###### June 12, 2014

# Quantum Contextuality Needed To Achieve “Magic” Required For Universal Quantum Computation

**Alan McStravick for redOrbit.com - Your Universe Online**

The difficulty in understanding the field of quantum computing just got a little easier, but only slightly.

New research from the University of Waterloo's Institute for Quantum Computing has confirmed, at least theoretically, that the concept of contextuality is a necessary resource required for achieving the advantages of quantum computation.

Contextuality is regarded as one of the weirder aspects of quantum theory and is a necessary resource required for the achievement of the “magic” required for universal quantum computation. Results of this study were recently published in the journal *Nature*.

As the research team, comprised of Joseph Emerson, Mark Howard and Joel Wallman, noted, a significant barrier to being able to harness the power of a universal quantum computer is the realization of a practical method to control the fragile quantum states.

"Before these results, we didn't necessarily know what resources were needed for a physical device to achieve the advantage of quantum information. Now we know one," said Mark Howard, a postdoctoral fellow at IQC and the lead author of the paper, in a statement. "As researchers work to build a universal quantum computer, understanding the minimum physical resources required is an important step to finding ways to harness the power of the quantum world."

One of the reasons quantum devices are so difficult to build is that they require a noise-resistant environment in which to operate. As noted above, the term “magic” specifically refers to an approach that is particular to the construction of a noise-resistant quantum computer. More properly, it is known as magic-state distillation. While crucial to the building of a quantum computer, magic-state distillation is difficult to both achieve and maintain. When successful, magic-state distillation is the single ingredient responsible for boosting the power of a quantum device's processing capabilities so that it is a universal quantum computer.

The research team points out that recognizing these magic-states as contextual will help others to be able to clarify the trade-offs involved in different approaches of building quantum devices. Additionally, this study's results might aid in the formulation of new algorithms able to exploit the special properties of these magic states more fully.

"These new results give us a deeper understanding of the nature of quantum computation. They also clarify the practical requirements for designing a realistic quantum computer," said Joseph Emerson, professor of Applied Mathematics and Canadian Institute for Advanced Research fellow. "I expect the results will help both theorists and experimentalists find more efficient methods to overcome the limitations imposed by unavoidable sources of noise and other errors."

Quantum theory was introduced to the concept of contextuality nearly a half century ago. Contextuality showed how it was impossible to explain measurements on quantum systems in the same way as classical systems.

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As an example, a measurement of a classical system, like color, is merely a revelation of a property already inherent in the system prior to measurement. Conversely, in the quantum world, a discovered property due to measurement is different than the property the system had prior to measurement. Putting it more plainly, the observed properties are dependent upon how the observation was carried out.

According to the researchers, an example of these differing concepts can best be understood via an analogy using standard playing cards. Should you turn over a simple playing card, you have a two-outcome measurement: It can either be a black suit or a red suit.

This analogy applied to quantum mechanics is starkly different. With nine playing cards placed in a 3x3 grid, the resulting observation would likely seem contradictory. This is because each row would require an even number of red cards while every column would require an odd number of red cards. It is impossible to conceive of a classical system that can replicate this outcome. This is because quantum measurements cannot be interpreted as merely revealing a pre-existing property in the same way that flipping a card reveals a red or black suit.

The outcome of measurement depends upon all of the other measurements performed. This, say the researchers, is the full context of the experiment. Contextuality, then, means that quantum measurements cannot be thought of as simply revealing some pre-existing properties of the system under study. And that is what makes quantum mechanics weird!

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