SymDPoly: symmetry-adapted moment relaxations for noncommutative polynomial optimization
arXiv:1808.09598
Abstract
Semidefinite relaxations are widely used to compute upper bounds on the objective of optimization problems involving noncommutative polynomials. Such optimization problems are prevalent in quantum information. We present an algorithm able to discover automatically and exploit the symmetries present in the problem formulation. We also provide an open source software library written in Scala ( https://denisrosset.github.io/symdpoly ) that computes symmetry-adapted semidefinite relaxations with interfaces to a variety of open-source and commercial semidefinite solvers. We discuss the advantages of symmetrization, namely reductions in memory use, computation time, and increase in the solution precision.
arXiv comment21 pages, comments most welcome. For associated software, see https://denisrosset.github.io/symdpoly
References in corpus (24)
- A computable measure of entanglement
- A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
- Bounding the set of quantum correlations
- A complete family of separability criteria
- Symmetry groups, semidefinite programs, and sums of squares
- Measurements incompatible in Quantum Theory cannot be measured jointly in any other local theory
- Sum-of-squares decompositions for a family of CHSH-like inequalities and their application to self-testing
- Symmetries of the Bell correlation inequalities
- Robust and versatile black-box certification of quantum devices
- Physical characterization of quantum devices from nonlocal correlations
- Bounding the set of finite dimensional quantum correlations
- Algorithm 950: Ncpol2sdpa---Sparse Semidefinite Programming Relaxations for Polynomial Optimization Problems of Noncommuting Variables
- Quantum Control of a Single Qubit
- Enabling computation of correlation bounds for finite-dimensional quantum systems via symmetrisation
- Bounds on Quantum Correlations in Bell Inequality Experiments
- Characterizing finite-dimensional quantum behavior
- Causal inference via algebraic geometry: feasibility tests for functional causal structures with two binary observed variables
- Bounding the set of classical correlations of a many-body system
- Optimal networks for Quantum Metrology: semidefinite programs and product rules
- Universal bound on the cardinality of local hidden variables in networks
- Is error detection helpful on IBM 5Q chips ?
- Improving the efficiency of joint remote state preparation in noisy environment with weak measurement
- Dimension reduction for semidefinite programs via Jordan algebras
- An Algorithm to Decompose Permutation Representations of Finite Groups: Polynomial Algebra Approach