The Quantum Formalization Drive

We give trade-offs between classical communication, quantum communication, and entanglement for processing information in the Shannon-theoretic setting. We first prove a unit-resource capacity theorem that applies to the scenario where only the above three noiseless resources are available for consumption or generation. The optimal strategy mixes the three…

A provable quantum advantage for approximate optimization via decoded quantum interferometry establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.

An Optimal Quantum Linear Systems Algorithm establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.

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

Efficient Exact Quantum Sampling from the Sun-Wootters Distribution for Optimal Polynomial Intersection establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.

Worst-Case Quantum Algorithm for Optimal Polynomial Intersection Beyond Decoded Quantum Interferometry establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.

Hamiltonian Decoded Quantum Interferometry for General Pauli Hamiltonians establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.

Multivariate Decoded Quantum Interferometry for Weighted Optimization establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.

Randomized and quantum approximate matrix multiplication establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.

Fast Convex Optimization with Quantum Gradient Methods establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.

Quantum Signal Processing and Quantum Singular Value Transformation on $U(N)$ establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.

Quantum speedups for stochastic optimization establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.

The Quantum Esscher Transform establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.

Explicit decoders using fixed-point amplitude amplification based on QSVT establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.

Amplitude Estimation from Quantum Signal Processing establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.

Single-shot decoding of good quantum LDPC codes establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.

Fast Estimation of Sparse Quantum Noise establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.

Provably efficient machine learning for quantum many-body problems establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.

Foundations for learning from noisy quantum experiments establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.

Robust shadow estimation establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.

A Grand Unification of Quantum Algorithms establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.

Quantum Expander Codes establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.

Simulating Hamiltonian dynamics with a truncated Taylor series establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.

Quantum algorithm for systems of linear equations with exponentially improved dependence on precision establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.

Quantum algorithms for zero-sum games establishes the selected mathematical guarantees below. The mission turns those original paper results into precise Lean proof targets.