# Grover Mixers for QAOA: Shifting Complexity from Mixer Design to State Preparation

arXiv: https://arxiv.org/abs/2006.00354 · HTML: https://mlsanity.com/paper/2006.00354/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 May 2020.

## Built on by (most cited first, 7 of 7)

- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [A Primer on Quantum Machine Learning](https://mlsanity.com/paper/2511.15969/) (2025)
- [MG-Net: Learn to Customize QAOA with Circuit Depth Awareness](https://mlsanity.com/paper/2409.18692/) (2024)
- [Learning to Learn with Quantum Optimization via Quantum Neural Networks](https://mlsanity.com/paper/2505.00561/) (2025)
- [Investigating layer-selective transfer learning of QAOA parameters for Max-Cut problem](https://mlsanity.com/paper/2412.21071/) (2024)
- [Quantum Optimization Algorithms](https://mlsanity.com/paper/2511.12379/) (2025)
- [Quantum Approaches to Urban Logistics: From Core QAOA to Clustered Scalability](https://mlsanity.com/paper/2512.10813/) (2025)

## Abstract (arXiv)

We propose GM-QAOA, a variation of the Quantum Alternating Operator Ansatz (QAOA) that uses Grover-like selective phase shift mixing operators. GM-QAOA 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. GM-QAOA 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 GM-QAOA on several optimization problem classes: for permutation-based 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(n2) qubits; for the hard constraint k-Vertex-Cover problem, and for an application to Discrete Portfolio Rebalancing, we show that GM-QAOA outperforms existing QAOA approaches.