Grover Mixers for QAOA: Shifting Complexity from Mixer Design to State Preparation
Abstract
We propose GMQAOA, a variation of the Quantum Alternating Operator Ansatz (QAOA) that uses Groverlike selective phase shift mixing operators. GMQAOA works on any NP optimization problem for which it is possible to efficiently prepare an equal superposition of all feasible solutions; it is designed to perform particularly well for constraint optimization problems, where not all possible variable assignments are feasible solutions. GMQAOA has the following features: (i) It is not susceptible to Hamiltonian Simulation error (such as Trotterization errors) as its operators can be implemented exactly using standard gate sets and (ii) Solutions with the same objective value are always sampled with the same amplitude. We illustrate the potential of GMQAOA on several optimization problem classes: for permutationbased optimization problems such as the Traveling Salesperson Problem, we present an efficient algorithm to prepare a superposition of all possible permutations of $n$ numbers, defined on $O(n^2)$ qubits; for the hard constraint $k$VertexCover problem, and for an application to Discrete Portfolio Rebalancing, we show that GMQAOA outperforms existing QAOA approaches.
 Publication:

arXiv eprints
 Pub Date:
 May 2020
 arXiv:
 arXiv:2006.00354
 Bibcode:
 2020arXiv200600354B
 Keywords:

 Quantum Physics;
 Computer Science  Data Structures and Algorithms
 EPrint:
 IEEE International Conference on Quantum Computing and Engineering, QCE'20, 7282, 2020