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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If T gates are now as expensive as CNOTs, what should be optimized?
Is there a simple circuit metric that describes the overhead of implementing a circuit with lattice surgery? If there is no such metric, does this imply that it no longer makes sense to optimize a ...
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Can a quantum computer operate efficiently in outer space due to extremely low temperatures?
I’m a high school student beginning my journey into quantum physics and quantum computing.I’m understand that quantum computers require extremely low temperatures and high isolation from environmental ...
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Non-deterministic detectors when simulating Floquet code
I'm using stim to simulate the 2d css honeycomb code https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuantum.4.020341, and first test the simplest case with just 12 qubits. And the ...
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Is the toric with rough/smooth boundaries a CW complex?
Usually, when talking about the toric code, we consider a tessellation of the torus $\mathbb{T}^2$ so that the 2-cells, 1-cells, 0-cells form a CW complex, and thus the toric code ($X,Z$-type ...
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Why is it helpful to use Majorana particle in topological quantum computing (they are just Fermions?!)
My basic understanding of topological quantum computing is that it makes use of anyons which are particles satisfying the following rule under wave-function swap:
$$ |\psi_1 \psi_2\rangle = e^{i \...
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Is there a simple way to understand why topological quantum computing with anyons is expected to be more noise resilient?
I understand the basic quantum mechanics definition of anyons through the very nice answer of "user1271772 No more free time" here. I guess (?!) it requires to use non-trivial anyons (i.e. ...
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The handling of radius in pymatching
In surface code, the weight connecting two nodes is determined using the Manhattan distance. However, in arXiv:2303.15933, the expansion of a region is illustrated using circles based on the radius ...
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Poking holes and cutting corners with the surface code: how do we get the stabilisers when turning defect lines around corners?
In Poking holes and cutting corners to achieve Clifford gates with the surface code (arXiv), I'm having trouble with Fig. 6. I understand what the stabilisers are across the defect line, and I ...
user23402
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How can I implement an MWPM decoder for heralded errors(biased error) in stim?
I am trying to use the ``HERALDED_PAULI_CHANNEL_1'' in stim to implement biased errors. However, if I use this feature, I understand that I won't be able to use stim's pymatching decoder'', so I need ...
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How does the surface code have four twist defects, one at each corner?
In Craig Gidney’s Y Basis paper he states “Recall that a surface code patch has four twist defects, one at each corner” and cites Ben Brown et al.’s ‘Poking’ paper. I do not understand how to ...
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Is there an upper bound on two-qubit fidelity improvements?
The higher the two-qubit fidelity, the lower the overhead for quantum error correction. This is especially preferable due to the fact that cheap QRAM would be useful for practical applications, QRAM ...
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Finding Fusion Matrix for simple non-abelian anyon model
Given the anyon particles: $\{1, \Lambda, \Phi\}$ and fusion rules:
$$\Lambda \times \Lambda = 1, \quad \Lambda \times \Phi = \Phi \times \Lambda = \Phi, \quad \Phi \times \Phi = 1 + \Lambda + \Phi$$
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How does one identify Pauli logicals in a hyperbolic surface code?
I understand how the Pauli X and Z logicals on the planar surface code work - they are stringlike operators between either the rough boundaries (in case of the Z logical) or between smooth boundaries (...
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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 ...
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How to get the surviving stabilisers of a fusion network
In Fig. 5 of PsiQuantum's Fusion-based quantum computation paper, it's clear to me how to get R, F, and C.
How do I get S? Just by looking at (a), I could obviously tell you that we end up with <...
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