Questions tagged [topological-quantum-computing]
Topological quantum computing is a theoretical quantum computing model that employs two-dimensional quasiparticles called anyons, whose world lines pass around one another to form braids in a three-dimensional spacetime (i.e., one temporal plus two spatial dimensions).
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Quantum dimension of an anyon
In the book Introduction to Topological Quantum Computation Jiannis K. Pachos page 60 Equ.(4.16) $\text{dim}(M_{(n)}) \propto d_a^n$, two lines after (4.16) said that,
The dimension of $M_{(n)}$ is ...
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Need help to understand topological color codes
I am doing work on topological color codes, but after searching a lot of papers I could not find one that explained some points. Why do we need the colors for? Why do we have different types of color ...
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Logical error rate of topological cluster state under erasure channel
Assume I use the topological cluster state (https://arxiv.org/abs/quant-ph/0703143) to protect against erasure. Assume also that the only noise or erasure that I have in my system is loss in the ...
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The effect of qubit loss/erasure on its neighbors in topological cluster state
I try to understand how to simulate the effect of heralded qubit loss (or erasure) in one of the gates during the creation a topological cluster state (as a part of an error-correction simulation).
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Is there a way to perform a defect-free logical CNOT on the toric code?
I was curious to whether the two logical qubits on the toric code can be entangled through, for instance, a logical CNOT operation. However, I cannot find any information on this, only how you can do ...
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Quantum entanglement as topological entanglement
According with Aravind:
the Hopf link, L2a1, corresponds to the Bell state $\frac{1}{\sqrt 2}\big (|00\rangle+|11\rangle\big )$,
the Borromean link (L6a4) can be considered as GHZ state $\frac{1}{\...
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Are there open source implementations of quantum error correction decoders?
To detect and correct for errors in a topological quantum memory (toric code for example) one needs a quantum error correction algorithm also known as decoder.
The minimum weight perfect matching (...
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Reference that explains how to read 3d topological diagrams for surface code computations
I like making diagrams to describe computations. For the surface code, an excellent tool is 3d topological diagrams. Here is an example diagram (made by me in SketchUp):
The basic idea is that white ...
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Is there a code version for the Quantum Mean Approximation algorithm?
I found this paper https://arxiv.org/pdf/1106.4267.pdf which describes a method to find the mean of all numbers in a list using a quantum algorithm. However, all it gives is the math behind it. Is ...
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What is a diference between solitons and anyons?
In the article Creation and annihilation of mobile fractional solitons in atomic chains the authors claim that they prepared 1D solitons which can be used in topological quantum computing. Based on ...
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Why Is This the Ground State of a Toric Code?
I am currently trying to study the ground state of the Toric Code. I am currently reading this paper. The Hamiltonian is given by the following, where $A_s$'s are the star operators made out a tensor ...
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Can you make anyons in 3 dimensions using rings?
I heard that anyons can only be made in 2 dimensions because when you visualize the spacetime diagram of a 2-dimensional system with point particles, you can get braids, but if you do the same with a ...
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Origin of braiding in measurement-only TQC
I have a technical question on the "measurement-only"-proposal for topological quantum computation on anyons. First some background:
Background.
While it has become a common idea that ...
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What is the status of confirming the existence of anyons?
In a comment on my answer to the question: What exactly are anyons and how are they relevant to topological quantum computing? I was asked to give specific examples of occurrence of anyons in nature. ...
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extracting the Pauli error on the data qubits at the end of circuit in stim
Let's say one implements the following circuit in stim from the stim tutorial:
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What is the Stabilizer of a Code?
I am currently reading the beginning of the paper Topological Quantum Memory and I am confused about one part:
The
check operators generate an Abelian group, the code’s
stabilizer.
When I learned ...
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Simulate Surface /Topological Code with Majorana - Huge Complexity Saving
This article "Correcting coherent errors with surface codes" is talking in the methods section, about simulating topological codes / surface codes, using Majorana equivalent. It is also ...
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Topological quantum computer and two dimensional materials
Recently I read thread on topological quantum computers. If I understood correctly, gates in such computers are based on "effects" in two dimensional spaces. Since our space is three dimensional, such ...
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Are there any other companies besides Microsoft pursuing topological QC?
Also, why is Microsoft placing such an emphasis on topological qubits when most other companies seem to be focusing on other qubit technologies?
I know topological qubits could handle noise far ...
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Simulating quantum computers using anyon braiding
I am new to the concept of topological quantum computation (TQC).
Recently I have been thinking about simulating a quantum computer on a classical computer. I know that if I use merely the unitary ...
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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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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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How does the size of a toric code torus affect its ability to protect qubits?
The Toric code Hamiltonian is:
$\sum_{x,y}\left( \prod_{i\in p(x,y)} Z_{ixy} + \prod_{i\in v(x,y)} X_{ixy} \right),$
where the $v$ and $p$ are defined according to this picture (courtesy of James ...
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What is the most economical and preferred basis for the qudit?
In Classical Simulation of Quantum Error Correction in a Fibonacci Anyon Code, the authors state on page 2 in section I. Background, A. Topological model:
We consider a system supporting nonabelian ...
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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 ...
glS♦
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Does this experimental discovery of anyons enables the topological quantum computer (e.g. Microsoft) to become a reality?
Microsoft has its own agenda regarding quantum computer - it is topological quantum computer being invented by the team lead by Michael Freedman https://www.microsoft.com/en-us/research/project/...
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Why does non-locality and the particle-hole symmetry not contradict each other?
Currently, I'm learning about topological quantum computers.
In one of the explained techniques, cooper pairs in superconductors are considered, where a cooper pair with a hole form a Majorana bound ...
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History of anyon theory, braidings and tensor categories
What was the first paper/who was the first person to phrase anyon theory in terms of tensor categories?
Going through Wilczek's book on fractional statistics, some of the reprinted papers anticipate ...
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How does topological quantum computing differ from other models of quantum computing?
I've heard the term Topological Quantum Computer a few times now and know that it is equivalent to quantum computers using circuits with respect to some polynomial-time reduction.
However, it is ...
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Measuring Ising anyons: What is a fusion measurement?
I have several doubts about measuring Ising anyons. Measurement is crucial for quantum computation and even more so for magic state distillation which is necessary to make Ising anyons universal.
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Topological anyonic molecule statistics
In the last chapter of John Preskill's Lecture Notes for Physics 219:
Quantum Computation (PDF), he mentions the following on pg.12.
This behavior is compatible with the spin-statistics connection: ...
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What is the correspondence between adiabatic phase and a topological phase?
In the adiabatic model, we have a system acquiring a Berry phase due to cyclic slow periodic evolution under a Hamiltonian. While in the topological phases, we talk about systems such as anyons which ...
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Correspondence between the Topological model and Quantum Circuit model
For example, given the $R$ & $F$ gates and Toric codes for a given problem, how to convert this code into the conventional circuit model and vice versa.
From the literature developed, it seems ...
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Is Gil Kalai's argument against topological quantum computers sound?
In a lecture, recorded on Youtube, Gil Kalai presents a 'deduction' for why topological quantum computers will not work. The interesting part is that he claims this is a stronger argument than the ...
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Is there any tool or simulator for Topological quantum gates and circuits? [duplicate]
I am starting to step into the field of Topological Quantum Information and Computation and am in search of tools which I can use to directly simulate or realize these transformations in a textual or ...
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Topological Circuit Simulator
Does something like Quirk exist for topological (eg. braided) circuits?
Alternatively, any ideas on how @CraigGidney is getting these circuits (or something similar)?
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Anyon alternatives in topological quantum computing
A topological quantum computer is a theoretical quantum computer that employs two-dimensional quasiparticles called anyons. -Wikipedia
Are there other instances of topological quantum computing ...
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Are there connections between long-range entanglement and topological quantum computation?
Long-range entanglement is characterized by topological order (some kinds of global entanglement properties), and the "modern" definition of topological order is the ground state of the system cannot ...
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What exactly are anyons and how are they relevant to topological quantum computing?
I have been trying to get a basic idea of what anyons are for the past couple of days. However, the online articles (including Wikipedia) seem unusually vague and impenetrable as far as explaining ...
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