SLIDES
It is believed that active quantum error correction will be an essential ingredient to build a scalable quantum computer. The currently favored scheme is the surface code due to its high decoding threshold and efficient decoding algorithm. However, it suffers from large overheads which are even more severe when parity check measurements are subject to errors and have to be repeated. Furthermore, the number of encoded qubits in the surface code does not grow with system size, leading to a sub-optimal use of the physical qubits.
We introduce quantum pin codes: a class of quantum CSS codes. Quantum pin codes are a vast generalization of quantum color codes and Reed-Muller codes. A lot of the structure and properties of color codes carries over to pin codes. Pin codes have …
We describe a computationally efficient heuristic algorithm based on a renormalization-group procedure which aims at solving the problem of finding a minimal surface given its boundary (curve) in any hypercubic lattice of dimension D 2. We use this …
Machine learning has the potential to become an important tool in quantum error correction as it allows the decoder to adapt to the error distribution of a quantum chip. An additional motivation for using neural networks is the fact that they can be …
We explore a distance-3 homological CSS quantum code, namely the small stellated dodecahedron code, for dense storage of quantum information and we compare its performance with the distance-3 surface code. The data and ancilla qubits of the small …
We show how a hyperbolic surface code could be used for overhead-efficient quantum storage. We give numerical evidence for a noise threshold of for the -hyperbolic surface code in a phenomenological noise model (as compared with for the toric …
We analyze the performance of decoders for the 2D and 4D toric code which are local by construction. The 2D decoder is a cellular automaton decoder formulated by Harrington which explicitly has a finite speed of communication and computation. For a …
We analyze the performance of decoders for the 2D and 4D toric code which are local by construction. The 2D decoder is a cellular automaton decoder formulated by Harrington which explicitly has a finite speed of communication and computation. For a model of independent X and Z errors and faulty syndrome measurements with identical probability we report a threshold of 0.133% for this decoder. We implement a decoder for the 4D toric code which is based on a decoder by Hastings.
We show how to obtain concrete constructions of homological quantum codes based on tilings of 2D surfaces with constant negative curvature (hyperbolic surfaces). This construction results in two-dimensional quantum codes whose tradeoff of encoding …