Complexity Theory and Its Applications in Linear Quantum Optics
PhD thesis — Louisiana State University, 2016. Full text: https://archive.org/details/arxiv-1607.02991
Arguments
Complexity Theory and Its Applications in Linear Quantum Optics
It traces how a result in abstract computational complexity becomes a sensor roadmap — the through-line from "a classical computer cannot efficiently simulate this" to deployable quantum metrology.
The 2010 discovery that the BosonSampling problem is likely hard for a classical computer to simulate opened a new technology path: passive linear optical networks with quantum states of light inherit the same computational hardness, and the intuitions behind BosonSampling led to developments in optical metrology suggesting quantum sensors could be viable within a few years with only marginal improvements in technology.
Why it matters
It traces how a result in abstract computational complexity becomes a sensor roadmap — the through-line from "a classical computer cannot efficiently simulate this" to deployable quantum metrology.
Use when: Today's abstract complexity result is tomorrow's hardware — when a problem is provably hard classically, the physics that makes it hard is itself the technology.