Quantum Code Design And Architecture
Lead Research Organisation:
University of Sheffield
Department Name: Physics and Astronomy
Abstract
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.
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.
Planned Impact
Please see Section 2 of main proposal document
Publications
Campbell E
(2019)
A theory of single-shot error correction for adversarial noise
in Quantum Science and Technology
Cullen A
(2022)
Calculating concentratable entanglement in graph states
in Physical Review A
Huang Z
(2021)
Quantum Hypothesis Testing for Exoplanet Detection.
in Physical review letters
Ouyang Y
(2019)
Computing spectral bounds of the Heisenberg ferromagnet from geometric considerations
in Journal of Mathematical Physics
Ouyang Y
(2021)
Quantum storage in quantum ferromagnets
in Physical Review B
Ouyang Y
(2022)
Robust Quantum Metrology With Explicit Symmetric States
in IEEE Transactions on Information Theory
Ouyang Y
(2022)
Linear Programming Bounds for Approximate Quantum Error Correction Over Arbitrary Quantum Channels
in IEEE Transactions on Information Theory
Ouyang Y
(2021)
Avoiding coherent errors with rotated concatenated stabilizer codes
in npj Quantum Information
Ouyang Y
(2020)
Compilation by stochastic Hamiltonian sparsification
in Quantum
Ouyang Y
(2020)
Linear programming bounds for quantum amplitude damping codes
| Description | Published results characterising single-shot error correction, which was one of the projects early milestones. Two projects currently being written up that develop the first general-purpose decoding algorithms for a promising class of quantum codes known as hypergraph-product codes. Generic LDPC codes and decoders: A collaboration between London (Burton) and Sheffield (Roffe & Campbell) investigated several improvements to the bit-flip decoder for quantum LDPC codes with a unifying theme being the use of belief-propagation (BP) decoders and the effects of noisy measurements. We developed a high performance open sourced implementation of the BP-OSD decoder, during the course of the research reported in [RWBC20]. We released a refined and improved version of this decoder, with both Python and C++ implementations, under the MIT license on github, https://github.com/quantumgizmos/bp_osd . This provides a powerful tool for the quantum error correction research community, enabling them to test the error correction performance of any LDPC code that is invented. Single-shot error correction: when measurements are noisy, to perform quantum error correction we either need to repeat these measurements or use a code with a special property called single-shot error correction. However, before this project, some example were known by the underpinning theory was poorly understood. The project produced two papers on the foundational theory of single-shot error correction. This culminated in a rigorous notion of confinement that is shared by all known examples of single-shot codes, thereby providing the first satisfying theory. We also showed how confinement can be ensured by using the homological product to generate higher-dimensional codes. Bosonic codes: The GKP encoding is a very promising approach to error corrections in the continuous variable regime, but due to its focus on phasespace shifts, it is not necessarily optimal when other errors such as phasespace rotations occur. The natural question is whether a CV code can be robust to different types of errors (i.e., phase space shifts and phase space rotations, for example) at the same time. In [OC21], the Sheffield team (Ouyang and Cambpell) address this question and establish trade-off relations for resilience with respect to different fault categories. They have shown that there is a trade-off between the parameter g (which ultimately determines the robustness to number-shift errors) and the tolerable standard deviation s of the phase rotation in a single bosonic mode. |
| Exploitation Route | Assist with design of quantum computers |
| Sectors | Digital/Communication/Information Technologies (including Software) |
| Description | SB at UCL |
| Organisation | University College London |
| Country | United Kingdom |
| Sector | Academic/University |
| PI Contribution | Joschka Roffe and David White at Sheffield developed the final OSD decoder software (a sophisticated belief propagation algorithm) used to obtain the results. |
| Collaborator Contribution | Simon Burton coded up an early version of a simple belief propagation algorithm which formed the starting point for subsequent development of the OSD decoder. |
| Impact | https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.2.043423 |
| Start Year | 2018 |
| Description | Topological Quantum Error Correction |
| Form Of Engagement Activity | A broadcast e.g. TV/radio/film/podcast (other than news/press) |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Public/other audiences |
| Results and Impact | Youtube video about Topological Quantum Error Correction |
| Year(s) Of Engagement Activity | 2018 |
| URL | https://www.youtube.com/watch?app=desktop&v=OU9_mrxLl3g&list=PLoLVttQYPLFXr3glgUwSV0qxJd7BTcxWj |