quantum codes

Single-Shot Decoding of Linear Rate LDPC Quantum Codes with High Performance

We construct and analyze a family of low-density parity check (LDPC) quantum codes with a linear encoding rate, polynomial scaling distance and efficient decoding schemes. The code family is based on tessellations of closed, four-dimensional, …

Machine learning logical gates for quantum error correction

Quantum error correcting codes protect quantum computation from errors caused by decoherence and other noise. Here we study the problem of designing logical operations for quantum error correcting codes. We present an automated procedure which …

The Present and Future of Quantum Error Correction

SLIDES A short talk on quantum error correction at the UCLQ Annual Industry Event 2019. It is aimed towards a broad audience and gives a brief overview over the field as well as an outlook towards the coming 10 years.

Introduction to Quantum Error Correction

QuID 2019 was a summer school aimed towards beginning PhD students to learn about several topics in quantum computing. I contributed a series of three lectures on quantum error correction. The course covered the fault-tolerance theorem, Shor’s code, the stabilizer formalism, topological codes and gate constructions for the surface code. SLIDES 1 SLIDES 2 SLIDES 3

Single-Shot-Decoding with High Thresholds in LDPC Quantum Codes with Constant Encoding Rate

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.

Quantum Pin Codes

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 …

Renormalization Group Decoder for a Four-Dimensional Toric Code

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 …

Scalable Neural Network Decoders for Higher Dimensional Quantum Codes

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 …

The small stellated dodecahedron code and friends

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 …

Hyperbolic and semi-hyperbolic surface codes for quantum storage

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 …