Quantum Code Design And Architecture

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

Abstract

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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 On the other hand, in yet unpublished work, we proved a no-go theorem to show that a broad family of hypergraph-product codes, a vast generalisation of the two-dimensional surface code, cannot have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)
 
Description Quantum error correction plays a fundamental role in the R&D roadmap of several large industry players and start-ups engaged in the development of quantum computation. The QCDA consortium has had several collaborative projects with industry and significant mobility between QCDA and industry. The project included a collaboration with IBM which developed simulation tools to improve understanding of coherent errors that impede standard quantum error correction methods. Superconducting qubit architectures, such as the one IBM is developing, can be especially prone to crosstalk errors due to unwanted interactions between qubits. These are a form of coherent errors, whereas standard quantum error correction assumes an incorrect (Pauli) noise process, and so the result has helped IBM's understandings of their dominant noise. In 2020, Earl Campbell left the consortium to work for Amazon Web Services (AWS) who had just started a large initiative aimed at building a fault-tolerant quantum computer. The work of QCDA directly impacted the AWS's research. For instance, the blueprint paper "Building a fault-tolerant quantum computer using concatenated cat codes" [PRX Quantum 3, 010329 (2022)]" builds on several of the significant results of QCDA. The blueprint builds on significant result 5 [VB19] as the CCZ transversality results there were adapted to design a magic-state factory tailored to cat qubit architectures. Furthermore, cat qubits are bosonic error correction codes and so this blueprint draws on the results and expertise of QCDA. Riverlane is a Cambridge-based startup developing an operating system for quantum computers. Initially, Riverlane was focused on near-term quantum algorithms, but in 2021 it pivoted it to focus on error-correction quantum computing including an aim to build the world's fastest decoder. to the best of our knowledge, it is the only company in Europe with a primary focus on quantum error correction. QCDA has had a significant impact on the direction on Riverlane. Earl Campbell worked as a part-time consultant for Riverlane (Feb 2019 - Dec 2019) during QCDA and since Jan 2022 has worked there full-time as Head of Architecture. Dan Browne has been an advisor to Riverlane since 2019 and is now also a part-time consultant. Furthermore, QCDA-collaborating PhD student Armanda Quintavalla (Sheffield), is currently taking a 6 month leave from her PhD studies to work as an intern at Riverlane. Especially important to Riverlane was the BP-OSD Decoder software that Riverlane uses and is building upon. Xanadu is a large start-up developing a photonic quantum computing device. QCDA-collaborating PhD student Mike Vasmer has gone on to collaborate with Xanadu on the paper "Blueprint for a scalable photonic fault-tolerant quantum computer" [Quantum 5 392] that described a bosonic approach to quantum computing and so draws on the bosonic error correction results and expertise of QCDA.
First Year Of Impact 2019
Sector Digital/Communication/Information Technologies (including Software)
Impact Types Economic
 
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