Quantum Code Design And Architecture

Lead Research Organisation: University College London
Department Name: Physics and Astronomy


General purpose quantum computers must follow a fault-tolerant design to prevent ubiquitous decoherence processes from corrupting computations. All approaches to fault-tolerance demand extra physical hardware to perform a quantum computation. Kitaev's surface, or toric, code is a popular idea that has captured the hearts and minds of many hardware developers, and has given many people hope that fault-tolerant quantum computation is a realistic prospect. Major industrial hardware developers include Google, IBM, and Intel. They are all currently working toward a fault-tolerant architecture based on the surface code. Unfortunately, however, detailed resource analysis points towards substantial hardware requirements using this approach, possibly millions of qubits for commercial applications. Therefore, improvements to fault-tolerant designs are a pressing near-future issue. This is particularly crucial since sufficient time is required for hardware developers to react and adjust course accordingly.

This consortium will initiate a European co-ordinated approach to designing a new generation of codes and protocols for fault-tolerant quantum computation. The ultimate goal is the development of high-performance architectures for quantum computers that offer significant reductions in hardware requirements; hence accelerating the transition of quantum computing from academia to industry. Key directions developed to achieve these improvements include: the economies of scale offered by large blocks of logical qubits in high-rate codes; and the exploitation of continuous-variable degrees of freedom.

The project further aims to build a European community addressing these architectural issues, so that a productive feedback cycle between theory and experiment can continue beyond the lifetime of the project itself. Practical protocols and recipes resulting from this project are anticipated to become part of the standard arsenal for building scalable quantum information processors.
Description The aim of the European Quant-era Quantum Codes Design and architecture project was to design a new generation of codes and protocols for fault-tolerant quantum computation. This summary focuses on outputs from UCL's node in the network only. Error correction is essential for large-scale quantum computation, and recently a number of novel quantum error correcting codes have been proposed, which could lead to alternative architectures for quantum computation. In UCL's node we focussed on two key themes, fault tolerant computation with novel codes, and error correction with such codes.

On the topic of fault tolerant computation we focussed on so-called "transversal gates", a special way to implement quantum computations in a code which do not spread errors within the code. We showed that a three-dimensional generalisation of the "surface code", currently the most prominent quantum code, supports a set of transversal gates which contain all of the gates required for native universal quantum computation. On the other hand, in yet unpublished work, we proved a no-go theorem to show that a broad family of hypergraph-product codes, a vast generalisation of the two-dimensional surface code, cannot have a native transversal universal set of gates, and the gates are limited to a sub-family called the Clifford group.

On error correction, we generalised the belief propagation algorithm, important in classical error correction, to a broad range of novel codes, and developed a novel cellular-automaton based error correction algorithm for three-dimensional topological codes.
Exploitation Route The results of this project provide new approaches to constructing fault-tolerant quantum computers, and also indicate some potential limitations of recently proposed approaches to quantum error correction. They can be built upon in the development of roadmaps for architectures for large-scale quantum computers and in the development of algorithms for error correction on these devices.
Sectors Digital/Communication/Information Technologies (including Software)

Title BP+OSD: A decoder for quantum LDPC codes 
Description This software implements the belief propagation with ordered statistics post-processing for decoding sparse quantum LDPC codes as described in arXiv:2005.07016. Note, this library has recently been completly rewritten using Python and Cython. The bulk of the code now resides in the LDPC repository. The original C++ version can be found in the cpp_version branch of this repository. 
Type Of Technology Software 
Year Produced 2022 
Open Source License? Yes  
Impact This decoder has been used in two follow up papers: https://arxiv.org/abs/2009.11790 https://arxiv.org/abs/2202.01702 
URL https://github.com/quantumgizmos/bp_osd