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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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What is the syndrome in Hastings and Haah honeycomb code?

In the honeycomb code proposed by Hastings and Haah, by measuring 2-body checks and multiplying these values, they obtain the values of plaquette stabilizers. In the decoding, do they use only the ...
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Intuitions for magic quantification in a particular state

Suppose we define a magic state on $2n + 1$ qubits as: \begin{equation} \prod_{i = 1}^{n} CCZ(0, i, i+n) |+\rangle^{\otimes 2n + 1}. \end{equation} Does anyone have an intuition for the scaling of the ...
Rohan Mehta's user avatar
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`predictions` and `fault_ids` in Stim and PyMatching for surface code decoding

When I tried to use Stim and PyMatching to decode errors in a Rotated Planar code, I noticed that, Regardedless of the code distance, predictions.shape, as well as ...
Yuhang Gu's user avatar
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Shadow weight enumerators

Is there any physical intuition or motivation behind the "shadow weight enumerator" of a quantum error correcting code?
user173611's user avatar
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Effect of rounds in surface-code simulation with Stim

I'm learning Stim with the official tutorial and have a question. I made a small program: ...
Yutaka Hirano's user avatar
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2 answers
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How exactly does measuring a syndrome operator work for 'non-discrete' errors?

I am reading a summary of the stabilizer formalism in this paper, which considers the following encoding of a single qubit in three qubits: $$ |\overline{0}\rangle=\frac{1}{\sqrt{2}}(|000\rangle+|111\...
Enigma's user avatar
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Can IBM Quantum hardware handle any CSWAP at all?

I am designing quantum algorithms where the quantum circuit uses CSWAP gates a lot. The result is very noisy on the quantum hardwares. So I designed really simple circuits to test whether it is indeed ...
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Deriving |𝐶𝐶𝑍⟩ magic states from |𝐶𝐶𝐶𝑍⟩?

Analogous to the $|T\rangle$ and $|CCZ\rangle$ magic states, one can define a $|C^n Z\rangle$ magic state. Is there any known quantification of the amount of magic of this state, and is there a way to ...
Rohan Mehta's user avatar
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Does one have multiple degrees of freedom in defining logical states and logical operators of a QEC?

Consider a rotated surface code. Let the surface code have $Z$ stabilizers along the top and bottom boundary and $X$ stabilizers along the left and right boundary. If I initialize all the physical ...
user29393's user avatar
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Obtaining the stabilizer outcome by small operators

Suppose we want to obtain the measurement outcome of the stabilizer $X_1X_2X_3X_4X_5X_6$. Of course, by measuring $X_1X_2$, $X_3X_4$, $X_5X_6$ in this order and combining these three outcomes, we can ...
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The understandings of logical operator

In quantum error correcting code, such as shor 3-qubit code, code space is spanned by the basis {|000>, |111>}. The logical X operator is XXX and the logical Z operator is IIZ. When the code ...
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Measurement outcomes in gauge fixing

I consider measuring Pauli operator m in either normal stabilizer codes and subsystem codes. In normal stabilizer codes, if m commutes with the stabilizer group, measurement outcome is deterministic (...
lassel's user avatar
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What is the physical operation behind "moving edges" and "moving corners" in Litinski's game of surface codes paper?

I was reading Litinski's A game of surface codes (https://quantum-journal.org/papers/q-2019-03-05-128/pdf/). In the introduction (page 2), the paper talks about operations like "moving edges"...
siddharth dangwal's user avatar
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What is the logical gate speed of a superconducting quantum computer?

What is the logical gate speed of a photonic quantum computer? says In a simple world the speed of a photonic quantum computer would just be the speed at which it’s possible to make small (fixed ...
Victory Omole's user avatar
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AGP Fault-tolerance of the flag qubit QEC for 7-qubit Steane code

I was trying to apply the flag qubit QEC (https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.121.050502) for 7-qubit Steane code. From the AGP method (https://arxiv.org/pdf/quant-ph/0504218), ...
이호준's user avatar
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How do Union-Find Decoders deal with Measurement errors through multiple measurement rounds?

I've read a few papers regarding to Surface Code and its decoding algorithms. I've learned that a Union-Find decoder need up to $d$ measurement rounds to deal with measurement errors. These ...
Yuhang Gu's user avatar
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How to find the undetected errors for general stabilizer codes in Stim?

In Stim, we use the detectors to track syndrome flips and infer the error pattern. However, the syndrome stays the same if the actual error pattern is a logical operator of the code by coincidence. It'...
user30824's user avatar
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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....
Ian Gershon Teixeira's user avatar
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2 answers
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Is working with the |+> , |-> basis any harder than the |0>, |1> basis?

Say I have a code, for example the $ [[5,1,3]] $ code, and I want to (fault tolerantly) prepare the logical $ |+ \rangle $ state. Is that any harder than preparing the logical $ | 0 \rangle $ state? ...
Ian Gershon Teixeira's user avatar
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3 answers
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Highest theoretical threshold to fight single-qubit depolarizing noise for noiseless error-correction

Let's consider that each qubit in the lab faces a single-qubit depolarizing channel $\mathcal{N}(\rho)=(1-p) \rho + p \mathbb{I}/2$. Is there a theoretical result indicating the largest value of $p$ ...
Marco Fellous-Asiani's user avatar
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Is it sufficient to assume a constant coherent error?

I've recently started working with quantum errors and noise and came across an intriguing but simple question. When we consider coherent errors in quantum gate operations, it's common to model them as ...
H_Infinity's user avatar
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Boundary conditions for surface code

I have a question about boundary conditions for surface codes. Do any surface codes have torus-like boundary conditions? Are there any surface codes that don't actually have boundary conditions, i.e. ...
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How is $(\langle \psi| E_{a}^\dagger E_{b} | \psi \rangle)^\dagger = C_{ba}^*\langle \psi| \psi \rangle $

I am reading through Daniel Gottesmans surviving as a quantum computer in a classical world. On page 36, he presents the following theorem: Theorem 2.7 (QECC Conditions). $(Q, \mathcal{E})$ is a $Q E ...
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Is every code with a universal set of transversal gates trivial?

The quantum repetition code is an $ [[n,1,1]] $ stabilizer code with stabilizer generators $ Z_iZ_{i+1} $ for $ i=1, \dots, n-1 $. The Eastin-Knill theorem states that a $ d >1 $ code cannot have a ...
Ian Gershon Teixeira's user avatar
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What does DETECTORs mean in the example circuit for rotated surface code in Stim?

In Stim, an example circuit for rotated surface code is provided: ...
lan's user avatar
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Advantages and disadvantages of rotated surface code

I think one of the advantages of rotated surface code is that it can express surface code with fewer physical bits. Are there any other advantages? Also, are there any disadvantages compared to ...
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1 answer
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What is the easiest way to get path graph from Stim?

In Stim, we can get a detector graph with the probability of each error mechanism occurring. Now I want to construct a path graph from the detector graph, which is usually done by Dijkstra's algorithm....
david's user avatar
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How does measurement based quantum computing (MBQC) behave under error propagation?

In the quantum circuit model, we know how to handle error propagation if we implement a unitary $U'$, which is $\varepsilon$-close to the ideal unitary $U$ and a state $|\psi'\rangle$, which is also $\...
Blau's user avatar
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Are close states still close after measurement (regarding trace distance)?

We are given two states $|\psi_1\rangle, |\psi_2\rangle \in \mathbb{C}^2 \otimes \mathbb{C}^2$ with trace distance $\leq \varepsilon$, so they are very close to each other. Now, assume we measure the ...
Blau's user avatar
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Necessary condition for transversal Hadamard by family of stabilizer codes

A necessary and sufficient condition for a stabilizer code having transversal $CNOT$ is that the code is a CSS code (see Theorem 11.5 here or the question here). I know that a sufficient condition for ...
qubitzer's user avatar
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1 answer
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Define the $k$-local transversal logical operation

For a $[[n, 1]]$ QEC code $\mathcal{Q}$, we say single logical gate $R$ is transversal if the logical $\bar{R}$ can be implemented with $R^{\otimes n}$. I am wondering if we could expand the ...
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1 answer
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Why can Pauli errors $E$ be decomposed as $E=T(S)LG$ with $T(S)$ "pure errors"?

I have a question about the decomposition of Pauli errors. Pauli error $E \in \{I,X,Y,Z\}^{{\bigotimes}n}$ that satisfies the syndrome $S$ can be decomposed into a product of pure error $T(S)$, ...
Kmai's user avatar
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6 votes
3 answers
482 views

Why focus on T gates and not some other single qubit rotation R making Clifford + R universal?

Background: In many error correction codes in particular the surface code, the Clifford operations generated by the S,H and CNOT are transversal for quantum computation (meaning that these logical ...
Frederik Ravn Klausen's user avatar
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Does two quantum error correcting codes having the same CSS Tanner Graph imply that they are locally equivalent?

I am studying CSS quantum LDPC codes and I am curious as to whether the Tanner Graph structure necessarily must have long-range connections in order to be a non-local qLDPC code. This is because the ...
freshcoconut's user avatar
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See error samples in Stim+Pymatching [duplicate]

I have a surface code circuit written in Stim. Following Stim's intro I can use sinter to get logical error rates. I'd like to see what error patterns could lead to ...
Pei-Kai Tsai's user avatar
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51 views

What sinter.plot_error_rate is actually doing with the data?

I don't quite understand what the **sinter.plot_error_rate** function is actually doing. From looking at the code, it seems to perform some kind of binomial fit. I'...
Omprakash Chandra's user avatar
6 votes
0 answers
139 views

Universal gate set for the $ [[15,1,3]] $ code

The $ [[15,1,3]] $ triorthogonal code implements transversal $ T $. Since it is a CSS code, two blocks will also have a transversal $ CNOT $ gate. To get a universal gate set all that is required is ...
Ian Gershon Teixeira's user avatar
3 votes
0 answers
25 views

Parameters for which there is a unique stabilizer code

Two stabilizer codes are said to be equivalent if they can be related by non-entangling Cliffords, i.e. by local Cliffords and SWAP gates. There are unique stabilizer codes for the parameters $ [[2,0,...
Ian Gershon Teixeira's user avatar
1 vote
0 answers
46 views

$\langle Z \rangle_L$ in the Distance Two Surface Code

In an experimental realization of the distance 2 surface code, the codewords are: $$|0\rangle_L = \frac{1}{\sqrt{2}} (|0000\rangle + |1111\rangle), |1\rangle_L = \frac{1}{\sqrt{2}} (|0101\rangle + |...
clunky monkey's user avatar
3 votes
1 answer
81 views

Will logical clock cycle time be a limiting factor for quantum computations?

Fault-tolerant quantum computation promises to strongly suppress the errors by scaling up the size of the systems. Right now, different physical implementations of proto quantum computers have very ...
Frederik Ravn Klausen's user avatar
2 votes
0 answers
39 views

Quantum error detection

I'm a bit confused regarding the definition of error detection. Let $H$ be a Hilbert space, $C$ a subspace, $P\colon H\to C$ the projection, and $E$ a linear operator on $H$. Consider these two ...
Tron's user avatar
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4 votes
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What is the domain of the dual map of a quantum channel?

Possibly a naive question...if the dual map of a quantum channel gives the evolution of the system in the Heisenberg picture by acting on observables, and observables are self-adjoint operators on the ...
Mara Jade's user avatar
2 votes
1 answer
73 views

How to verify that a certain gate was applied to a quantum code

Suppose I have a quantum error correcting code $|\psi \rangle = \alpha | 0 \rangle + \beta | 1 \rangle$, say the $[[7,1,3]]$ Steane code for concreteness. Suppose there is a black box that either ...
Eric Kubischta's user avatar
4 votes
1 answer
84 views

Is there any machine learning method for finding quantum error correction codes?

To define a quantum error correction code, first one needs to model noise, such as Pauli noise, dephasing noise, etc. Then according to the noise, look for the code space, stabilizer, and logical ...
mingo's user avatar
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1 answer
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Obtaining and Applying XX and ZZ Parity in Stim for Controlled Paulis

I am attempting to perform a CNOT between two surface code qubits in Stim, based on this paper by Daniel Litinski and Felix von Oppen. The CNOT they perform is shown in the figure below (Figure 3 from ...
Maxwell Poster's user avatar
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3 answers
67 views

Does the threshold estimation of the surface code not need a fault-tolerant setup?

The threshold estimation of the $[[9,1,3]]$ surface code in stim's getting started tutorial extracts the syndromes by having a single ancilla for each stabilizer generator. It is the same setup as in ...
qubitzer's user avatar
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4 votes
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What is the definition of color codes?

Is there a generally accepted definition of what a color code is? I have found two definitions that I am not able to reconciliate with each other: The error correction zoo defines color codes via ...
qubitzer's user avatar
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explain_detector_error_model_errors complains "no single circuit error had these exact symptoms"

I am using the explain_detector_error_model_errors() method, unfortunately I am receiving this: ...
edp23's user avatar
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1 vote
1 answer
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Does there exist a general way of finding the size of the stabilizer group $|S|$?

So I know that, for a stabilizer code, the stabilizer group $S$ has $n-k$ commuting generators. Is there a general way of knowing what the order of the full group of $S$ is, aside from writing out all ...
am567's user avatar
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Why do Surface codes generate so much measurement data?

I read in the Sparse Blossom paper: "A surface code superconducting quantum computer with a million physical qubits will generate measurement data at a rate of around 1 terabit per second". ...
Daniel Mandragona's user avatar

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