Introducing Moment: A toolkit for semi-definite programming with moment matrices

Understand

Non-commutative polynomial optimization is a powerful technique with numerous applications in quantum nonlocality, quantum key distribution, causal inference, many-body physics, amongst others.

• The standard approach is to reduce such optimizations to a hierarchy of semi-definite programs, which can be solved numerically using well-understood interior-point methods.
• A key, but computationally costly, step is the formulation of moment matrices, whose size (and hence cost) grows exponentially with the depth of the hierarchy.
• It is therefore essential to have highly-optimized software to construct moment matrices.