Comments about the article in Nature: Exploring the quantum speed limit with computer games.

Following is a discussion about this "Letter" in Nature Vol 532 14 April 2016, by Jens Jakob W.H. Sorenson et al.

• The text in italics is copied from the article
  
• Immediate followed by some comments
  

In the last paragraph I explain my own opinion.

This article is about the video game "Quantum Moves". In the same Nature Vol 532 there are two more articles about the same issue:

• In the section "News" Quantum world may be intuitive
• In the section "Research" Quantum problems solved through games

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Introduction

Humas routinely solve problems of immense computational complexity by intuitively forming, low-dimensional heuristic strategies.

Intuitively my feeling is that this is not true. See Also Reflection 1

Here we report on "Quantum Moves", an online platform gamifying optimization problems in Quantum physics. We show that human players are able to find solutions to difficult problems associated with the task of quantum computing.

That is in principle possible, but it is not quaranteed that that is the only way.

Players succeed where purely numerical optimization fails and analysis of their solutions provide insights into the problem of optimization of a more profound and general nature.

In a sense Sorensen et al claim that humans can outperform computers. To make such a claim requires detailed information.

In second paragraph page 210 we read:

Finding the optimal path of the tweezer from one lattice site to another is a difficult problem when the available time is "limited".

The problem is to find the x,y position of the tweezer at a sequence of n events tn with maximum return and smallest value for n.

In fourth paragraph page 210 we read:

BringHome Water belongs to the class of one-dimensional quantum optimal control of individual atoms with one or two control parameters.

IMO there the two control parameters are the position and speed of the atom. One problem is that both parameters are a function of t. What makes this whole excersize so difficult are two constraints: To find a solution in the shortest time and to score 100%. This means that the empty atom at the start should be completely filled at the finish.

In fifth paragraph page 210 we read:

Recall that the standard approach for solving a problem such as BringHome Water is to use a multistart of tailored local optimization algorithms such as the Krotov algorithm.

If you want to simulate and calculate the optimum solution on your own PC you need the algorithms to calculate the shape of the atom. What you also need is the "potential" function.
What is also possible that the specific challenge has no solution. This means that it is impossible to transport the atom completely i.e. with a fidelity of 1.
For the krotov algorithm read this: http://arxiv.org/abs/1103.5435">http://arxiv.org/abs/1103.5435 "Efficient Algorithms for Optimal Control of Quantum Dynamics: The 'Krotov' Method unencumbered"
My first impression is that the krotov algorithm is not a very good tool to solve the 20 "challenges" of "Quantum Moves". IMO this requires a much more tailor made approach.

Figure 1. The Bring Home Water challenge as seen by the players The atom is represented by the square of its wavefuntion Psi(x,t)^2 The player controls the optical tweezer by moving a computer cursor, picks up the atom and drags it back to the target area. Figure 1 does not represents what the player usely sees: The atom in (C) is empty.

This KASS optimization formed our most successful bare computer optimization method.

What this

b. The sweeps from the seeds (initial conditions) that are generated by players (Yellow and blue) and computers (red).

What Figure 2b demonstrates is that the initial conditions based on the results by players is much better than the results based on a computer program.
It is important to state that we are speaking here about "intial conditions" (seeds) and not on solutions.

Figure 2. Fidelities of the transport problem for different solution durations. a. A subset of the solutions found by the players as turquoise dots What Figure 2 shows are the results. The optimum results are in an area defined between the Fidelity of 0.6 and 0.8 with a duration larger than 0.28. There are only a few cases with Fidility larger than 0.9 A perfect result is Fidility = 1. No player has the correct strategy to reach that result. The 4 curves show the best solutions found by computer optimizations for each duration. What these 4 curves show that the computer completely outperforms the players.

Reflection 1

The article is based on two studies:

• "Do fielders know where to go to catch the ball or how to get there"
  In sports the basic answer is: To form a team, to train, to collect statistics and by experience.
• "Simple Heuristics That Make Us Smart" The general answer is: To read as much as possible, to be critical and to Think.

The problem is that both studies have nothing to do with Quantum Mechanics. But that is not the point. To sport generally speaking does not involve mathematics. To win a football match is not considered an effort "of immense computational complexity". To consider sport as such is a misnomer.
The exceptions are: To play chess, Backgammon, Poker and the game Go.

Reflection 2 - My own experience with the game "Quantum Moves"

• first of all I have extensivily tested the 20 excercises. For the results read this: Quantum Moves - Experimental Data
• Secondly I have written a simpler version of the program in Visual Basic 5.0.
  For an explanation read this: VB Quantum Moves

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