The Grand Challenge of Quantum Applications

Abstract

This perspective outlines promising pathways and critical obstacles on the road to developing useful quantum computing applications, drawing on insights from the Google Quantum AI team. We propose a five-stage framework for this process, spanning from theoretical explorations of quantum advantage to the practicalities of compilation and resource estimation. For each stage, we discuss key trends, milestones, and inherent scientific and sociological impediments. We argue that two central stages -- identifying concrete problem instances expected to exhibit quantum advantage, and connecting such problems to real-world use cases -- represent essential and currently under-resourced challenges. Throughout, we touch upon related topics, including the promise of generative artificial intelligence for aspects of this research, criteria for compelling demonstrations of quantum advantage, and the future of compilation as we enter the era of early fault-tolerant quantum computing.

Figures (2)

• Figure 1: The stages of quantum application development. This framework is a conceptual model of application research maturity and progression is not always linear. Some seminal works, like Shor's factoring algorithm, addressed multiple stages at once (I, II, and III), while other research paths may skip stages entirely. For example, research into "tests of quantumness" often focuses on minimizing resource requirements tasks with quantum advantage irrespective of practical applications. Ultimately, this framework serves to categorize research and identify the key bottlenecks on the path to realizing practical quantum applications.
• Figure 2: These figures illustrate that Stage IV research has reduced the resources required to solve important problems by many orders of magnitude over the last decade as function of publication year in both space such as for breaking 2048 bit RSA encryption (left), and time as approximated by the Toffoli count estimating the ground state energy of FeMoco to chemical accuracy for "small" $54$-orbital Reiher2017Elucidating and "large" $76$-orbital active spaces Li2019Electronic (right). The left plot includes Refs. jones2012layeredfowler2012surfaceo2017quantumgheorghiu2019benchmarkingGidney2025Factoring and the right plot includes Refs. Reiher2017ElucidatingLee2020hypercontractionvonBurg2021Quantumrocca2024reducingLow2025Fast.