The Quantum Formalization Drive

Sample-optimal tomography of quantum states establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.

A Faster Cutting Plane Method and its Implications for Combinatorial and Convex Optimization (Lee, Sidford, Wong) establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.

Upper bounds on quantum query complexity inspired by the Elitzur-Vaidman bomb tester (Lin, Lin) establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.

A Quantum Approximate Optimization Algorithm (Farhi, Goldstone, Gutmann) establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.

A Quantum Approximate Optimization Algorithm Applied to a Bounded Occurrence Constraint Problem (Farhi, Goldstone, Gutmann) establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.

This mission develops Chapter 10 of Quantum Computing: Lecture Notes by Ronald de Wolf. The chapter's selected results describe the mathematical guarantees below.

This mission develops Chapter 20 of Quantum Computing: Lecture Notes by Ronald de Wolf. The chapter's selected results describe the mathematical guarantees below.

Textbook quantum theory starts from postulates about Hilbert spaces, density matrices and completely positive maps, none of which has an evident operational meaning. A long line of work, from Birkhoff–von Neumann quantum logic through Ludwig, Hardy (quant-ph/0101012), Dakić–Brukner and Masanes–Müller (arXiv:1004.1483), asks whether the formalism can instead…

A QMA verifier receives a quantum witness and checks it with a circuit generated efficiently from the input. An acceptance probability separated by an inverse-polynomial gap is enough to define the class, but applications often need the probability of a wrong answer to be exponentially small. Repeating the verifier on many supplied witness registers…

In a scattering experiment a particle arrives from far away, interacts with a target, and leaves again. Far from the target the forces are negligible, so long before and long after the collision the particle should move like a free particle. Scattering theory makes this precise by comparing two quantum dynamics: the free evolution $\mathrm e^{-\mathrm itH_0}$…

Quantum mechanics describes mixed states by density operators: positive operators $\rho$ on a Hilbert space with $\operatorname{tr}(\rho) = 1$. Expectation values are traces $\operatorname{tr}(\rho A)$, perturbation determinants and spectral shift functions are built from traces of resolvent differences, and scattering theory (the Kato–Rosenblum and Birman–Krein…