Quantum computing holds great promise for simulating complex quantum many-body systems. This was identified already by Feynman in his 1982 speech at the very beginning of quantum computing as a research field. It remains the most promising application of quantum computing, both near-term and longer-term. The huge potential for large-scale quantum computers to address concrete problems in materials modelling, condensed matter physics and quantum chemistry that are beyond the reach of accurate simulation on classical computers has been mapped out in the decades since. Sophisticated quantum algorithms -- both rigorous and heuristic -- have been developed over the past two decades to address many of the most important fundamental quantum simulation tasks: time-dynamics simulation, ground state problems, spectral estimation and sampling from thermal states. However, there is a very large gap between the resources required to apply these algorithms to real simulation tasks of interest in research and in industry, and the resources available on current or foreseeable quantum computing hardware. For example, recent estimates of the resources required to simulate Strontium Vanadate (an important electron-transfer material used for a range of applications including battery technology and next generation solar cells) using the standard state-of-the-art algorithms require in excess of 800 qubits and circuit depths on the order of 10^8\. Whereas the largest quantum hardware platforms currently available have on the order of 100 qubits and are limited by noise to circuit depths on the order of 1000\. The overarching goal of this project is to bridge this gap and make the next significant advance in quantum simulation of many-body systems by combining the development of new theory approaches for the description and representation of said systems with new application-specific and hardware-specific algorithm design and optimisation techniques. With this project, we bring together 5 of the leading teams in Europe from industry and academia to deliver this: with expertise spanning from underpinning theory, through quantum algorithm and software, to quantum hardware design we are uniquely positioned to advance all three of these pathways in a coordinated way, which will enable us to make the most of the synergies between the three approaches.

Nowadays, most people and businesses rely on a regular and reliable supply of energy for their day-to-day activities, making the energy grid a critical infrastructure for the country. Building and maintaining grid connections is a costly exercise: building an electric grid can cost up to £1.5m per km of line - costs that are ultimately borne by either the taxpayer or the energy consumer. Being able to determine the optimal parameters for the network's infrastructure can therefore lead to significant cost savings, as well as potentially improving the network's resilience against vulnerabilities such as extreme weather events. The move towards Net Zero is also affecting the requirements on the power grid. Where once the network only needed to focus on a small number of generators with similar performance characteristics, it is now required to connect millions of smaller renewable generators, whose energy output is highly variable and often unpredictable. The increased complexity of the system translates into an exponential increase in the running time of the algorithms that have been traditionally used to optimise the grid, making them effectively no longer fit for purpose. It has long been suggested, though, that quantum computing has the potential to answer these sort of optimisation questions more efficiently than classical computers. Until recently, this was only believed possible in the longer term (requiring full-scale quantum hardware) but recent innovations by Phasecraft have changed this perspective, showing that even in the near term (when quantum computers are expected to be small-scale and noisy) there is the potential for quantum algorithms to outperform classical ones. Building on the first Phase of this project, we will continue to work with the SuperGen Energy Networks Hub and the Department for Energy Security and Net Zero to develop a quantum software solution to this problem, initially addressing proof-of-principle instances. This will ultimately facilitate future network planning and accelerate the deployment of renewables (both key goals within the _Powering Up Britain_ strategy published earlier in 2023).

Nowadays, most people and businesses rely on a regular and reliable supply of energy for their day-to-day activities, making the energy grid a critical infrastructure for the country. Building and maintaining grid connections is a costly exercise: building an electric grid can cost up to £1.5m per km of line - costs that are ultimately borne by either the taxpayer or the energy consumer. Being able to determine the optimal layout for the network's infrastructure can therefore lead to significant cost savings, as well as potentially improving the network's resilience against vulnerabilities such as extreme weather events. The move towards Net Zero is also affecting the requirements on the power grid. Where once the network only needed to focus on a small number of generators with similar performance characteristics, it is now required to connect millions of smaller renewable generators, whose energy output is highly variable and often unpredictable. The increased complexity of the system translates into an exponential increase in the running time of the algorithms that have been traditionally used to determine the grid's layout, making them effectively no longer fit for purpose. It has long been suggested, though, that quantum computing has the potential to answer these sort of optimisation questions more efficiently than classical computers. Until recently, this was only believed possible in the longer term (requiring full-scale quantum hardware) but recent innovations by Phasecraft have changed this perspective, showing that even in the near term (when quantum computers are expected to be small-scale and noisy) there is the potential for quantum algorithms to outperform classical ones. With this project, we will work with the Department for Energy Security and Net Zero to identify the priority questions related to network planning and optimisation, and we will then build a quantum software solution to these problems. This will facilitate future network planning and accelerate the deployment of renewables (both key goals within the _Powering Up Britain_ strategy published earlier in 2023).

Quantum computers are expected to be able to solve hard computational challenges that are beyond the reach of our best standard supercomputers. After many years of research in both academia and industry, quantum computers are at the point of outperforming their standard ("classical") counterparts in certain specialised problems. One of the most exciting and plausible applications for near-term quantum computers is modelling quantum-mechanical systems. Understanding such systems is essential for many practical applications, ranging from the design of more efficient catalysts and solar panels to the development of novel drugs. However, exact modelling of a quantum system using a classical computer rapidly becomes infeasible as the system size increases. Quantum computers could overcome this limit and enable us to model currently inaccessible physical systems. Although there have been many years of theoretical work on quantum algorithms for this modelling task, standard algorithms for these applications require quantum hardware that is still decades away. Quantum software startup Phasecraft's goal is to maximise the potential of near-term quantum technologies for real world application. To achieve this, it has adopted a new approach to quantum algorithm development that has led to results so significant as to bring applications of quantum computing to materials modelling into the near-term quantum computing realm. These breakthroughs are already integrated into a quantum software demonstrator. The focus of this feasibility study is to make the next advance in quantum simulation algorithms, beyond even these ground-breaking recent results. This next step requires tight integration between quantum algorithm design, quantum hardware design and the specific applications in catalyst modelling. As well as their significant industrial importance, catalysts also represent the next challenge for quantum computation beyond crystalline materials, as it requires simulation of both structured crystalline materials and less structure molecules. The goal of the project is show how quantum simulation of this type of system can be made feasible on near-term quantum hardware, run proof-of-principle demonstrations on Oxford Ionics' ion trap quantum hardware and QuERA's cold atom hardware (accessed through AWS), and integrate the new algorithms into Phasecraft's quantum software. Our consortium includes world-renowned experts in quantum software and algorithms (Phasecraft), catalyst research (UCL), ion trap quantum hardware (Oxford Ionics), and commercial materials development (Johnson Matthey). Only this combination of expertise will be able to deliver on this ambitious goal.

The 'Powering Up Britain' action plan launched in early 2023 by the UK government builds on the net zero strategy and sets clear directions for the country's green energy transition. Increased use of renewable energies sources and better energy storage capacities feature prominently in the action plan as key mechanisms to deliver Net Zero. However at the current state of the art, the technologies underpinning this transition (from wind turbines to solar panels and batteries for electric vehicles) are all heavily reliant on a small number of so-called 'critical materials' (typically only produced by a small number of countries and in limited supply). This poses a risk in terms of both availability and affordability, which could potentially compromise the successful transition to a low-carbon economy. Research into the discovery of new materials and the characterisation of known ones goes back many decades, and has enabled the development of ground-breaking technologies such as solar cells (first developed in the 1880s based on knowledge of selenium and then improved in the 1950s with the understanding of the properties of silicon). In recent years, though, the technical requirements for materials modelling have become much more stringent, making many of the existing computational tools unable to satisfy the users' requirements. Therefore, materials discovery has become an extremely challenging and costly exercise, relying on a combination of inaccurate modelling and expensive experiments. Through work undertaken in previous projects, Phasecraft has shown that quantum computers could change this paradigm drastically, and that this could be done in the near term (when quantum computers are expected to be small-scale and noisy). Indeed, through the use of proprietary quantum computational techniques and algorithms, Phasecraft has demonstrated how to characterise faster and with (much) greater accuracy materials of interest to industry. Past work from Phasecraft has focused on selected classes of materials. But Phasecraft's underlying algorithms and quantum software pipeline are readily adaptable to broader classes of materials relevant to the energy sector. The nature of the challenges in the classical simulation is similar across many energy materials, hence the significance of quantum simulation's ability to transform the materials discovery process in this sector. This could ultimately lead to the identification of new materials, or the revisiting of materials that have been overlooked due to approximations made within classical simulation, thus playing an important role in delivering the materials improvements needed to deliver energy security and net zero.

The 'Powering Up Britain' action plan launched in early 2023 by the UK government builds on the net zero strategy and sets clear directions for the country's green energy transition. Increased use of renewable energies sources and better energy storage capacities feature prominently in the action plan as key mechanisms to deliver Net Zero. However at the current state of the art, the technologies underpinning this transition (from wind turbines to solar panels and batteries for electric vehicles) are all heavily reliant on a small number of so-called 'critical materials' (typically only produced by a small number of countries and in limited supply). This poses a risk in terms of both availability and affordability, which could potentially compromise the successful transition to a low-carbon economy. Research into the discovery of new materials and the characterisation of known ones goes back many decades, and has enabled the development of ground-breaking technologies such as solar cells (first developed in the 1880s based on knowledge of selenium and then improved in the 1950s with the understanding of the properties of silicon). In recent years, though, the technical requirements for materials modelling have become much more stringent, making many of the existing computational tools unable to satisfy the users' requirements. Therefore, materials discovery has become an extremely challenging and costly exercise, relying on a combination of inaccurate modelling and expensive experiments. Through work undertaken in previous projects, Phasecraft has shown that quantum computers could change this paradigm drastically, and that this could be done in the near term (when quantum computers are expected to be small-scale and noisy). Indeed, through the use of proprietary quantum computational techniques and algorithms, Phasecraft has demonstrated how to characterise faster and with (much) greater accuracy materials of interest to industry. Past work from Phasecraft has focused on selected classes of materials. But Phasecraft's underlying algorithms and quantum software pipeline are readily adaptable to broader classes of materials relevant to the energy sector. The nature of the challenges in the classical simulation is similar across many energy materials, hence the significance of quantum simulation's ability to transform the materials discovery process in this sector. This could ultimately lead to the identification of new materials, or the revisiting of materials that have been overlooked due to approximations made within classical simulation, thus playing an important role in delivering the materials improvements needed to deliver energy security and net zero.

Nowadays, most people and businesses rely on a regular and reliable supply of energy for their day-to-day activities, making the energy grid a critical infrastructure for the country. Building and maintaining grid connections is a costly exercise: building an electric grid can cost up to £1.5m per km of line - costs that are ultimately borne by either the taxpayer or the energy consumer. Being able to determine the optimal layout for the network's infrastructure can therefore lead to significant cost savings, as well as potentially improving the network's resilience against vulnerabilities such as extreme weather events. The move towards Net Zero is also affecting the requirements on the power grid. Where once the network only needed to focus on a small number of generators with similar performance characteristics, it is now required to connect millions of smaller renewable generators, whose energy output is highly variable and often unpredictable. The increased complexity of the system translates into an exponential increase in the running time of the algorithms that have been traditionally used to determine the grid's layout, making them effectively no longer fit for purpose. It has long been suggested, though, that quantum computing has the potential to answer these sort of optimisation questions more efficiently than classical computers. Until recently, this was only believed possible in the longer term (requiring full-scale quantum hardware) but recent innovations by Phasecraft have changed this perspective, showing that even in the near term (when quantum computers are expected to be small-scale and noisy) there is the potential for quantum algorithms to outperform classical ones. With this project, we will work with the Department for Energy Security and Net Zero to identify the priority questions related to network planning and optimisation, and we will then build a quantum software solution to these problems. This will facilitate future network planning and accelerate the deployment of renewables (both key goals within the _Powering Up Britain_ strategy published earlier in 2023).

Accurate simulation of complex materials yields useful insights, guiding experimental efforts and technological advancements. In photovoltaic applications, these can help to increase solar cell efficiency, their durability and manufacturability, key challenges in the industry. Designing novel materials for clean energy use, or even gaining a full understanding of existing materials, is currently a major challenge due to the necessity of taking quantum effects into account. Standard modelling techniques are unable to solve the required problems with sufficient speed and/or accuracy, implying that costly experiments in the lab are often needed in order to characterise the properties of materials. Quantum computers can natively represent quantum-mechanical systems and could efficiently solve materials modelling problems that are beyond the reach of today's best supercomputers. This could enable "in quanto" materials design and selection, where many materials are screened for their properties without needing to perform experiments. After many years of development of quantum computing technology, quantum computers have outperformed the world's fastest supercomputers for certain targeted problems. Nevertheless, the capabilities of current quantum computers are insufficient to enable standard quantum simulation algorithms to be run, and therefore the development of targeted quantum software is critical to harness the potential of existing quantum technologies. In this project we will develop efficient quantum algorithms and software to solve modelling problems in photovoltaics. Our algorithms will be targeted at specific use-cases developed in collaboration with end-users, while being sufficiently general to address other materials modelling challenges. Based on our encouraging previous results, we expect to find significant improvements on previously known algorithmic complexities, reducing the resources required to simulate quantum systems, and bringing the solution of previously unfeasible problems into reach.We will implement our quantum software on a leading quantum hardware platform, and will evaluate it against the requirements of our expert end-users Oxford PV, and also against the results of classical simulation performed by UCL. Our results will enable the development of a roadmap for future exploitation and will open the door to quantum computing solving hard materials modelling challenges beyond the capability of standard methods.

Optimisation and constraint satisfaction problems are ubiquitous in industry, ranging from straightforward tasks such as arranging a timetable to exceptionally challenging ones such as laying out a telecommunications network or a high-performance integrated circuit. Problems like this are associated with the need to search over exponentially many potential solutions to find the best possible solution. Finding better solutions to optimisation problems could enable outcomes as diverse as reducing shipping costs for package deliveries and increasing the capacity of cellular networks. Yet these problems remain exceptionally challenging for standard computers, despite many years of effort from theorists and practitioners. It has been known since the 1990s that quantum computers could solve optimisation problems significantly more quickly than standard computers. For example, Grover's famous quantum search algorithm can solve optimisation problems with a runtime that scales like the square root of the runtime of classical unstructured search. However, this approach and others for solving optimisation problems are suitable only for long-term, fault-tolerant quantum computing, raising the question of whether quantum computers can be applied to optimisation problems in the near future, enabling them to unlock the associated value. In this project we will determine the potential for near-term gate-model quantum computing to solve optimisation problems. Project partner BT will identify problems, in particular in the domain of telecoms network optimisation, that are particularly suited to being solved by quantum computers. Project partner Phasecraft will design and implement quantum algorithms for these and related problems, which will be executed and evaluated on cutting-edge quantum hardware developed by project partner Rigetti. Commercial feasibility of the results of the project will be evaluated by comparing against leading classical approaches for solving optimisation problems. Our work will build on the results of a previous InnovateUK funded feasibility study, which explored the potential for fault-tolerant quantum computers to solve optimisation problems relevant to telecom networks in the long term, but did not implement near-term algorithms on real hardware. We will hold an innovation workshop targeted at leading organisations for whom optimisation problems are relevant to their businesses, to determine which problems are the most promising to be addressed by quantum computing and to present the results of the project. We expect that the project will deliver a quantum solution for solving optimisation problems, demonstrated on real quantum hardware, as well as a clear roadmap for applicability to real-world problems.

Quantum computers harness the strange features of quantum mechanical systems in order to solve computational problems that cannot be solved using current (classical) computing technology. The most well-known task where quantum computers outperform classical computers is factoring large numbers, which can be used for breaking encryption. Quantum computers also naturally excel at simulating quantum systems, a notoriously difficult computational problem that has applications in materials science and drug design. The potential of quantum computers has attracted investments from technology giants including Google, IBM and Amazon, as well as from national governments and venture capitalists. Quantum technology has matured to the point where researchers now have excellent control over the elementary building blocks of a quantum computer: quantum bits (qubits). Unfortunately, state-of-the-art quantum processors still suffer from errors caused by unwanted interaction of the fragile qubits with their environment. In our project, we are developing robust implementations of quantum algorithms that can run successfully on today's error-prone quantum processors. Our project unites experts in industry and academia with extensive experience in quantum computing research. The industrial partners are PhaseCraft, a quantum software start-up based in London (UK), and Quantum Benchmark, a quantum software start-up based in Kitchener (Canada). PhaseCraft has world-leading expertise in designing error-resilient algorithms for near-term quantum computing hardware. Quantum Benchmark is the leading provider of software tools for characterizing the errors that occur in different quantum processors, delivering a deep understanding of the capabilities and limitations of different quantum processors. The academic partners are the University of Waterloo, University College London, and Perimeter Institute for Theoretical Physics. All three are leading quantum computing research centres, with particular strength in the fields of quantum error correction and fault-tolerant quantum computing. Together, our work will hasten the demonstration of quantum advantage for industrially relevant problems such as the simulation of quantum systems, thereby realizing the potential of quantum computing.

Rigetti Computing, Oxford Instruments, Standard Chartered, Phasecraft, and the University of Edinburgh will collaborate to advance quantum computing in the UK. The team will address several key aspects of quantum computing including: 1) hardware, infrastructure, and supply chain; 2) accelerating industrial applications; and 3) developing the quantum ecosystem to help solve important but currently intractable problems. This work positions the UK as a global leader in the emerging quantum industry, expected to be £4B by 2024, growing to £350B/year by 2050\. The project's main focus area are: _**1\. Infrastructure deployment**_ Rigetti will leverage its London-based team to assemble and operate a quantum computer in the UK, accessible via the cloud. This new investment into the UK's growing technology sector is an important milestone---no commercially available quantum computing platform currently exists in the UK. To support the infrastructure, Oxford Instruments will mature cryogenic technology reliability and provide initial hosting. To maximise long-term value, the team will migrate the infrastructure to align with national strategic initiatives such as the UK National Quantum Computing Centre. _**2\. Core applications development**_ Building on the infrastructure, the applications development team will validate the value of quantum computing to end users in the UK's economy. The approach builds on academic research and industry-led quantum software capability in the UK to transition knowledge to economic value. Phasecraft, a UK quantum software start-up, will build a quantum simulation work package that brings quantum computing to end users in the most promising near-term application area---quantum chemistry. Phasecraft is a UK quantum software start-up, founded by quantum computing researchers Toby Cubitt, Ashley Montanaro, and John Morton. From the University of Edinburgh, Professor Elham Kashefi's group will deliver quantum hardware verification and testing, with a focus on machine learning applications. They will also collaborate with Standard Chartered, complementing their work on financial synthetic data generation (Kondratyev & Schwarz, "The Market Generator"). _**3\. Broad initiatives to grow the UK's quantum computing sector**_ To demonstrate value beyond this project, the consortium will develop the UK's nascent quantum ecosystem to extend industry capabilities in finance, energy, pharmaceuticals, aerospace, and automotive. Through existing relationships and forums, the consortium will expand the community by delivering workshops, computing credits, and technical support, helping end users to validate their research and business concepts.

Quantum computers are expected to be able to solve hard computational challenges that are beyond the reach of our best standard supercomputers. After many years of research in both academia and industry, quantum computers are at the point of outperforming their standard ("classical") counterparts in certain specialised problems. One of the most exciting and plausible applications for near-term quantum computers is modelling quantum-mechanical systems. Understanding such systems is essential for many practical applications, ranging from the design of more efficient catalysts and solar panels to the development of novel drugs.However, exact modelling of a quantum system using a classical computer rapidly becomes infeasible as the system size increases. Quantum computers could overcome this limit and enable us to model currently inaccessible physical systems. Although there have been many years of theoretical work on quantum algorithms for this modelling task, there remain significant challenges associated with applying these results to practically-relevant problems, and with calculating their complexity.Here our focus will be on modelling problems relating to battery materials. Batteries are essential in many areas of technology, especially for sustainable energy applications, yet modelling their behaviour on a quantum-mechanical level is a daunting challenge for classical methods. This area has been proposed as a likely and important target for quantum algorithms to address, yet little is currently known about whether quantum computing techniques will truly outperform the best classical approaches.We will develop quantum software that demonstrates how to solve battery materials modelling problems of direct relevance to practitioners, and will benchmark these results against leading practical methods. Our consortium includes experts in quantum software (PhaseCraft), computational materials design (UCL) and commercial battery materials (Johnson Matthey). We will bring together these areas to determine the feasibility of quantum computing for battery material design, and will develop roadmaps that will determine the requirements on quantum computing for their potential to be achieved. A key deliverable of the project will be a demonstrator suitable for integration within an end-user workflow. This project aims to open the door to some of the first commercially relevant applications of quantum computing beyond the classically emulable regime.