Color code with a logical control-$S$ gate using transversal $T$ rotations
- URL: http://arxiv.org/abs/2411.15035v1
- Date: Fri, 22 Nov 2024 16:08:33 GMT
- Title: Color code with a logical control-$S$ gate using transversal $T$ rotations
- Authors: Benjamin J. Brown,
- Abstract summary: Three-dimensional examples of the color code have shown us how its structure, specifically the intersection of the supports of logical operators, can give rise to non-Clifford $T$ and $CCZ$.
Here we present a color code with a logical control-$S$ gate that is accomplished with $Tdagger$ rotations on its physical qubits.
- Score: 2.1756081703276
- License:
- Abstract: The color code has been invaluable for the development of the theory of fault-tolerant logic gates using transversal rotations. Three-dimensional examples of the color code have shown us how its structure, specifically the intersection of the supports of logical operators, can give rise to non-Clifford $T$ and $CCZ$ gates. Here we present a color code with a logical control-$S$ gate that is accomplished with transversal $T$ and $T^\dagger$ rotations on its physical qubits.
Related papers
- Targeted Clifford logical gates for hypergraph product codes [61.269295538188636]
We construct explicit targeted logical gates for hypergraph product codes.
As a concrete example, we give logical circuits for the $[[18,2,3]]$ toric code.
arXiv Detail & Related papers (2024-11-26T02:32:44Z) - Convolutional Differentiable Logic Gate Networks [68.74313756770123]
We propose an approach for learning logic gate networks directly via a differentiable relaxation.
We build on this idea, extending it by deep logic gate tree convolutions and logical OR pooling.
On CIFAR-10, we achieve an accuracy of 86.29% using only 61 million logic gates, which improves over the SOTA while being 29x smaller.
arXiv Detail & Related papers (2024-11-07T14:12:00Z) - Geometric structure and transversal logic of quantum Reed-Muller codes [51.11215560140181]
In this paper, we aim to characterize the gates of quantum Reed-Muller (RM) codes by exploiting the well-studied properties of their classical counterparts.
A set of stabilizer generators for a RM code can be described via $X$ and $Z$ operators acting on subcubes of particular dimensions.
arXiv Detail & Related papers (2024-10-10T04:07:24Z) - Quantum Rainbow Codes [0.0]
We introduce rainbow codes, a novel class of quantum error correcting codes generalising colour codes and pin codes.
Rainbow codes can be defined on any $Ddimensional simplicial complex that admits a valid $(D+1)$colouring of its $0simplices.
arXiv Detail & Related papers (2024-08-23T14:56:55Z) - Logical Operators and Fold-Transversal Gates of Bivariate Bicycle Codes [1.8416014644193066]
Quantum low-density parity-check (qLDPC) codes offer a promising route to scalable fault-tolerant quantum computation with constant overhead.
Recent advancements have shown that qLDPC codes can outperform the quantum memory capability of surface codes even with near-term hardware.
arXiv Detail & Related papers (2024-07-04T14:49:35Z) - Non-Clifford and parallelizable fault-tolerant logical gates on constant and almost-constant rate homological quantum LDPC codes via higher symmetries [1.3194391758295114]
We study fault-tolerant quantum computing for families of homological quantum low-density parity-check codes defined on 3-manifolds with constant or almost-constant encoding rate.
We have developed a generic formalism to compute the triple intersection invariants for 3-manifolds.
arXiv Detail & Related papers (2023-10-25T20:33:59Z) - Code conversion with the quantum Golay code for a universal transversal gate set [0.13597551064547497]
The $[[7,1,3]]$ Steane code and $[[23,1,7]]$ quantum Golay code have been identified as good candidates for fault-tolerant quantum computing via code concatenation.
A crucial ingredient to this procedure is the $[49,1,5]]$ triorthogonal code, which can itself be seen as related to the self-dual $[[17,1,5]]$ 2D color code.
arXiv Detail & Related papers (2023-07-26T18:00:04Z) - Morphing quantum codes [77.34726150561087]
We morph the 15-qubit Reed-Muller code to obtain the smallest known stabilizer code with a fault-tolerant logical $T$ gate.
We construct a family of hybrid color-toric codes by morphing the color code.
arXiv Detail & Related papers (2021-12-02T17:43:00Z) - Finding the disjointness of stabilizer codes is NP-complete [77.34726150561087]
We show that the problem of calculating the $c-disjointness, or even approximating it to within a constant multiplicative factor, is NP-complete.
We provide bounds on the disjointness for various code families, including the CSS codes,$d codes and hypergraph codes.
Our results indicate that finding fault-tolerant logical gates for generic quantum error-correcting codes is a computationally challenging task.
arXiv Detail & Related papers (2021-08-10T15:00:20Z) - The cost of universality: A comparative study of the overhead of state
distillation and code switching with color codes [63.62764375279861]
We compare two leading FT implementations of the T gate in 2D color codes under circuit noise.
We find a circuit noise threshold of 0.07(1)% for the T gate via code switching, almost an order of magnitude below that achievable by state distillation in the same setting.
arXiv Detail & Related papers (2021-01-06T19:00:01Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.