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)
790
questions
0
votes
1
answer
22
views
Are there standard forms for non-additive quantum codes?
Stabilizer codes have a well known standard form for the stabilizers, logicals and destabilizers.
Are there any counterparts for non-additive codes?
In particular I'd like to get a standard form ...
0
votes
0
answers
8
views
Feedback control with feedback Hamiltonian vs quantum error correction
I stumbled upon a pretty old paper from 2003 by C. Ahn, H.M. Wiseman and G.J. Milburn. They use quantum control with feedback Hamiltonian to perform error correction. The paper proposes to encode $n-1$...
0
votes
1
answer
20
views
Fault tolerance of turning off a stabilizer measurement for later rounds of error correction?
Suppose during a smooth lattice merge operation, I perform one round of error correction, treating the two code patches as one single lattice that stretches across the intermediate qubits. Then, one ...
0
votes
0
answers
15
views
Can we somehow relate quantum volume with the total number of gates present in a circuit which the machine can succesfully run without large errors
Let's say I have a circuit which contains x number of gates and a machine with quantum volume y, Can I relate x and y somehow to determine if the circuit can be succesfully run on the machine without ...
0
votes
1
answer
27
views
Surface code with measurement errors
I am trying to implement error correction to a surface code with circuit-based noise model. In this model, there is a probability $p$ for an error in: initialization, Hadamard, CZ (or CNOT) and ...
11
votes
1
answer
717
views
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 ...
3
votes
1
answer
62
views
What are the main motivations for pursuing CSS codes over general 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 ...
1
vote
1
answer
34
views
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:
<...
3
votes
1
answer
53
views
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}(\...
3
votes
1
answer
116
views
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 ...
1
vote
0
answers
41
views
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 ...
2
votes
1
answer
54
views
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 ...
0
votes
1
answer
35
views
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 ...
1
vote
1
answer
69
views
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 ...
2
votes
1
answer
48
views
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, ...
0
votes
0
answers
22
views
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 ?
7
votes
2
answers
298
views
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 ...
7
votes
2
answers
81
views
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):
$$
F(\rho, \sigma) = \text{Tr}\left( \sqrt{ \sqrt{\rho} \sigma \sqrt{\rho}}\right)^2.
$$
...
3
votes
1
answer
61
views
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 ...
2
votes
0
answers
30
views
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 ...
2
votes
3
answers
84
views
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 ...
2
votes
2
answers
56
views
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 ...
0
votes
0
answers
22
views
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 ...
0
votes
1
answer
57
views
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 $\vert 0\rangle$ ...
2
votes
0
answers
44
views
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 ...
4
votes
0
answers
63
views
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 ...
0
votes
1
answer
53
views
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 \...
2
votes
0
answers
29
views
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 ...
3
votes
0
answers
60
views
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 ...
3
votes
1
answer
65
views
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-...
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 \...
2
votes
2
answers
55
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 ...
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, ...
1
vote
0
answers
23
views
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 $\...
1
vote
1
answer
30
views
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 *
...
1
vote
0
answers
16
views
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?
5
votes
1
answer
312
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 ...
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 ...
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 ...
1
vote
1
answer
74
views
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 ...
1
vote
0
answers
33
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 ...
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 ...
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 ...
1
vote
0
answers
18
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?
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 ...
2
votes
1
answer
47
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 =...
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 ...
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:
...
3
votes
0
answers
22
views
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 ...
5
votes
0
answers
44
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 ...