Part One · Quantum computing
Quantum computers don't outperform classical ones across the board. Their advantage, where it exists, is concentrated in problems whose structure — combinatorial explosion, native quantum behavior, or hidden periodicity — maps onto how qubits actually compute.
Routing, scheduling, and resource-allocation problems where the number of possible arrangements grows factorially with size, quickly overwhelming exhaustive classical search. The Quantum Approximate Optimization Algorithm searches this space using interference between qubit states rather than brute enumeration.
Example domains: logistics network routing, workforce and flight scheduling, portfolio construction under constraints.
Molecules are themselves quantum systems, so simulating their electron interactions on a classical computer requires resources that scale exponentially with molecule size. A quantum computer can, in principle, represent those interactions natively using the Variational Quantum Eigensolver and related methods.
Example domains: candidate drug-molecule screening, battery electrolyte and catalyst design, nitrogen-fixation chemistry.
Shor's algorithm, published in 1994, efficiently factors large integers and computes discrete logarithms on a sufficiently large, error-corrected quantum computer — the two hard-math problems that underpin RSA and elliptic-curve cryptography today. This single capability is the reason Part Two of this page exists.
Status: requires a fault-tolerant machine far beyond anything built to date — see the resource estimates in Part Two.
Certain quantum feature-mapping techniques can, in theory, encode high-dimensional data into a comparatively small number of qubits, offering a different computational path for pattern recognition in complex, structured datasets than classical neural networks use.
Status: an active research area; provable, broad quantum advantage over classical ML remains unproven for most real-world datasets.
Quantum amplitude estimation offers a theoretical quadratic speedup over classical Monte Carlo sampling — the technique underlying derivatives pricing, portfolio risk simulation, and other finance workloads that rely on repeated random sampling to converge on an estimate.
Status: theoretical speedup demonstrated on small problem instances; not yet realized at production scale on noisy hardware.