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19 January, 2021

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If anyone would get a superpower, then most of us would ask for the power to stop the time, who doesnâ€™t like to stop the time and take a break for months? Well for humans it seems impossible, but not for computers. Everyoneâ€™s always talking about traveling through time and some legends like Albert Einstein also proposed the theory of relativity.

A pair of studies about quantum algorithms, from independent research teams, recently graced the arXiv preprint servers. Theyâ€™re both basically about the same thing: using clever algorithms to solve nonlinear differential equations.

And if you observe like a squint at them through the lens of Soft Science and if you have a little knowledge of science then you could realize, as I have, that theyâ€™re a recipe for computers that can basically stop time in order to solve a problem requiring a near-immediate solution.

Remembered your high school mathematics where you learned to solve the linear equations by hand? Well those linear equations are a piece of cake for the modern computers. Computers just crunch the numbers and find the pattern in the linear relationship of the equation (If you know about Linear Regression Machine Learning model, you could relate). But non-linear equations are the real thing and the non-linear differential equations are tougher.

Now you can ask can a computer solve such tough equations? Well humans are still preparing for this. Do you remembered how Google showed their Quantum Supremacy ? We humans are still building the quantum computers and the hope is that one day quantum computers will break the difficulty barrier and make these hard-to-solve problems seem like ordinary compute tasks.

When computers solve these kinds of problems, theyâ€™re basically predicting the future. Todayâ€™s AI can still predict the next movies you should watch if you provide the enough data. You can add a few more movies to the equation and the computer will still get it right most of the time.

But if you reach the point where scale of interactivity just provides the feedback and doesnâ€™t resembles any meaning, such as observing the evaporation of water and predicting where does the air flow for the next few seconds or, for example spreading feathers up in the sky and predicting the movement of a feather, a classical computers doesnâ€™t have such computational power to calculate the physics at that scale.

This tell us why we still canâ€™t predict the weather. There are so many interactions or factors that affect the weather which becomes harder for the computer to predict the weather.

But with quantum computers you bypass the binary rules of classical computing. A classical or a normal computers understand just 0 and 1, right? But quantum computers doesnâ€™t obey the binary rules. Quantum computers not only can represent 0 and 1 but also they can represent 1 while 0 and 0 while representing 1. Understand this concept by the sides of coin. A normal computer can either show Head or Tail of coin but Quantum can show Tail while showing Head and also can show Head while showing Tail and surprisingly they can even show nothing, neither Head nor Tail. Isnâ€™t this amazing? For our purposes, this means they can potentially solve difficult problems such as â€śwhere is every single piece of feather going to be in .02 seconds?â€ť or â€śWhat is the optimal route for the air that evaporatedâ€ť.

In order to understand the whole idea behind this concept, we can refer some robust research papers. The first one comes from the University of Maryland which say,

〝In this paper we have presented a quantum Carleman linearization (QCL) algorithm for a class of quadratic nonlinear differential equations. Compared to the previous approach of, our algorithm improves the complexity from an exponential dependence on T to a nearly quadratic dependence, under the condition R < 1.

〞

And letâ€™s take a peek at the second paper. This oneâ€™s from a team at MIT:

〝This paper showed that quantum computers can in principle attain an exponential advantage over classical computers for solving nonlinear differential equations. The main potential advantage of the quantum nonlinear equation algorithm over classical algorithms is that it scales logarithmically in the dimension of the solution space, making it a natural candidate for applying to high dimensional problems such as the Navier-Stokes equation and other nonlinear fluids, plasmas, etc..

〞

Both papers are fascinating but for now let me simplify it. The paper shows the detail how we can build algorithms for quantum computers to solve those really hard problems.

So what does that mean? We hear about how quantum computers can solve drug discovery or giant math problems but what happens behind the scenes? What I mean is If classical computers can give us the power to land a rover on the moon, then what this quantum computers going to do?

Now itâ€™s easier for you to believe that itâ€™s potentially going to give quantum computers the ability to essentially stop time. Now, as you can imagine, this doesnâ€™t mean any of us will get a remote control with a pause button on it to stop time while in an examination hall.

What it means that the powerful-enough quantum computer running the greatest of the greatest, highly customized and trained algorithms that developed today (which of course will get better in future) might hold the ability to determine the particle-level physics state of any element with the enough speed and accuracy that will eventually surpass the speed of time and make it non-factor and by which time will have no longer have any effect on the element during the execution of the algorithm.

So, theoretically, if someone in the future threw a handful of marbles or glitters or feathers at you and you had the access to quantum-powered defense drones, they could instantly respond by perfectly positioning themselves between you and the particles coming from the marbles to protect you. And yes they can predict the weather too with near-perfect accuracy over extremely long periods of time.

This ultimately means quantum computers could one day operate in a time resistant world, solving problems at nearly infinitely small moment of time which can literally break or stop the time to affect it.

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