Marin Ivezic
Two proposals reach the same investment committee in one quarter. The first asks for a pilot applying quantum optimization to fleet routing. The second asks for funding to build a quantum-ready screening workflow for industrial catalysts. Both cite a speedup, both name a hardware partner, and both quote the same market forecast.
Only one of them has published evidence behind it. Sorting the two apart doesn’t require a physics background and doesn’t require waiting for the hardware. It requires three questions, asked in a fixed order.
Reading a quantum claim in three steps
The speedup class
Every serious quantum claim rests on an algorithm, and every algorithm belongs to a speedup class. A quadratic speedup cuts the number of steps to roughly the square root of the classical count, so a search across a million items drops to about a thousand operations. Grover’s algorithm, the general-purpose quantum search routine, is the standard example. An exponential speedup differs in kind: the classical cost doubles with each variable added to the problem, the quantum cost grows far more slowly, and the gap widens without limit as instances get bigger.
Quadratic sounds generous until the overhead is counted. Fault-tolerant machines do not compute on raw hardware. Hundreds to thousands of physical qubits are combined and continuously monitored to produce one logical qubit, meaning a qubit stable enough to survive a long calculation, and every logical operation costs many physical operations underneath. Quantum clock speeds are also slow compared with classical processors. A square-root improvement can be consumed entirely by error correction before it ever reaches the business case.
The classical baseline
The second question asks what the quantum machine is actually racing. Monte Carlo risk simulation runs across thousands of cores and gets faster every time a firm adds hardware. Commercial routing and scheduling solvers have absorbed forty years of engineering effort. A speedup measured against a naive implementation is a benchmark artifact, not a competitive advantage.
Classical methods also move in response to quantum proposals. In 2018, Ewin Tang published a classical algorithm matching the performance of a quantum recommendation-systems result, which removed the claimed advantage outright. Several quantum machine learning proposals have been dequantized the same way since. Any claim resting on a heuristic rather than a proof carries that risk permanently.
The problem’s physics
The third question decides most cases. Is the problem itself quantum mechanical? Simulating the electronic structure of a molecule means tracking a state that grows exponentially with the number of interacting electrons, which is why classical chemistry codes rely on approximations that break down precisely where the interesting chemistry happens. Reiher and colleagues made this concrete in 2017 with a resource estimate for FeMoco, the nitrogenase cofactor behind biological nitrogen fixation.
We teach the questions in this order for a practical reason. The first two are cheap to run and eliminate most of the market. The third one is where the genuine cases survive.
Scoring the two proposals
Run the fleet routing pilot through the screen. The speedup is heuristic, with quadratic as the theoretical ceiling. The classical baseline is a mature commercial solver already producing routes the operations team accepts. The problem is combinatorial, not quantum mechanical. It fails all three, and the failure is mathematical rather than a matter of waiting for better hardware.
Now the catalyst workflow. The target is electronic structure, where classical scaling is exponential and current approximations are least reliable. The advantage is proven rather than heuristic. The problem instances are small enough to fit early fault-tolerant machines. It passes all three, and the remaining uncertainty concerns delivery dates instead of principle.
The short list, and the long one
Five domains currently support quantum advantage on published evidence: pharmaceutical R&D targeting enzyme active sites, industrial catalysis, battery materials and degradation chemistry, correlated-electron materials, and condensed-matter physics. They share one trait. In each, the computational bottleneck is the simulation of quantum-mechanical behaviour, so the classical wall is exponential and the quantum machine faces no equivalent wall.
The longer list appears constantly in vendor decks: supply chain optimization, scheduling, routing, fraud detection, recommendation engines, natural language processing, computer vision, insurance underwriting, grid management, macro-scale climate modelling. The proposed advantage in these cases is quadratic, heuristic, or already dequantized, and we have yet to see a peer-reviewed end-to-end resource estimate showing super-polynomial advantage on a practical instance in any of them.
Algorithmic discovery is unpredictable, and a proven advantage in quantum optimization would rewrite this assessment. The screen is what would catch it. That is the argument for teaching the method rather than distributing the list.
The ordering most roadmaps get backwards
A common planning assumption holds that cryptanalysis is the most demanding quantum application, so years of visible chemistry milestones will arrive first and provide warning. Published resource estimates reverse that order.
Gidney and Ekera estimated in 2021 that RSA-2048 could be broken in roughly eight hours on 20 million noisy physical qubits, and Gidney’s 2025 follow-up cut that requirement to fewer than one million noisy physical qubits, with the calculation running over a period of days rather than hours. Credible estimates still put the machine in the hundreds of thousands of physical qubits at minimum. Set against those figures, the flagship chemistry targets documented in the Quantum Utility Map analysis are the more demanding workload. A cryptographically relevant quantum computer, meaning one capable of breaking deployed public-key cryptography, therefore arrives before the machine that runs industrial chemistry, not after it.
That ordering makes cryptographic migration the one action item independent of sector. Harvest-now-decrypt-later describes the mechanism: encrypted traffic captured today, stored cheaply, and decrypted once the hardware exists. Any data with a confidentiality requirement measured in decades is already exposed to it. The deadlines are institutional rather than speculative. NIST published ML-KEM, ML-DSA and SLH-DSA as standards in August 2024, with FN-DSA to follow, and procurement and regulatory schedules across several jurisdictions now reference them directly. Migration methodology is covered in depth at pqcframework.org.
What this means for a training budget
Organizations in the five strong domains need computational teams who can identify which internal problems are quantum-amenable, specify hybrid workflows, and read a resource estimate without depending on the vendor who supplied it. Readiness of that kind takes two to five years to build, which is the same order of magnitude as the hardware timeline.
Organizations outside those domains face a shorter list. Fund the cryptographic migration, keep a lean monitoring capability, and develop enough analytical literacy internally to evaluate quantum claims as they arrive, including claims about suppliers, competitors and acquisition targets in the sectors that will change.
Both paths need the same underlying skill: the judgment to score a claim before committing capital to it. Quantum Academy builds its certification programs around that judgment rather than around vendor roadmaps. Explore the programs at quantumacademy.com/, and if the question is which roles this expertise leads to, QuantumCareers.com maps the paths.