How many known problems exist where there is a quantum algorithm that would clearly work?

A Reddit user compared Shor’s algorithm to historical hypercomputer architectures, questioning whether quantum computing faces a similar "one-algorithm" limitation like Thinking Machines’ hypercube systems, which only efficiently ran fast Fourier transforms. Shor’s algorithm stands out as a rare, proven quantum solution for integer factorization and discrete logarithms, demonstrating exponential speedup over classical methods but leaving uncertainty about broader quantum utility. The post highlights parallels with 1980s hypercomputers, where hardware outpaced algorithm development, leading to commercial failure despite theoretical promise, raising concerns about quantum computing’s practical scalability. Beyond Shor’s, few quantum algorithms (e.g., Grover’s search, HHL for linear systems) offer clear speedups, but their real-world applicability remains limited by error correction and hardware constraints. The discussion underscores a critical challenge: quantum computing’s success hinges on discovering more "killer apps" to justify infrastructure investment, much like classical computing’s early algorithmic breakthroughs.