Too often, quantum computer scientists seek to create new algorithms entirely fresh from new cloth when there are extensive and optimized classical algorithms that can be generalized wholesale. At the same time, one may seek to maintain classical advantages of performance and runtime bounds, while enabling potential quantum improvement. Hybrid quantum algorithms tap into this potential, and here we explore a class of hybrid quantum algorithms called iterative quantum algorithms (IQA) that are closely related to classical greedy or local search algorithms, employing a structure where the quantum computer provides information that leads to a simplified problem for future iterations. Specifically, we extend these algorithms beyond past results that considered primarily quadratic problems to arbitrary $k$-local Hamiltonians, proposing a general framework that fundamentally incorporates logical inference. As an application, we develop a hybrid quantum version of the well-known classical Davis-Putnam-Logemann-Loveland (DPLL) algorithm for satisfiability problems, which embeds IQAs within a complete backtracking-based tree search framework. Our results also provide a general framework for handling problems with hard constraints in IQAs. We further show limiting cases of the algorithms where they reduce to classical algorithms, and provide evidence for regimes of quantum improvement.

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• Quantum algorithms
• Quantum algorithms & computation