# Quantum theory > 9 AI-made results on quantum theory, each explained in plain English. Mathematics behind quantum mechanics and quantum information: states, measurements… Canonical: https://closedform.nishachay.tech/topic/quantum/ Last updated: 2026-10-14 Mathematics behind quantum mechanics and quantum information: states, measurements and quantum channels. 9 AI-made results on quantum theory, from 23 papers in the OpenAI math collection, each explained in plain English. 6 have a formal Lean proof listed; 3 are claimed in a paper and not yet machine-checked. They span 3 fields, led by mathematical physics (7), algebraic and complex geometry (1) and probability and statistical mechanics (1). The oldest question here dates back to 1925: [Positive-temperature Bose–Einstein condensation and exact quantum depletion](https://closedform.nishachay.tech/e/openai-math-2026-267/). ## Results (9) - [Global quantum geometric Langlands at irrational level](https://closedform.nishachay.tech/e/openai-math-2026-069/) - Entry 069 · A claimed proof of quantum geometric Langlands duality on any smooth complex curve at every irrational level. (Claimed, not checked) - [The geometric phase diagram, diffusion, and spectra of random planar maps](https://closedform.nishachay.tech/e/openai-math-2026-211/) - Entry 211 · Random FK planar maps are claimed to look like random surfaces for q ≤ 4 and like a random tree above 4. (Formal proof listed) - [Positive-temperature Bose–Einstein condensation and exact quantum depletion](https://closedform.nishachay.tech/e/openai-math-2026-267/) - Entry 267 · Proves condensation in every ground state of the dilute hard-sphere Bose gas; claims thermal and depletion laws. (Formal proof listed) - [Bloch's law, its lattice correction, and the spherical magnetization law](https://closedform.nishachay.tech/e/openai-math-2026-271/) - Entry 271 · Proves 3D quantum Heisenberg ferromagnets magnetize at low temperature; claims Bloch's T^(3/2) law and its correction. (Formal proof listed) - [Parity is not in QAC 0](https://closedform.nishachay.tech/e/openai-math-2026-274/) - Entry 274 · Proves constant-depth quantum circuits with polynomially many qubits cannot compute parity, settling Moore's conjecture. (Formal proof listed) - [Classical capacity of generalized amplitude damping](https://closedform.nishachay.tech/e/openai-math-2026-276/) - Entry 276 · Proves an exact formula for the classical capacity of every generalized amplitude-damping qubit channel. (Formal proof listed) - [Exact quantum factoring over a fixed finite gate set](https://closedform.nishachay.tech/e/openai-math-2026-279/) - Entry 279 · Proves polynomial-size quantum circuits over a fixed gate set factor every integer with probability exactly one. (Formal proof listed) - [Polynomial-time unitary synthesis from a Boolean oracle](https://closedform.nishachay.tech/e/openai-math-2026-283/) - Entry 283 · Claims a polynomial-size quantum circuit can carry out any n-qubit operation, given a suitable Boolean oracle. (Claimed, not checked) - [The optimal quartic separation between randomized and quantum queries](https://closedform.nishachay.tech/e/openai-math-2026-284/) - Entry 284 · Claims functions where randomized queries need nearly the fourth power of quantum queries, refuting a cubic conjecture. (Claimed, not checked) ## Related - [Lean-checked results](https://closedform.nishachay.tech/trust/lean-checked/) - Trust · 242 results - [Open since the 2010s](https://closedform.nishachay.tech/open-since/2010s/) - Era · 31 results - [Claimed, not yet checked](https://closedform.nishachay.tech/trust/claimed/) - Trust · 130 results - [Open since before 1940](https://closedform.nishachay.tech/open-since/before-1940/) - Era · 16 results - [Erdős problems](https://closedform.nishachay.tech/topic/erdos-problems/) - Topic · 13 results - [Named conjectures](https://closedform.nishachay.tech/topic/named-conjectures/) - Topic · 85 results - [Ramsey theory](https://closedform.nishachay.tech/topic/ramsey-theory/) - Topic · 5 results - [Prime numbers](https://closedform.nishachay.tech/topic/prime-numbers/) - Topic · 12 results - [Graph theory](https://closedform.nishachay.tech/topic/graph-theory/) - Topic · 40 results - [Distances and packing](https://closedform.nishachay.tech/topic/distances-and-packing/) - Topic · 5 results - [Mathematical physics](https://closedform.nishachay.tech/science/mathematics/mathematical-physics/) - Field · 7 here - [Algebraic and complex geometry](https://closedform.nishachay.tech/science/mathematics/algebraic-and-complex-geometry/) - Field · 1 here - [Probability and statistical mechanics](https://closedform.nishachay.tech/science/mathematics/probability-and-statistical-mechanics/) - Field · 1 here - [All topics](https://closedform.nishachay.tech/topics/) - Every way to browse