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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Does the Quantum Fourier Transform require universality?

Background: In most setups of fault-tolerant quantum computation, universality is achieved using Clifford gates such as $(S, H, \text{CNOT})$ and the $T$-gate. The Eastin-Knill theorem can be ...
Frederik Ravn Klausen's user avatar
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demotivation for non-CSS codes

It seems like most research regarding stabilizer codes focused on CSS codes, which can be understand as a "tensor product" of two classical linear codes. However, I feel like non-CSS codes ...
Yunzhe's user avatar
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Implement parity check gadget using stim

I want to implement the logical $\left|00\right\rangle$ state preparation for $C_4$([[4,2,2]]) code using Stim. And the circuit is as below: I have written a piece of code that seems to be effective: <...
Arkham Yu's user avatar
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1 answer
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In context of stabilizer codes, are logical gates and Pauli operators the same?

I was reading this blog post and as I understood, a unitary operator is logical if and only if it's in $\mathcal{N}(\mathcal{S})$, and a Pauli operator is Logical if and only if it's in $\mathcal{C}(\...
Hamed's user avatar
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how to construct a ((7,2,3)) code and verify its properties

These two recent papers describe a process to construct (non-stabilizer) codes with "exotic" transversal gates : paper1 paper2 Most of the codes have distance $d=2$ which makes them less ...
unknown's user avatar
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Is this quantum circuit design more prone to noise?

I am designing a quantum circuit which uses one qubit as the control of many $\text{CSWAP}$ operations. And then, this qubit will be measured. Will the result be more prone to noise since all the ...
Deren  Liu's user avatar
2 votes
1 answer
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How to convert stim circuit to a detector check matrix and a logical observable matrix?

I would like to output a detector check matrix and a logical observable matrix defined in this paper. I've also learned from the related question: How to convert stim encoder circuit to a parity ...
Qingwei Wang's user avatar
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How to Use Stim for Noisy Simulation with Adaptive Circuit and Noise Tracking?

I am trying to learn stim to simulate noisy quantum circuits. My goal is to construct an adaptive circuit in which I can add quantum gates one by one and observe the changes in the circuit's check ...
iknownothing's user avatar
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How is Magic State Distillation (MSD) compatible with Stabiliser Measurement?

Suppose I have the rotated surface code in which I want to inject a $T$-state. What I don't get it is: suppose we do end up with the logical state $|0_L\rangle+e^{i\pi/4}|1_L\rangle$, then we must ...
JoJo P's user avatar
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How is a surface code state measured?

What is the exact operation required to measure the logical state of a surface code? Does one need to measure every data qubit, or only some subset of them to perform the measurement? For simplicity, ...
Whitman's user avatar
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What is the role of color in color code? ( theoritically and exprimentally)

We know that the color code has an extra element relative toric code . It is color . I want to know what is the role of color ?
Mohsen's user avatar
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How can quantum error correction correct small rotations/continuous errors?

I'm having trouble understanding the so-called "digitization of errors" argument in QEC. Suppose I have to encode my logical qubit into $n$ physical qubits to do error correction. I will use ...
Joan's user avatar
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What is the definition of physical gate error rate?

The fidelity of two quantum states $\rho$ and $\sigma$ is a well-defined (up to discussions about a square): $$ F(\rho, \sigma) = \text{Tr}\left( \sqrt{ \sqrt{\rho} \sigma \sqrt{\rho}}\right)^2. $$ ...
Frederik Ravn Klausen's user avatar
3 votes
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Can you produce Non-Clifford gates via Lattice Surgery?

Is there any theorem stating that lattice merge/split operations (or perhaps more generally, so-called gauge-fixing) cannot produce a non-Clifford gate that can complete the universal gateset for the ...
user29631's user avatar
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How can I obtain the rotated surface code from the original unrotated one?

I am trying to understand the equivalence between the original planar surface code and the rotated version. Looking at Tomita and Svore's paper (2014), they say "The number of qubits [from ...
Ezequiel Rodriguez Chiacchio's user avatar
2 votes
3 answers
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Rotated surface code vs unrotated surface code - Boundary stabilizers

I use these image for the questions below: When we look at the surface code, we can define it in two slightly different ways. The first figure shows a way where we keep all the data qubits and ...
user1936752's user avatar
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Can Interaction with the environment cause $|0\rangle$ to evolve into a superposition like $|+\rangle$?

We say if a qubit is in state $|0\rangle$, and it is possible if it interacts with the environment it can result in a bit flip to a state $|1\rangle$, so I was wondering why can't it go to a ...
Kutubkhan Bhatiya's user avatar
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How to deal with logical gates which map Logical Paulis to non-Pauli products?

I am trying to figure out the action of logical gates on quantum codes. I am trying to check the logical operations that the logical gate performs on the code. I can do it in simple cases, for example ...
am567's user avatar
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Initialization of surface code into a logical state

I read this nice answer about how to initialize a surface code into a logical state but have a basic question about it. If I take a surface code patch with all physical qubits in the $\vert 0\rangle$ ...
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Question about fault-tolerant measurement in Nielsen&Chuang page 490

The fault-tolerant procedures for state preparation and logical operation consider the procedure successful if only a one-qubit error occurs in each encoded block of the output. So, I thought that the ...
이호준's user avatar
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Magic state distillation, eigenvectors of Clifford gates, and transversal gates

I have some (possibly mistaken) ideas about magic state distillation. Please disabuse me of them? In section III "Universal Quantum Computation with Magic States" of the original paper on ...
Ian Gershon Teixeira's user avatar
0 votes
1 answer
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Fault Tolerance of 2-transversal gates

Suppose I have a single block $n$-qubit stabilizer code that can correct a weight 1 error (so the distance is $d=3$). If I apply a $1$-transversal gate of the form $U = U_1 \otimes U_2 \otimes \cdots \...
Eric Kubischta's user avatar
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Procedures for fault-tolerant nondestructive logical measurements

Definition 2 on page 20 in Daniel Gottesman's An Introduction to Quantum Error Correction and Fault-Tolerant Quantum Computation states that a nondestructive logical measurement procedure is fault ...
Peter-Jan's user avatar
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How to perform logical operations between logical qubits in a $[\![8,3,2]\!]$ quantum code?

I have a small question on codes like $[\![8,3,2]\!]$, which encodes physical qubits to multiple logical qubits. How do we perform logical operations in between these logical qubits? Of course, if I ...
AndyLiuin's user avatar
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1 answer
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Fault-tolerant correlated measurement on logical qubits

So I have an encoded Bell pair $(|\overline{0}\overline{0}\rangle+|\overline{1}\overline{1}\rangle)$ in CSS code(e.g. Steane code) and I hope to perform stabilizer measurement of $\overline{XX}$ non-...
AndyLiuin's user avatar
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6 votes
1 answer
87 views

How to get smaller stabilizer codes with Gottesman's construction?

I'm following the construction from Section 3.5 of Daniel Gottesman's thesis (third paragraph), which is supposed to allow us to construct an $\left[ \hspace{-1pt} \left[ n-1, \, k + 1, \, d - 1 \...
Ben Criger's user avatar
2 votes
2 answers
54 views

Why I am continuously getting "failed to decompose hyperedges into edges" in Stim?

I have written a Hypergraph product quantum error correction circuit on Stim. The code is $[\![65,9,4]\!]$. I have put circuit level noise and I am using the sinter ...
Omprakash Chandra's user avatar
1 vote
1 answer
45 views

Relating different surface code diagrams

How do I relate the surface code plaquette and vertex stabilisers of this depiction of the surface code (where the qubits are the edges): to this depiction (measurement qubits are the black dots, ...
compp's user avatar
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What happens after the ancilla is measured in a parity measurement?

Measurement of qubits results in collapsing the wavefunction/state in $|0\rangle$ or $|1\rangle$. I have a doubt about Parity Measurement (Source). We entangle physical qubits with ancilla qubits by $\...
Akash Yadav's user avatar
1 vote
1 answer
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Error while plotting the resulting distribution

I am using this code, as a test of my qiskit, but I am having errors on using the simulator Building the circuit We begin by importing Qiskit. from qiskit import * ...
Dilma David's user avatar
1 vote
0 answers
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How to model the IBM quantum errors?

I'm conducting a study of the quantum channel errors, and a question has arisen: Is it possible to model the errors of an IBM quantum computer with Kraus operators?
Leandro Matheus Morais da Silv's user avatar
5 votes
1 answer
305 views

What exactly is a subsystem code?

I'm sure I'm just tripping up on terminology here. I'm new to the wonderful field of QEC, and so far am familiar with the stabiliser formalism and basic codes such as the generic surface code. I keep ...
compp's user avatar
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4 votes
2 answers
117 views

Compute the exact minimum distance of a QECC with integer linear programming method

Recently I'm reading the paper of Bivariate Bicycle(BB) QLDPC code proposed by IBM. The paper mentioned that: The actual distance of each candidate code was computed using the integer linear ...
Inm's user avatar
  • 505
2 votes
1 answer
55 views

Teleportation of Transversal Hadamard Gate from the $[[8,3,2]]$ to $[[4,2,2]]$ codes

I'm trying to understand the circuit from Appendix A of the paper Fault-Tolerant One-Bit Addition with the Smallest Interesting Colour Code. Here the top 3 qubits represent the 3 logical qubits of ...
tbg's user avatar
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1 vote
1 answer
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Toffoli gate not included in the normalizer group

While reviewing the stabilizer formalism in Nielsen and Chuang, I could not understand why the Toffoli and the $\frac{\pi}{8}$ cannot be described as normalizers, even though they map Pauli group ...
Amazon Forrest's user avatar
1 vote
0 answers
32 views

How do I perform an two-qubit erasure error in stim?

I try to simulate two-qubit erasure error by using CORRELATED_ERROR, ELSE_CORRELATED_ERROR, and an ancilla which is mentioned in How do I perform an erasure error in stim?. Then I simulate two-qubit ...
You Chang's user avatar
2 votes
0 answers
43 views

Understanding Polynomial Quantum Error Correcting Codes

I am currently studying the paper Secure Multiparty Quantum Computation with (Only) a Strict Honest Majority and had a really hard time understanding the Quantum Authentication Scheme provided by the ...
Giorgos Mitropoulos's user avatar
1 vote
1 answer
29 views

question about z-stabalizer

I'm learning quantum error correction. I also had a hard time understanding the following stabilizer form. I read this paper, which gives two circuits for Z-Stabilizer, I can understand a but I don't ...
Ruilin Zhou's user avatar
1 vote
0 answers
17 views

GKP code or Cat code Any rotation gate

In a bosonic code such as GKP code or cat code, is there any way to perform the rotation operation in a single operation without using the expansion T-H-gates by Kitaev's theorem?
kaluza19's user avatar
1 vote
0 answers
51 views

Transversal CNOT implementation on stim

Re: a recent paper on the arXiv, Correlated decoding of logical algorithms with transversal gates (https://arxiv.org/abs/2403.03272). As MWPM (pymatching and stim) cannot handle errors that flip more ...
user avatar
2 votes
1 answer
46 views

Are the logical states of the corresponding unencoded state unique?

Given the generators of a stabilizer code and this code's orthogonal projector is $\Pi$. Take five qubit code as am example, the logical state of $\vert 0 \rangle$ is calculated as $\vert 0^L \rangle =...
Michael.Andy's user avatar
2 votes
1 answer
53 views

Stim - Error Detector Model - Understanding approximate_disjoint_errors and decompose_errors

I am looking for clarification on two arguments for the detector error models used in Stim, appproximate_disjoint_errors and ...
Maxwell Poster's user avatar
1 vote
1 answer
43 views

How to implement a controlled gate in Stim with the following control logic?

I'm trying to implement the $[\![7,1,3]\!]$ Steane code on Stim. My circuit is below: ...
user1936752's user avatar
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3 votes
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How many $ [[9,1,3]] $ surface codes are there?

Two codes are said to be equivalent if their code spaces are related by a non-entangling gate, i.e., a gate from $U(2)^{\otimes n} \rtimes S_n$, the local unitaries together with permutations. The ...
Ian Gershon Teixeira's user avatar
5 votes
0 answers
43 views

Finding all small stabilizer codes

Given some choice of parameters $ [[n,k,d]] $ with $ n $ small, is there any computationally easy way to find all of (or at least many of) the stabilizer codes with those parameters? For certain ...
Ian Gershon Teixeira's user avatar
2 votes
1 answer
41 views

BP + OSD decoder with both loss and Pauli errors

I am trying to implement a bp+osd decoder, using the build-in python package from here: https://github.com/quantumgizmos/bp_osd One of the parameters for the decoder is "channel_probs", ...
David Dentelski's user avatar
3 votes
1 answer
53 views

What are examples of scalable classical LDPC codes?

Where can I find examples of "scalable" good LDPC codes, namely classical codes with properties [n, O(n), O(n] and an explicit prescription of how to increase the bit number n? I am new to ...
Yaron Jarach's user avatar
6 votes
1 answer
126 views

Is the Steane code the only $ [\![7,1,3]\!] $ CSS code?

Is the Steane code the only $ [\![7,1,3]\!] $ CSS code? This paper claims there are 10 non-equivalent $ [\![7,1,3]\!] $ stabilizer codes. How many of these are CSS codes? Is it just the Steane code?
Ian Gershon Teixeira's user avatar
4 votes
1 answer
603 views

Why is it not a good idea to run Shor's algorithm on a big noisy quantum computer?

Suppose I try to run Shor's algorithm on a big noisy quantum computer. For a given input I repeat the circuit many times and collect statistics for the measurements of each qubit. Now based on the ...
Frederik Ravn Klausen's user avatar
1 vote
1 answer
48 views

Error correction conditions for bit flip code

I am reading Nielsen and Chuang's chapter on error correction. I have a very basic question about this theorem: Theorem 10.8 (Error-correction conditions for stabilizer codes): Let $S$ be the ...
William Schober's user avatar

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