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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6 votes
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149 views

Why do we need to keep of history of $d$ cycle for surface code in order to resist against data *and* measurement errors

I am trying to understand why we need to keep in memory $d$ clock cycles in order to correct efficiently for the surface code where the syndrome qubits are also faulty ($d$ is the code distance). [...
4 votes
1 answer
94 views

compatibility of stim's error model with conventional decoding schemes

I am working with stim's excellent code generator together with pymatching, using stim's generated error model and the glue code in the tutorial here. I am trying to understand better what the output ...
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2 votes
1 answer
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Analytical Approximation of Pseudothreshold for Steane Code

Is there an analytical way by which one can approximately find the pseudothreshold of the Steane code? My supervisor told me that there is a way, using the physical error rate and the number of gates ...
2 votes
1 answer
63 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 vote
1 answer
103 views

Information about the output of %qiskit_backend_overview

Does anyone know where can I find more information about the meaning of some parameters outputted by %qiskit_backend_overview ? I mostly refer to "Avg. T1/T2&...
5 votes
1 answer
136 views

Algorithm resource estimation: why "usually" only the $T$ gate count is being provided. When the Clifford count is provided, does that include Id gate

[edit] I am not necessarily focused on topological error correction (as the answer already provided reasons in this context). Even in the case of topological error correction I am not sure to ...
4 votes
2 answers
333 views

How to find the stabilizer generators for a post-measurement state?

My question is closely related to this one. A bit of vocabulary and a reminder of basic properties: I consider the total Hilbert space of the problem has dimension $2^n$. I call a "well defined ...
1 vote
2 answers
62 views

Are ancillary qubits necessary to represent a syndrome measurement in the circuit model?

From my understanding, in QEC with stabiliser codes, one can use the operator formalism and state to perform a measurement over a space which is orthogonal to the code space. This allows to not ...
2 votes
1 answer
137 views

Lattice splitting: understanding mathematically why it works based on the stabilizer formalism

I am struggling to understand why the lattice splitting procedure works precisely. I am following the appendix in this paper. [edit]: While the answer in this topic answers the question, the concept ...
2 votes
1 answer
130 views

I don't understand the lattice splitting procedure for surface code

I am trying to understand the lattice splitting as described in Horsman paper. In short: I don't understand why measuring the data qubit to split the surface doesn't change the stabilizer results. ...
1 vote
1 answer
170 views

Why do we require that the elements of a stabilizer group commute?

I read about the stabilizer code as a set characterized by elements stabilized by an abelian group, i.e one whose elements commute. I can imagine that requiring commutation helps to define new codes ...
3 votes
3 answers
172 views

State of the art logical gate implementations for surface code

I am currently learning surface code. In this framework, we can either do a quantum memory (for which we have good knowledge of how to do it), but we can also "in principle" perform an ...
1 vote
2 answers
46 views

Noise on the ancilla for syndrome measurement

To detect noise through stabiliser measurement, in the circuit formalism, there is usually an ancilla which stores a parity check result. However, what happens if also the ancilla suffers from the ...
0 votes
1 answer
73 views

The meaning of non-destructive measurements in QEC

I am starting to study quantum error correction and it's the first time that I see the operators (usually Pauli) as projective measurements which seem to just identify a syndrome but do not destroy ...
1 vote
0 answers
65 views

Moving qubits in surface code: I don't get why it works

I am reading this paper, in particular the part where they explain it is possible to move qubits in the surface code. I don't understand the procedure that allows to move logical qubits on the array. ...
3 votes
1 answer
47 views

How to know whether or not we have an X-cut or Z-cut without information on the boundaries

I am reading this paper, in particular the part where X-cut and Z-cut are being defined. My question is highly connected (but different) to this one I previously asked. In this paper, they show the ...
2 votes
1 answer
42 views

How to read a graph representing the stabilizers and data qubits in surface code

I am trying to understand to properly read the graph below, provided in this post It is said that the black elements are the $Z$ stabilizers and the grey ones are the $X$ stabilizers. I am trying to ...
2 votes
2 answers
119 views

Reference for surface code error correction

I am reading surface code theory with this paper. The paper is great but there are some parts of the explanations for which I am struggling to understand. In such cases, another source is always nice ...
1 vote
1 answer
73 views

Initializing a logical qubits in $|g\rangle$ for an X-cut logical qubit in surface code: understanding question

I am reading surface code theory with this paper. In this paper, it is explained how to initialize a logical qubit in the $|g_L\rangle$ state when the qubits has been created through an X-cut. I ...
1 vote
1 answer
54 views

General reason behind why $X_L$ and $Z_L$ can be processed on software for error correction

I am reading surface code theory with this paper. It is explained there that the $X_L$ and $Z_L$ (logical $X$ and $Z$ operator) can be pushed at the end of the circuit and they actually do not have to ...
4 votes
1 answer
157 views

Threshold for quantum Repetition Code

I'm learning about the Threshold theorem but I struggle with the computations of the threshold which are usually presented (even the one in the book by Nielsen & Chuang). To clear my head, I would ...
1 vote
2 answers
159 views

How do we create logical qubits in the surface code: understanding check

I am learning the basics of surface code theory through this paper I am trying to understand how we create multiple logical qubits. The goal of my post is to check my understanding. What I understood ...
5 votes
1 answer
92 views

Does the Eastin-Knill theorem hold for repetition codes?

The Eastin-Knill theorem states that For any nontrivial local-error-detecting quantum code, the set of transversal, logical unitary operators is not universal. see original paper. Does this theorem ...
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2 votes
2 answers
147 views

How to calculate the number of qubits in surface code, for given physical error rate

I am working on improvement of physical qubit error probability. I would like to know: how to calculate the size I need for surface code, given that I need that the logical error probability will be ...
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2 votes
1 answer
164 views

Struggle to understand the derivation of the probability of logical error per surface code cycle

I am following this introduction paper for the surface code theory. The question: I am struggling to understand the derivation of the equation (12) of this paper. This equation gives the probability ...
2 votes
2 answers
87 views

Defining logical X operator for surface code: equivalent possible definitions

I am currently learning the surface code and I wanted to know if there is an easy and intuitive way to find out all the equivalent possible definitions for the $X_L$ (Pauli-X logical operator). In the ...
2 votes
1 answer
205 views

Incorporating Idling Errors while using Stim

Is there a smart way to incorporate idling errors for a quantum error correction code using the open-source tool Stim (preferably using the tableau simulator)? I have perused the github website (https:...
0 votes
1 answer
44 views

Is it possible for public users to run experiments using Qiskit's surface code?

I'm an undergrad who would like to run some experiments using the surface code. I've been able to use their quantum repetition code (https://qiskit.org/textbook/ch-quantum-hardware/error-correction-...
3 votes
1 answer
103 views

Efficient Way to Create an LUT in Stim

What is the fastest and most resource-efficient way to create an LUT decoder for a quantum error correction code using Stim (https://quantum-journal.org/papers/q-2021-07-06-497/)? Specfically, I am ...
2 votes
1 answer
67 views

Accuracy of Grover algorithm is 100% for 2 qubit, 94.5% on 3 qubit and 96.2% for 4 qubit on simulator. Why it decreasing and then again increasing?

The accuracy of Grover's algorithm decreases for 3 qubit then increases for 4 qubit and then again increases for 5-qubit on simulator (qasm simulator) with pi/4(sqrt N) iterations. What is the reason ...
1 vote
1 answer
76 views

Correcting Coherent errors with Surface Codes

Following this article: Correcting coherent errors with surface codes I wonder about the modeling of coherent error and its effect on syndrome after measurement. They say that applying U on the ...
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5 votes
0 answers
77 views

Which improvements can we expect in Quantum Error Correction?

According to this article: The surface code is currently the most widely pursued quantum error correction scheme (Emphasis mine). It is also said: However, there are drawbacks to the surface code, ...
6 votes
2 answers
192 views

Simulating flag qubits and conditional branches using Stim

In a quantum error correcting code using flag qubits, it's common to have flag measurements that tell you it's necessary to do some extra measurements for safety. So, for example, I want to say: ...
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2 votes
0 answers
40 views

Show that ${\cal C}(\rho)={\rm Tr}[U(\rho\otimes|0\rangle\!\langle0|)U^\dagger]$ can be corrected iff $t=0$, where $U=I+(e^{it}-1)|\Psi^-〉〈\Psi^-|$

Let $ \mathcal{C} $ be the quantum channel defined by $$ \mathcal{C}(\rho)=\operatorname{Tr}_{2}\left[U(\rho \otimes|0\rangle\langle 0|) U^{\dagger}\right], $$ where $ U $ is the two-qubit unitary ...
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7 votes
1 answer
274 views

Is Toffoli a fault tolerant transversal gate of the repetition code on bit-flip-error-only qubits?

Suppose you have physical qubits that only have bit flip noise (no phase flip noise, no unwanted measurements, no leakage, no amplitude decay, etc; just unwanted X rotations). Such qubits can be kept ...
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3 votes
1 answer
101 views

How can I add readout error in constructing a quantum noise model?

I'm trying to construct a quantum noise model with readout error only: qiskit.providers.aer.noise.NoiseModel.add_readout_error. However, when I try to specify the ...
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2 votes
0 answers
18 views

Is there any software package tracking Pauli errors in stabilizing circuits with GUI?

I want to track the Pauli errors propagating in stabilizer circuits like surface code. I wonder whether there is any developed package that can do this elegantly. It will be better if it has GUI that ...
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3 votes
1 answer
171 views

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?
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1 vote
0 answers
137 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?
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3 votes
1 answer
86 views

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 ...
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3 votes
1 answer
100 views

How to determine the threshold value of the quantum error correction code

How to determine the threshold value of the quantum error correction code, what is the specific method, such as surface code, how to determine the threshold value of the color code with a decoder, I ...
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3 votes
1 answer
122 views

Stabilizer codes to Classical codes over GF(4)

In the work [1] it was shown that stabilizer codes could be mapped to binary codes (albeit with a symplectic norm) which further can be mapped to additive codes over GF(4). Can someone explain why it ...
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4 votes
0 answers
66 views

Is it interesting to look at surface codes where the boundary conditions give the shape of a Mobius strip, Klein bottle, or the projective plane?

I was reading about the Toric code and how the boundary codes give it a shape of of a torus. Is it interesting to look at other ways to orient the edges of a square lattice? I.e. a mobius strip, Klein ...
1 vote
0 answers
35 views

Are there differences in how quantum error correcting codes are applied on superconducting vs. trapped ion systems?

Are there any differences in how quantum error correcting codes are currently applied on superconducting vs. trapped ion systems?
8 votes
2 answers
281 views

Magic state distillation: why is it harder to prepare the encoded $|A_{\pi/4}\rangle$ than $|0 \rangle$

My question is the following Let's assume I am using Steane concatenated code to do error correction. I consider that the stabilizers are extracted fault-tolerantly through the Steane method. The ...
4 votes
2 answers
124 views

Why aren’t repetition codes used to encode qubits in superposition states?

I just finished reading the section of the qiskit textbook on quantum error correction using repetition codes(https://qiskit.org/textbook/ch-quantum-hardware/error-correction-repetition-code.html) and ...
3 votes
1 answer
67 views

Doubt in CSS error correction step

At the end of page 3 in Simple proof of security of the BB84 QKD, the following equation (equation 4) is given : $$ \begin{array}{r} \frac{1}{2^{n}\left|C_{2}\right|} \sum_{z}\left[\sum_{w_{1}, w_{2} ...
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2 votes
1 answer
60 views

Measurement bitstrings to detection event bitstrings in stim

Does Stim have exposed functionality for converting a measurement outcome string into a detection event string? I.e. I feed stim a string of 0,1's corresponding to measurements in a circuit along with ...
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0 votes
0 answers
104 views

Four-qubit error correction code

$\newcommand{\ket}[1]{\left|#1\right>}$ Consider the following 4-qubit code which allows you to detect a bitflip and/or a phaseflip. The logical 0 and 1 are encoded as: \begin{align*} \ket{0}_{...
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3 votes
1 answer
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Doubt in Simple proof of Security of the BB84 QKD

I am not able to understand an argument from Simple proof of Security of the BB84 QKD; I need your help. In page 2 it is mentioned that "Alice can measure her half of the encoded EPR pairs before ...
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