Researchers Discover “Magic” Ingredient for Quantum Computing

Contextuality Supplies the Magic for Quantum Computation

This geometric figure illustrates the concept of magic states and their relation to contextuality. The triangular region contains quantum states that are not magic and do not exhibit contextuality. States outside the triangle do exhibit contextuality and may be useful as a resource in the magic-state model of quantum computing. Credit: University of Waterloo

A newly published study establishes that quantum contextuality is a critical resource for quantum speed-up within the leading model for fault-tolerant quantum computation, magic state distillation.

A form of quantum “weirdness” has been found, by researchers at Waterloo’s Institute for Quantum Computing (IQC), to be a key ingredient for building a quantum computer.

In a paper published in the journal Nature, IQC researchers have shown that quantum contextuality is a necessary resource to achieve the “magic” required for universal quantum computation.

“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 lead author of the paper. “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 major hurdles to harnessing the power of a universal quantum computer is finding practical ways to control fragile quantum states. In this context, Howard and IQC researchers Joseph Emerson and Joel Wallman have confirmed theoretically that contextuality is a necessary resource required for achieving the advantages of quantum computation.

What is contextuality?

Contextuality is one of the “weird” features of quantum theory that distinguishes the quantum world from the classical one. In the classical world, measurements simply reveal properties that the system had, such as color, prior to the measurement.

In quantum, the property you discover through a measurement is not simply a property that the system actually had prior to the measurement process. What you observe necessarily depends on how you carried out the observation – it depends on the “context” of the experiment.

Magic quantum states are contextual

One of the reasons quantum devices are extremely difficult to build is because they must operate in an environment that is noise-resistant. The term “magic” refers to a particular approach to building noise-resistant quantum computers known as magic-state distillation. To overcome the detrimental effects of unwanted noise, techniques called “fault-tolerant” have been developed.

Magic states are a crucial, but difficult to achieve and maintain, extra ingredient that boosts the power of a quantum device to achieve the improved processing power of a quantum computer. By identifying these magic states as contextual, researchers will be able to clarify the trade-offs involved in different approaches. It might help design new algorithms that exploit the special properties of these magic states more fully.

“The result gives us a deeper understanding of the nature of quantum computation and also clarifies the practical requirements for designing a realistic quantum computer,” said Emerson, associate professor of Applied Mathematics and Canadian Institute for Advanced Research (CIFAR) 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.”

Contextuality and playing cards

To better understand contextuality – imagine turning over a playing card. It will be either a red suit or a black suit – a two-outcome measurement.

Now imagine nine playing cards laid out in a grid with three rows and three columns. Quantum mechanics predicts something that seems contradictory – there must be an even number of red cards in every row and an odd number of red cards in every column. Try to draw a grid that obeys these rules and you will find it impossible. It’s 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. This is part of the weirdness of quantum mechanics.

Reference: “Contextuality supplies the ‘magic’ for quantum computation” by Mark Howard, Joel J. Wallman, Victor Veitch and Joseph Emerson, 11 June 2014, Nature.
DOI: 10.1038/nature13460
arXiv: 1401.4174

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