Randomized Satisfiability Checking for Non-Linear Arithmetic over Finite Fields

Squaring Up by Selection: NP-Completeness at Three Simple Roots

To solve an overdetermined polynomial system numerically, one first makes it square, usually by replacing the given equations with as many random linear combinations as there are unknowns. This is a provably safe step, but it can substantially enlarge the supports. The alternative is to keep that many of the given equa...

Satisfiability of Multivalued Circuits with Lists

The Satisfiability Problem

This book explains how algorithms work, for example, by exploiting the structure of the SAT problem with an appropriate logical calculus, like resolution, but also algorithms based on “physical” principles are considered.

Complexity Barriers to State Preparation in Quantum Approximate Optimization

This work proves that the barrier to reaching the classical threshold does not arise from a need for entanglement, and separates the effects of relaxation tightness and energy approximation from operational accessibility.

Treewidth and the complexity of box-constrained quadratic programs

We consider the problem of minimizing a sparse quadratic function over the unit hypercube. In binary quadratic programming, treewidth of the interaction graph is a central parameter for tractability: bounded treewidth yields polynomial-time solvability. Motivated by this fact, we investigate whether treewidth plays a s...

Polynomial Time Quantum Approximation Schemes for Constrained Optimisation

Heavy-Hitter QAOA is introduced, which preserves finite-depth and finite-shot guarantees for Constraint-Enhanced QAOA and preserves these conditional guarantees while reducing the retained candidate set and classical post-processing cost by one power of the problem size.