Theory to Enable Practical Quantum Advantage
Lead Research Organisation:
UNIVERSITY OF OXFORD
Department Name: Materials
Abstract
Quantum computers have already reached a scale that they can fundamentally outperform any conventional supercomputer (often referred to as classical computers) on artificial benchmarking tasks. However, the ultimate goal of the field is to reach practical quantum advantage (PQA), i.e., the point where quantum computers perform otherwise-infeasible useful functions for users beyond the immediate community. For example, a materials scientist or chemist who would calculate properties of novel materials/drugs for screening purposes to forgo expensive laboratory research.
Most hardware companies aim to ultimately build error-corrected quantum computers, however, the implied engineering complexity is so vast that it is generally believed that large-scale, fully quantum-error-corrected machines will not be feasible within a decade or more. Unfortunately, every operation current and near-future machines will perform are substantially flawed, i.e., noisy and thus the most pressing issue currently is: how can we make use of quantum computers that are expected to emerge in the near future and in the early-fault tolerant era?
The overarching objective of this project is to understand and overcome the challenges posed by noisy quantum computers and will deliver key innovations in exploiting early quantum computers that we expect will emerge in the period we call (late) NISQ and early fault tolerant. The project has three distinct but closely interlinked targets that will all play a key role in lowering barriers for practical quantum advantage.
First, the project aims to exploit powerful classical supercomputers in order to enhance the capabilities of noisy quantum computers. In particular, recent developments in classical shadow tomography will be exploited in order to efficiently extract large amounts of information from a quantum computer that is post-processed classically.
Second, error mitigation techniques will be developed that make tradeoffs between accuracy and measurement overhead thereby improving the practicality of noisy quantum computers -- this includes error mitigated classical shadows. Furthermore, one of the goals of this project is to better understand the fundamental limitations of noisy quantum computers with an emphasis on tradeoffs between accuracy and measurement overhead.
Finally, in order to achieve an optimal hardware implementation of quantum algorithms, hardware-level protocols will be developed for improved control of the quantum computer as well as protocols will be tailored to specific hardware architectures.
Ultimately, this project aims to reduce the barriers for achieving practical quantum advantage thereby leading to useful applications of early quantum computers. These applications include, simulating chemical systems for discovering novel drugs, atomistic modelling in materials science to develop novel materials, batteries, solar cells, or performing binary optimisation in logistics. The project is supported by an impressive range of both quantum hardware and software companies.
Most hardware companies aim to ultimately build error-corrected quantum computers, however, the implied engineering complexity is so vast that it is generally believed that large-scale, fully quantum-error-corrected machines will not be feasible within a decade or more. Unfortunately, every operation current and near-future machines will perform are substantially flawed, i.e., noisy and thus the most pressing issue currently is: how can we make use of quantum computers that are expected to emerge in the near future and in the early-fault tolerant era?
The overarching objective of this project is to understand and overcome the challenges posed by noisy quantum computers and will deliver key innovations in exploiting early quantum computers that we expect will emerge in the period we call (late) NISQ and early fault tolerant. The project has three distinct but closely interlinked targets that will all play a key role in lowering barriers for practical quantum advantage.
First, the project aims to exploit powerful classical supercomputers in order to enhance the capabilities of noisy quantum computers. In particular, recent developments in classical shadow tomography will be exploited in order to efficiently extract large amounts of information from a quantum computer that is post-processed classically.
Second, error mitigation techniques will be developed that make tradeoffs between accuracy and measurement overhead thereby improving the practicality of noisy quantum computers -- this includes error mitigated classical shadows. Furthermore, one of the goals of this project is to better understand the fundamental limitations of noisy quantum computers with an emphasis on tradeoffs between accuracy and measurement overhead.
Finally, in order to achieve an optimal hardware implementation of quantum algorithms, hardware-level protocols will be developed for improved control of the quantum computer as well as protocols will be tailored to specific hardware architectures.
Ultimately, this project aims to reduce the barriers for achieving practical quantum advantage thereby leading to useful applications of early quantum computers. These applications include, simulating chemical systems for discovering novel drugs, atomistic modelling in materials science to develop novel materials, batteries, solar cells, or performing binary optimisation in logistics. The project is supported by an impressive range of both quantum hardware and software companies.
Organisations
- UNIVERSITY OF OXFORD (Lead Research Organisation)
- Moderna (Collaboration)
- Quantum Motion Technologies Ltd (Collaboration)
- IBM (Collaboration)
- Thales Group (Collaboration)
- Osaka University (Collaboration)
- University College London (Collaboration)
- Quantum Motion (Project Partner)
- PhaseCraft Ltd (Project Partner)
- Oxford Ionics (Project Partner)
Publications
Anonymous
(2025)
Exponential distillation of dominant eigenproperties
in PRX Quantum
Anonymous
(2025)
Quantum snakes on a plane: Mobile, low dimensional logical qubits on a 2D surface
in PRX Quantum
Araki T
(2025)
Space-time trade-off in networked virtual distillation
in Physical Review A
Benjamin C. B. Symons
(2025)
Sequences of Bivariate Bicycle Codes from Covering Graphs
Boyd G
(2025)
High-dimensional subspace expansion using classical shadows
in Physical Review A
Cai Z
(2025)
Biased estimator channels for classical shadows
in Physical Review A
Chan H
(2025)
Algorithmic Shadow Spectroscopy
in PRX Quantum
Erle J
(2026)
A Shadow Enhanced Greedy Quantum Eigensolver
| Description | Substantial research progress has been made since the award start date as 13 papers have been published in this period and a further 7 manuscripts have been made available online as arXiv preprints that are currently under review. The research output of the present grant supports the following high-level observations. First, with the rapid development of quantum technologies, quantum computing hardware is now capable of performing certain quantum simulation tasks, which have practical relevance (albeit rather limited), that are challenging to outperform using conventional computers. Research outcomes of this award directly contribute to these efforts in the field, e.g., we developed near-term quantum algorithms [PRX Quantum 6 (1), 010352; Quant Sci Techn 10 (4), 045071; Phys Rev Research 8, 013250; Phys Rev A 111 (2), 022423] that substantially lower resource requirements and improve the practicality of near-term applications - our techniques have been consequently implemented by independent teams in hardware experiments using, e.g., state-of-the-art IBM devices and neutral atom processors [Nature Physics (21) 289-297 (2025); arXiv:2510.25640; arXiv:2601.13881]. On the other hand, classical computational techniques are becoming increasingly more sophisticated and pose hard competition - with impressive developments in engineering quantum error correction capabilities, the field is therefore shifting focus towards early fault tolerant and fully fault tolerant applications. Balint Koczor co-founded a conference series Seeking Quantum Advantage (SEEQA)-and has been the lead organiser-which has been providing a platform for high level discussions in the community around the potential of achieving quantum advantage. These discussions also motivated us to write a high level community perspective article we published with colleagues on "Myths around quantum computation before full fault tolerance: What no-go theorems rule out and what they don't." [arXiv:2501.05694]. We conclude that some form of quantum error correction is necessary for achieving substantial commercial and practical quantum advantage and research outcomes of this award directly contribute towards lowering barriers for practical, error corrected quantum computation. First, both PDRAs funded by this award are quantum error correction experts and have developed novel error correction techniques and protocols [arXiv:2511.13560; arXiv:2603.05481; PRX Quantum 7 (1), 010339] in collaboration with, e.g., IBM and Quantum Motion. We have also developed improved early fault tolerant algorithms that exploit the power of conventional supercomputers [arXiv:2602.17615; PRX Quantum 7 (1), 010334; arXiv:2603.05475], some of which work was carried out in collaboration with Quantum Motion and Moderna. Finally, we have substantially lowered resource costs for fully fault tolerant quantum algorithms [arXiv:2508.16719; arXiv:2508.06236; Physical Review A 111 (6), 062420], some of which work was carried out with Boehringer Ingelheim, which is a major German Pharmaceutical company. Overall, it seems increasingly more likely that achieving substantial practical and commercial advantage requires some form of quantum error correction, however, substantial progress is required in both improving quantum error correction capabilities and lowering resource costs of quantum algorithms - the present research outcomes contribute substantially to both of these research areas. |
| Exploitation Route | As noted above, our techniques have already been implemented by independent teams in hardware experiments using state-of-the-art IBM devices and neutral atom processors [arXiv:2510.25640; arXiv:2601.13881; Nature Physics (21) 289-297 (2025)]. Furthermore, we are working closely with quantum companies, e.g., Quantum Motion and IBM, so that our techniques have direct relevance in practical applications and we aim to accelerate their adoption by working closely with end users, e.g., Boehringer Ingelheim and Moderna, |
| Sectors | Aerospace Defence and Marine Chemicals Digital/Communication/Information Technologies (including Software) Financial Services and Management Consultancy Manufacturing including Industrial Biotechology Pharmaceuticals and Medical Biotechnology |
| Description | 1. Building a world-leading research group Since applying for the FLF, BK has secured a permanent position at the Mathematical Institute and has begun building his research group. The award has been particularly valuable, enabling the hiring of two highly talented and promising early-career researcher PDRAs funded through the grant. Group development has progressed extremely well; in the meantime, a third postdoctoral researcher has joined on a personal fellowship, alongside several DPhil students. The group now comprises 13 members (https://www.maths.ox.ac.uk/groups/mathematical-physics/research-areas/quantum-computation-and-cryptography). The group has also been highly successful in securing further funding. We attract extremely strong DPhil applicants who have been very successful in obtaining departmental and university-level scholarships. In addition, several DPhil students are supported by industrial partners, including Quantum Motion, Moderna, and Thales. While the initial FLF application was ambitious in terms of group building, progress to date has exceeded expectations. Finally, BK has played a key role in establishing the new MSc in Quantum Technologies course in Oxford and he is currently a member of it's supervisory committee. BK is also a member of the Mathematical and Theoretical Physics MSc Supervisory Committee. ______________________________________________________ 2. Influencing the research community and beyond BK, working together with Prof Simon Benjamin, established and consolidated a new conference series, Seeking Quantum Advantage (SEEQA) (https://conference.seeqa.org/). Support from the FLF award contributed significantly to the success of these events. The second meeting in the series was held in August 2025 and sold out within a week of ticket release-well before the registration deadline. Beyond the scientific programme-which brings established leaders and outstanding early-career researchers to Oxford for invited talks-SEEQA has featured high-level panel discussions, and in 2025 included a formal debate in the Oxford Union Debate Chamber with the proposition: "This house believes that quantum computers will have a greater impact on our lives than conventional ones." These community-facing discussions have been extremely highly rated and have helped motivate and shape research directions in the field, including our paper "Myths around quantum computation before full fault tolerance" (arXiv:2501.05694). Recognising the increasing importance of early fault-tolerant quantum computation, BK also established a new special collection at npj Quantum Information (a leading journal in the field) titled "Algorithms, Protocols and Architectures for Early Fault Tolerance" (https://www.nature.com/collections/icffgjdggg). In addition, BK is currently the lead organiser of QCTiP (https://qctipconf.github.io/), which will be held in Oxford for the first time and focuses on practical aspects of quantum computing. The event's relevance to the University's strategic priorities is endorsed by Prof Ian Walmsley, Director of the Oxford Quantum Institute (https://www.oqi.ox.ac.uk/home). ______________________________________________________ 3. Team member career development 3 A. Balint Koczor (BK) during the period supported by the FLF award has: - Co-authored 13 journal publications and 7 additional arXiv preprints currently under review. - Advanced research that brings practical quantum computing closer to reality, including the following contributions: - Novel quantum algorithms spanning near-term, early fault-tolerant, and fully fault-tolerant regimes. - New quantum error mitigation techniques and detailed analyses of their efficacy. - Resource estimates for performing practical tasks in early fault tolerance. - Played a key role in two grant applications (currently under review), and is working with colleagues on a major grant proposal involving a large number of business partners. 3. B. Abhishek Rajput (AR) has developed a growing international collaboration network, including partners at INRIA (Paris) and colleagues in Australia (Iceberg and the University of Sydney). He is also initiating early-stage collaborations with researchers at Caltech and the Polish Academy of Sciences. In addition, he has engaged with industry through part-time contracting work with Xanadu. His research applies tools from pure mathematics-especially homological algebra-to the design and systematic search for practical code instances, and to understanding how decoding properties (e.g., decoding radius and threshold) transfer between codes with specific homological relationships. This line of work aims to: - Bring qLDPC codes closer to practical deployment by substantially lowering the overhead associated with quantum error correction (QEC). - Advance the theory of decoding algorithms by mapping difficult decoding problems for certain codes to simpler related variants. A key focus is the bivariate bicycle (BB) family of quantum LDPC codes, which are widely studied due to high encoding rates and distances, and an error threshold comparable to the surface code. Despite this, there has been limited progress in constructing well-understood families of BB codes and in establishing how their properties vary across instances. AR's recent work shows that one can generate infinite sequences of new BB codes from a seed BB code via covering graphs. This construction enables bounds on the behaviour of code parameters across the sequence and allows lifting/projecting logical operators and automorphisms between related codes. Practically, this simplifies the analysis of BB code properties in terms of smaller "seed" codes and supports more informed choices of code instances for implementation. 3. C. Armands Strikis (AS) developed a new framework for designing high-performance syndrome extraction circuits applicable to many practical quantum error-correcting codes. This work accelerates progress towards fault-tolerant quantum computing by reducing the required space and time overheads, thereby improving the feasibility of near- to mid-term implementations. AS and BK have also co-authored a major publication [PRX Quantum 7, 010339] in collaboration with Quantum Motion -- this work develops a novel architecture in silicon quantum devices to engineer early fault tolerant quantum computers. |
| First Year Of Impact | 2025 |
| Sector | Other |
| Impact Types | Economic |
| Description | Collaboration with IBM Quantum and UCL |
| Organisation | IBM |
| Country | United States |
| Sector | Private |
| PI Contribution | Armands Strikis (a member of the research team) initiated a multi-year academic research project on practical quantum computing, to which he is currently the primary researcher. |
| Collaborator Contribution | Researchers from IBM Quantum and UCL contributed to the project by researching selected topics and sharing their expertise. |
| Impact | The initial output of this project is a pre-print https://arxiv.org/abs/2603.05481, focusing on the implementation of quantum error-correcting codes. The nature of the work is inherently interdisciplinary, involving computer science, mathematics, and physics. |
| Start Year | 2024 |
| Description | Collaboration with IBM Quantum and UCL |
| Organisation | University College London |
| Country | United Kingdom |
| Sector | Academic/University |
| PI Contribution | Armands Strikis (a member of the research team) initiated a multi-year academic research project on practical quantum computing, to which he is currently the primary researcher. |
| Collaborator Contribution | Researchers from IBM Quantum and UCL contributed to the project by researching selected topics and sharing their expertise. |
| Impact | The initial output of this project is a pre-print https://arxiv.org/abs/2603.05481, focusing on the implementation of quantum error-correcting codes. The nature of the work is inherently interdisciplinary, involving computer science, mathematics, and physics. |
| Start Year | 2024 |
| Description | Collaboration with Moderna |
| Organisation | Moderna |
| Country | United States |
| Sector | Private |
| PI Contribution | Together with Quantum Motion and Moderna we decided to collaborate on developing quantum algorithms for mRNA folding. These two companies are jointly funding a fully funded international studentship for Jona Erle who is based in my group. |
| Collaborator Contribution | Quantum Motion and Moderna jointly fund a fully funded international DPhil studentship in the Mathematical Institute in Oxford |
| Impact | This research is highly interdisciplinary: the aim is to develop quantum algorithms to predict mRNA folding and for designing optimal mRNA sequences at Moderna. The research stretches over multiple disciplines, including mathematics, computer science, quantum physics, biology, bio engineering etc. Jona Erle, the DPhil student funded by this project started in October 2025 but has already finished a very exciting manuscript in collaboration with Moderna and Quantum Motion: https://arxiv.org/pdf/2602.17615 |
| Start Year | 2025 |
| Description | Collaboration with Quantum Motion on quantum algorithms |
| Organisation | Quantum Motion Technologies Ltd |
| Country | United Kingdom |
| Sector | Private |
| PI Contribution | I am supervising a DPhil student, Po-Wei Huang, who is fully funded by an EPSRC CASE award: https://gtr.ukri.org/projects?ref=studentship-2929079 |
| Collaborator Contribution | Quantum Motion funds the industrial contribution to this CASE award. |
| Impact | Quantum Motion co-funds Po-Wei's studentship who is focusing on quantum algorithm development. Last year he collaborated with Quantum Motion, Boehringer Ingelheim (a major German pharmaceutical company) and with the University of Toronto that resulted in the major publication: https://arxiv.org/pdf/2508.16719 This work is highly interdisciplinary as it develops a new quantum algorithm for molecular dynamics simulation. Therefore, the work is at the intersection of mathematics, computer science, quantum physics, quantum chemistry and thermodynamics Further outputs of Po-Wei Huang include: https://arxiv.org/pdf/2510.07195 |
| Start Year | 2024 |
| Description | Collaboration with Thales |
| Organisation | Thales Group |
| Department | Thales UK Limited |
| Country | United Kingdom |
| Sector | Private |
| PI Contribution | I co-supervise a DPhil student, Oscar Scholin, who is co-funded by Thales via an EPSRC CASE award. |
| Collaborator Contribution | Thales co-fund a studentship project that focuses on quantum algorithms for image processing. |
| Impact | The studentship project started relatively recently in October 2025 and the student, Oscar Scholin, has made impressive progress, however, has not yet released a preprint or publication. |
| Start Year | 2025 |
| Description | Collaboration with University of Osaka |
| Organisation | Osaka University |
| Country | Japan |
| Sector | Academic/University |
| PI Contribution | I was hosting Dr Chusei Kiumi from Osaka University and supervised his project which resulted in the publication [Quantum Science and Technology 10 (4), 045071, https://iopscience.iop.org/article/10.1088/2058-9565/ae1160/meta]. |
| Collaborator Contribution | Dr Chusei Kiumi's travel and living expenses for the duration of his stay were fully covered by a grant in Japan. |
| Impact | The collaboration resulted in the publication https://iopscience.iop.org/article/10.1088/2058-9565/ae1160/meta and the preprint: https://arxiv.org/pdf/2601.13881 |
| Start Year | 2024 |