# Whats Is Quantum Analysis?

Whats Is Quantum Analysis?

From gene mapping to space exploration, humanity continues to generate ever-larger sets of data — far more information than people can actually process, manage, or understand.

Machine learning systems can help researchers deal with this ever-growing flood of information. Some of the most powerful of these analytical tools are based on a strange branch of geometry called topology, which deals with properties that stay the same even when something is bent and stretched every which way.

Such topological systems are especially useful for analyzing the connections in complex networks, such as the internal wiring of the brain, the U.S. power grid, or the global interconnections of the Internet. But even with the most powerful modern supercomputers, such problems remain daunting and impractical to solve. Now, a new approach that would use quantum computers to streamline these problems has been developed by researchers at MIT, the University of Waterloo, and the University of Southern California.

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The team describes their theoretical proposal this week in the journal Nature Communications. Seth Lloyd, the paper’s lead author and the Nam P. Suh Professor of Mechanical Engineering, explains that algebraic topology is key to the new method. This approach, he says, helps to reduce the impact of the inevitable distortions that arise every time someone collects data about the real world.

In a topological description, basic features of the data (How many holes does it have? How are the different parts connected?) are considered the same no matter how much they are stretched, compressed, or distorted. Lloyd explains that it is often these fundamental topological attributes “that are important in trying to reconstruct the underlying patterns in the real world that the data are supposed to represent.”

It doesn’t matter what kind of dataset is being analyzed, he says. The topological approach to looking for connections and holes “works whether it’s an actual physical hole, or the data represents a logical argument and there’s a hole in the argument. This will find both kinds of holes.”

Using conventional computers, that approach is too demanding for all but the simplest situations. Topological analysis “represents a crucial way of getting at the significant features of the data, but it’s computationally very expensive,” Lloyd says. “This is where quantum mechanics kicks in.” The new quantum-based approach, he says, could exponentially speed up such calculations.

Lloyd offers an example to illustrate that potential speedup: If you have a dataset with 300 points, a conventional approach to analyzing all the topological features in that system would require “a computer the size of the universe,” he says. That is, it would take 2300 (two to the 300th power) processing units — approximately the number of all the particles in the universe. In other words, the problem is simply not solvable in that way.

“That’s where our algorithm kicks in,” he says. Solving the same problem with the new system, using a quantum computer, would require just 300 quantum bits — and a device this size may be achieved in the next few years, according to Lloyd.