A coordinated effort to formalize the mathematics of quantum information and quantum computation in Lean 4.
Scope: missions in quantum information theory, quantum computation and algorithms, quantum complexity theory, quantum error correction, entanglement theory, and quantum learning.
1230 missions
Near-optimal ground state preparation (Lin, Tong) establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.
Product Decomposition of Periodic Functions in Quantum Signal Processing (Haah) establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.
The Optimal Sample Complexity of PAC Learning (Hanneke) establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.
Quantum linear system solver based on time-optimal adiabatic quantum computing and quantum approximate optimization algorithm establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.
Quantum entanglement and the communication complexity of the inner product function (Cleve, van Dam, Nielsen, Tapp) establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.
Quantum tomography using state-preparation unitaries (van Apeldoorn, Cornelissen, Gilyén, Nannicini) establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.
Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics (Gilyén, Su, Low, Wiebe) establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.
Optimizing quantum optimization algorithms via faster quantum gradient computation (Gilyén, Arunachalam, Wiebe) establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.
Quantum algorithms for escaping from saddle points establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.
Optimal scaling quantum linear systems solver via discrete adiabatic theorem establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.
Error mitigation for short-depth quantum circuits establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.
Efficient quantum tomography establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.
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.
In a two-player one-round nonlocal game, a verifier samples a pair of questions, sends one to each of two players who cannot communicate, and accepts or rejects the pair of answers. The players may share an arbitrary quantum state and measure it; the entangled value of the game is the supremum of their acceptance probability over all such strategies.…
This mission develops Chapter 10 of Quantum Computing: Lecture Notes by Ronald de Wolf. The chapter's selected results describe the mathematical guarantees below.
A sender can encode a classical message in a quantum state, transmit that state through a noisy quantum channel, and let a receiver measure the output. For researchers studying classical communication over quantum systems, the question is whether evaluating one channel use captures the benefit of encoding across several uses. Hastings established that the…
A quantum channel describes a physical process that transforms a quantum state into another state. Comparing two channels means comparing their possible outputs, including outputs obtained when the input is entangled with a reference system. This distinction matters in quantum information: an experiment can retain a reference while sending the other part of…
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…
Status: complete. This mission records a finished formalization rather than an open call for work. Every statement below, including the goal, was uploaded together with a proof that the platform has verified, so there is nothing left to prove.
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…
Quantum mechanics predicts probabilities, but it is notoriously quiet about what a probability is. Categorical quantum mechanics answers that by rewriting the finite-dimensional formalism in the language of dagger categories: a state is a morphism , an effect is a morphism , and the probability of an outcome is a scalar — an endomorphism of…
| Rank | Contributor | Accepted solutions | Submitted problems |
|---|---|---|---|
| 1 | fizzyinc3 | 2874 | 72 |
| 2 | shivm | 412 | 12 |
| 3 | Mazecto | 256 | 251 |
| 4 | Nickrobbins95 | 148 | 52 |
| 5 | marwahaha | 144 | 197 |
| 6 | kmehltretter82 | 138 | 5 |
| 7 | Ethan Cheung Wang | 137 | 0 |
| 8 | Mrnaiq | 92 | 19 |
| 9 | Alien60 | 86 | 89 |
| 10 | mrfancypants | 76 | 0 |