Study finds weird magic ingredient for quantum computing

June 11, 2014
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 form of quantum weirdness is a key ingredient for building quantum computers according to new research from a team at the University of Waterloo's Institute for Quantum Computing (IQC).

In a new study published in the journal Nature, researchers have shown that a weird aspect of called contextuality is a necessary resource to achieve the so-called magic required for universal quantum computation.

One major hurdle in harnessing the power of a universal quantum computer is finding practical ways to control fragile quantum states. Working towards this goal, IQC researchers Joseph Emerson, Mark Howard and Joel Wallman have confirmed theoretically that contextuality is a necessary resource required for achieving the advantages of 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 the 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."

Quantum devices are extremely difficult to build 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. So-called magic states act as 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 universal quantum computer.

By identifying these magic states as contextual, researchers will be able to clarify the trade-offs involved in different approaches to building . The results of the study may also help design new algorithms that 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."

Contextuality was first recognized as a feature of quantum theory almost 50 years ago. The theory showed that it was impossible to explain measurements on quantum systems in the same way as classical systems.

In the classical world, measurements simply reveal properties that the system had, such as colour, prior to the measurement. In the , the property that you discover through measurement is not the property that the system actually had prior to the measurement process. What you observe necessarily depends on how you carried out the observation.

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.

Measurement outcomes depend on all the other measurements that are performed – the full context of the experiment.

Contextuality means that quantum measurements can not be thought of as simply revealing some pre-existing properties of the system under study. That's part of the weirdness of quantum mechanics.

Explore further: Researchers find nondestructive method to study quantum wave systems

More information: Paper: Contextuality supplies the magic for quantum computation, DOI: 10.1038/nature13460

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5 / 5 (1) Jun 12, 2014
1 / 5 (1) Jun 14, 2014
To give a quick example one could say that contextuality is much like the different ways that one can observe light. One can look directly at the source with the Mark I Eyeball, one can look at light hitting paper with the same eyes, one can look at the light coming through the paper with the Mk I Eye as well, or see it's reflection, or, one can measure it with photometers and get a result shown in the change of electrical current...and all of these are just simple, basic ways of observing light.

When one gets down to the quantum state/level the method of observation is ever so much more important, and the ways that one determines what is actually being observed have to take so many different things into account that having the 'noise' removed from the system depends partially on what the researcher thinks the signal is. So where different experiments get different answers, but they can all be distilled down to single sets of relevant data working within the varied contexts bounds
not rated yet Jun 14, 2014
The context is the main aspect of so called weak measurement. You may imagine it like the attempt to detect the path of falling droplets from dripping faucet with their impact to pencil placed into path of droplets (i.e. in purely mechanical way). This method indeed works, but each droplet is destroyed during this (we are saying in quantum mechanics, the wave function of droplet collapsed). But we can arrange the measurement in stroboscopic way and measure the path of each droplet gradually in sequence of repetitive way. Each droplet will be still destroyed, but in CONTEXT of all measurement we can get the complete path of droplets as if they would survive the detection of path unharmed. A deeper analysis reveals, it's not context but a memory of observer, which assigns the observation into its proper context: the observed objects are entangled with observer, who mediates the context of precedented and subsequent observations.
not rated yet Jun 14, 2014
In quantum mechanics the state of each object including the observer is determined with its wave function, which we can imagine like the surface wave of undulating droplet. The observer is formed with such an undulating droplets too, and when he touches the falling droplet, its surface undulations will add to his (i.e. observer's) surface undulations and they will be resonating here (observer servers as a memory device for wave function). The sharing of surface undulations i.e. wave functions is called the entanglement. Because the observer is massive, the original surface wave of droplet will be destroyed during this (wave function collapse) and replaced with surface wave of observer. But it will not be destroyed completely and it will still survive in form of surface undulations of observer. So when the observer touches another droplet, these undulations will merge with the surface state of new droplet and they together will help to restore the state of original droplet.
not rated yet Jun 14, 2014
In deBroglie wave mechanics each particle is surrounded with invisible wake wave, which results from its motion relative to vacuum. Because the vacuum is never at complete rest, the deBroglie wave is formed even around particles, which don't move macrosopically. This wave is invisible for light waves, but it still interferes and it affect the undulations of de Broglie waves of another particles during their approaching (no direct contact is actually necessary here). Now you can replace the surface waves from previous post with their deBroglie waves and you'll get nearly complete notion of what actually happens during sequence of weak measurements. This process is complex but still fully imaginable. Best of all, it can be nearly completely modeled with experiments involving droplets jumping at the water surface. It's not actually magic, as it has its tangible macroscopic analogy.
Jun 14, 2014
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