of channel?

It says on wikipedia that quantum error correction can (at best) correct phase flips and bit flips. A popular form of representing a quantum channel is in its Kraus representation (scroll down to ...
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Quantum Error Correction implementation in Qiskit, OpenQASM or other languages based on Python

Where can we find example(s) of implementation code in a programming language of Quantum Error Correction, whether with the standard method of measurement or the automatic method without measurement (...
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How to write the general state of a corrupted n-qubit codeword in quantum error correction?

I am reading the chapter on quantum error correction in Quantum Computer Science by David Mermim. Which says, for a single qubit in a random state $|\Phi\rangle$ of the superposition of $|0\rangle$ ...
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Can one easily compute the weight enumerator of a CSS code constructed from two binary codes $M_1,M_2$?

Consider a CSS code, which is constructed from two binary codes $M_1$ and $M_2$, so its symplectic matrix is of the form: $$ \begin{pmatrix} M_1 & 0 \\ 0 & M_2 \end{pmatrix}.$$ Suppose one ...
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How to implement Majority Vote

I am trying to boost the success propability of standart phase estimation by repeating the procedure enought times and taking a majority vote that will be encoded in a quantum register. My problem is ...
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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 ...
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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 ...
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Applying a projector to a qubit in a qiskit circuit

I'd like to be able to apply $|0 \rangle \langle 0|$ to project a qubit to the state $|0 \rangle$ in the middle of qiskit circuit (see, for example, the attached circuit). I wonder if, in general, ...
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Stabilizer code: error detection why does it matter?

State vectors take more space when we have to specify certain states. In stabilizer formalism, we can specify these states in a much more compact way. But in error correction then we say that the ...
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How do we find the stabilizer generators for the three-qubit bit-flip code spanned by $|000\rangle$ and $|111\rangle$?

In Nielsen & Chuang's book "Quantum Computation and Quantum Information" section 10.5.6, page 467 there is the following statement Consider the familiar three-qubit bit-flip code ...
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How to do the counting when computing the fault tolerant threshold of quantum codes?

Here, I want to ask a basic question about how to compute the fault tolerance threshold of quantum codes. As I know, maybe, the most usual way is to do some simulations. Howvever, I am more intersted ...
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How to compute the error threshold for the $9$-qubit Shor code?

I was trying to calculate the threshold of $9$-qubit Shor's code. The error channel is $$E=(1-p)I+p/3X+p/3Y+p/3Z.$$ But I got the threshold is equal to 1. How can I get the right threshold (I believe ...
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Can Shor‘s code correct two- or three-qubit errors?

I have read some articles about Shor's code (e.g. this one). It is said that Shor's code can correct a single-qubit error. What about two qubit errors? Three qubit errors? It confused me a lot...
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CSS Code in disguise

Suppose I have a quantum error correcting code described by a set of stabilizers. Is there any easy way of checking whether or not it is equivalent to a code constructed using the CSS construction, ...
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Are applications with only polynomial speedup worth chasing after? (since error correction adds a heavy overhead)

A number of ML algorithms have demonstrated to have polynomial speed-up: But this (I'm assuming) is without error correcting qubits. How practical are algorithms that only exhibit polynomial speed-up ...
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Proper definition of logical operation in Q.E.C

My question is related to this topic I consider working with error correcting code on which I want to define logical operations. Let's assume I want to define a logical operation on logical qubit. In ...
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Understanding transversal gates for the 7 qubit steane code

How can one derive the complete list of transversal operators for the 7-qubit Steane code? I can derive the Clifford operators that are transversal, but I do not understand an easy way to check for ...
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Necessary and sufficient condition to define logical operation (stabilizer code)

My question is highly related to this topic It is about defining logical operation on a Stabilizer code. I call $S$ the stabilizer group of a code space $C$, and I assumed it is generated by a family $...
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187 views

Transversal logical gate for Stabilizer (or at least Steane code)

I know that for Steane code, we can implement transversally some gates like cNOT, Hadamard and Pauli. What I am looking for is a resource in which it is explained why implementing those gate give rise ...

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