Accelerating Simulation by Quantum Computing

Conventional HPC algorithms are usually optimized for the specific hardware (including GPUs, FPGAs, etc.), i.e., they avoid operations that run inefficiently on the respective hardware or explicitly prefer algorithmic components that exploit the hardware in an optimal way. Quantum computing is disruptive in this context because it completely changes the list of standard (e.g., linear algebra) operations that should or should not be used. Eigenvalue problems, binary optimization problems, training of neural networks, and some np-hard problems are solvable with unprecedented speed or accuracy on (future) quantum systems. These insights can fundamentally challenge best practices in higher-level algorithm design such as solvers for partial differential equations.

The scientific challenge is to decide which algorithms are good candidates for acceleration by exchanging sub-components and offloading them to quantum systems, and even beyond this: For which problems completely new algorithms would have to be designed to be able to exploit the potential of quantum computing, or hybrid quantum-conventional computing?

Currently, the power of quantum computing is still limited in terms of the maximal problem size and the number of subsequent operations due to the inherently noisy operations. However, these limitations have to be seen in the light of an enormous speed of growth in terms of the system size (qubits) of quantum computers. This growth allows for both larger problems and noise reduction by redundancy. Thus, we expect a similar development as for GPUs and other accelerator hardware in the past two decades that were first used for very specific algorithmic components instead of the entire simulation codes. The difference for quantum computing might be the much more disruptive nature of hardware properties.

RQ 1: How can we best exploit heterogeneous systems including quantum computers as ‘accelerators’?
For example, PDE solvers and machine learning can be accelerated, but how do we have to design heterogeneous algorithms and problem formulations to exploit the QC components?

RQ 2: How can we detect which problem classes and subproblems are promising candidates for quantum acceleration?
For example: How can the inherent noise of operations on quantum systems not only be reduced by hardware improvements but may be exploited for stochastic problems?

RQ 3: Which components of traditional simulation problems can be replaced by algorithms running more efficiently on quantum systems?