# Algorithms Clearly Beat Gamers at Quantum Moves. A Verification

## TL;DR

This paper demonstrates that simple, well-implemented algorithms like GRAPE and coordinate ascent outperform human players and previously claimed algorithms in solving the Quantum Moves game, challenging earlier assertions about human intuition's advantage.

## Contribution

The paper verifies that basic algorithms outperform both players and complex algorithms derived from player solutions, contradicting prior claims about human intuition's superiority.

## Key findings

- Coordinate ascent outperforms all players and algorithms based on player solutions.
- GRAPE significantly outperforms human players and matches or exceeds other algorithms.
- Previous claims about human intuition being crucial are refuted by these results.

## Abstract

The paper [S{\o}rensen et al., Nature 532] considers how human players compare to algorithms for solving the Quantum Moves game BringHomeWater and design new algorithms based on the intuition extracted from players. The claim by [S{\o}rensen et al., Nature 532] is that players outperform widely used algorithms, in particular the KASS algorithm, based on the Krotov algorithm, and that player intuition is crucial to develop improved methods. However, as initially discussed by D. Sels [D. Sels, Phys. Rev. A 97], a standard Coordinate Ascent algorithm outperforms all players by a large margin. Albeit D. Sels only compare to player solutions, the simple algorithm outperforms all algorithms based on player solutions and Krotov, and it does so using much less time and iterations. In this paper we elaborate on the methods discussed by D. Sels and verify that the presented algorithm, solves the problem better than all players and algorithms derived from player solutions in [S{\o}rensen et al., Nature 532]. We also verify the theoretical analysis presented by D. Sels, that gives a theoretically derived protocol that outperforms all players. We add a comparison with gradient ascent or GRAPE. Starting from uniform random values, GRAPE outperforms all players by a large margin. GRAPE works at least as well as the methods from [S{\o}rensen et al., Nature 532] initialized with player solutions. A standard analysis of the results from GRAPE provides a starting point for GRAPE, that outperform all algorithms from [S{\o}rensen et al., Nature 532]. We compare with a basic Krotov algorithm, and get results similar to GRAPE, clearly outperforming players and the KASS algorithm. These experiments verify and underline the result in [D. Sels, Phys. Rev. A 97] that the conclusions from [S{\o}rensen et al., Nature 532] regarding algorithms are untenable. In fact the opposite conclusions are true.