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The quantum computing revolution draws ever nearer, but the need for a computer that makes correctable errors continues to hold it back.

Through a collaboration with IBM led by Cornell, researchers have brought that revolution one step closer, achieving two major breakthroughs. First, they demonstrated an error-resistant implementation of universal quantum gates, the essential building blocks of quantum computation. Second, they showcased the power of a topological quantum computer in solving hard problems that a conventional computer couldn't manage.

In the article "Realizing String-Net Condensation: Fibonacci Anyon Braiding for Universal Gates and Sampling Chromatic Polynomials" in Nature Communications, an international collaboration between researchers at IBM, Cornell, Harvard University and the Weizman Institute of Science demonstrated, for the first time, the ability to encode information by braiding鈥攎oving in a particular order鈥擣ibonacci string net condensate (Fib SNC) anyons, which are exotic quasi-particles, in two dimensional space.

"This is really the first step toward universal topological quantum computing, or fault-tolerant computing," said co-corresponding author Eun-Ah Kim, Hans A. Bethe Professor of physics in the College of Arts and Sciences.

"The two-dimensionality is very important for being very fault tolerant and resistant to error. If you only do everything in one dimension, there is no such potential for fault tolerance," said co-corresponding author Chao-Ming Jian, assistant professor of physics (A&S).

The researchers demonstrated the power of their method on a known hard problem, rather than one invented for the experiment. On a small scale, they could verify the quantum computer's results using a classical computer as a proof of principle.

The hard problem they chose involved chromatic polynomials, originated from a counting problem of graphs with different colored nodes and a few simple rules. Classical computers can calculate how many possible colorings are allowed in a simple graph with just a few nodes and a few colors. But as soon as the graph enlarges with many nodes and many connections, the number of possibilities quickly becomes exponentially large. A classical computer cannot compute that many possibilities.

The protocol the researchers used鈥攕ampling the chromatic polynomials for a set of different graphs where the number of colors is the golden ratio鈥攊s scalable, so other researchers with quantum computers can duplicate it at a larger scale.

"Someone can follow our protocol and do something that is classically not possible," said Kim. "We set it out as a challenge to anybody."

Studying topologically ordered many-body quantum systems鈥攕ystems with a large number of interacting quantum particles鈥攁nd their applications in quantum computation presents tremendous challenges for quantum researchers. Being able to draw on the resources, expertise and insight of scientists from around the world鈥攊n both industry and academia鈥攆or their team was essential to achieve their results, said Kim.

"The researchers at IBM were critical in understanding the theory of the topological state and how to design a protocol to implement it on a quantum computer, which they provided," she said. "Our other colleagues made essential contributions with the hardware simulations, connecting theory to experiment and determining our strategy."