Exploration of the timeliness and value of Quantum Algorithms

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There has been substantial recent progress in developing hardware for quantum computing (QC). A major challenge now is to develop algorithms that open applications of this hardware for real-world end-user applications. This is true both when we consider future quantum computing devices (e.g., large-scale, fault-tolerant systems), and also when we ask what is possible with hardware available in the next 5-10 years. This project will involve the development of quantum algorithms for partial differential equations, especially computational fluid dynamics. We will work in direct collaboration with scientists from AWE to test novel algorithms we develop for classes of relevant problems, and benchmark them against existing classical computing methods.One of the most important current challenges is that algorithms used on existing HPC infrastructure cannot be used directly on a quantum computer. Instead, choosing the tasks relevant to the programme we must design algorithms that take advantage of the unique operating mechanisms of QC. Broadly seen, there are two approaches to developing applications for quantum computers:1) Software for large-scale, fault tolerant devices. Here, the algorithm design is hardware-agnostic. It can be proven that these machines will have an advantage over classical HPC, at least for certain classes of linear differential equation. However, the timescale for development of this hardware might be 10-15 years away, or longer for large-scale implementation of linear equations2) Software for near-term machines, which takes advantage of specific properties of the hardware implementations. These special-purpose machines come in several distinct forms, referred to in the literature as Quantum Simulators, Quantum Annealers, or Noisy Intermediate-Scale Quantum (NISQ) computers. Proof of advantage tends to be heuristic. But they offer the potential for impact on a much shorter scale (within the next 5-10 years). In addition, the heuristic algorithms that are demonstrated can sometimes be run on classical hardware, offering a quantum-inspired speedup over existing classical algorithms. A good example has been the development of new algorithms for logistics optimization (e.g., of routing and traffic flows).We aim to explore each of these approaches for developing quantum software to solve specific classes of partial differential equations. We will identify the most promising way, and also whether near-term gains might be achieved by developing quantum-inspired classical algorithms.The specific objectives of this project are to- Identify problems that have the potential to be solved with a speed-up on a quantum computer- Develop algorithms to solve these problems with QC in the near or long term, while also testing quantum-inspired classical algorithms for these problems- Compare the computational cost to existing (classical) methods, looking to identify the potential for a quantum advantage - Identify the most promising algorithms and scope on what timescales quantum computing is likely to have an impact on the corresponding area.The student will be directly involved in developing quantum algorithms, and developing classical simulations of their implementations, as well as implementations of quantum-inspired classical algorithms.