The extensive research required to uncover useful quantum computing applications can be divided into five main stages, and an idea typically goes through all of them on its way to real-world impact.
Phase I – Discovery: A new abstract quantum algorithm – such as Simon’s algorithm for finding hidden patterns, Grover’s algorithm for unstructured search or the quantum phase estimation algorithm – is discovered and analyzed. These algorithms can theoretically tackle problems faster than classical methods and provide fundamental results in a given field, but their direct practical applicability is often uncertain or limited at this early stage. This work is often built on the most basic, foundational research into the functions and limitations of quantum computing (stage 0).
Phase II – Find the right problem cases: This phase focuses on finding and characterizing concrete, verifiable problem cases where a quantum algorithm shows a true advantage over all known classical methods. For example, solving an abstract Phase I problem such as “finding a molecule’s lowest energy state” requires identifying specific molecules (the “problem instances”) for which a quantum computer will provide an advantage. This can be challenging because many instances of real-world problems can often be solved by classical computers. The quantum advantage can only be guaranteed in the most complex cases, and classically hard cases can be difficult to identify. The quantum algorithm must successfully compete against a wide range of constantly improving classical approaches to pass this stage.
Step III – Establishing Real-World Benefits: This is the “so what?” stage. After characterizing problem instances that we can solve better than classical ones, this phase asks if these instances connect with specific, the real world utility cases. For example, how does simulating particular molecules that we know are classically challenging (the stage II “problem instances”) create value for drug discovery? The first common problem at this stage is that the devil is in the details, and it is often challenging to find real-world use cases that fit the criteria for quantum advantage identified in Phase II. There is also a knowledge gap for both quantum and application domain experts. For example, quantum algorithms often do not know the fine details of an application area such as battery chemistry, and battery engineers do not know the fine print of quantum algorithms.
Stage IV – Engineering for Use: Once we have a real-world problem instance with quantum advantage, we need to understand how much it will actually cost computationally. This phase is where we do practical optimization, multiple layers of compilation and resource estimation for a specific use case. Key questions here include: how many qubits and gates? How long should the algorithm run? For fault-tolerant quantum computing cases (ie, cases that use quantum error correction), step IV also involves mapping how this error correction will be implemented.