Noname manuscript No. (will be inserted by the editor) DIFFERENTIAL GEOMETRIC TREEWIDTH ESTIMATION IN ADIABATIC QUANTUM COMPUTATION Chi Wang · Edmond Jonckheere · Todd Brun Received: date / Accepted: date Abstract The D-Wave adiabatic quantum computing platform is designed to solve a particular class of problems—the Quadratic Unconstrained Binary Optimization (QUBO) problems. Due to the particular “Chimera” physical architecture of the D-Wave chip, the logical problem graph at hand needs an extra process called minor embedding in order to be solvable on the D-Wave architecture. The latter problem is itself NP-hard. In this paper, we propose a novel polynomial-time approximation to the closely related treewidth based on the differential geometric concept of Ollivier-Ricci curvature. The latter runs in polynomial time and thus could significantly reduce the overall com- plexity of determining whether a QUBO problem is minor-embeddable, and thus solvable on the D-Wave architecture. Keywords: Adiabatic Quantum Computation, Chimera architecture, minor embedding, treewidth, Ollivier-Ricci curvature 1 Introduction 1.1 Quantum annealing Adiabatic Quantum Computation (AQC), first proposed in [17], was originally designed to solve such general optimization problems as 2-SAT and 3-SAT. In the more specific D-Wave implementation, it maps a Quadratic Unconstrained Binary Optimization (QUBO) problem, defined as min X E(x 1 ,x 2 , ..., x n )= c 0 + n  i=1 c i x i + n  i<j=1 c ij x i x j , x i ∈{0, 1}, (1) Dept. of Electrical Eng., University of Southern California, Los Angeles, CA 90089, USA