A new theoretical advance explains where the power of quantum computation comes from, and will help researchers design and build better computers and algorithms.

The strange properties of quantum mechanics give quantum computers the potential to perform some computations exponentially faster than conventional computers. But where the extra power comes from – and how best to take advantage of it – is in many ways still an open question.

A new paper in the journal Nature by CIFAR Fellow Joseph Emerson of the program in Quantum Information Science, along with colleagues at the Institute of Quantum Computing at the University of Waterloo, is a step towards solving the questions.

The paper shows that a quantum property called contextuality is the key. Contextuality refers to the fact that in quantum systems, a measurement will necessarily affect the thing being measured. For instance, if you want to measure the spin of a particle, it's wrong to think that there is a "real" spin just waiting to be revealed. Instead, the very act of measuring the spin helps determine what it will be.

"One way of thinking about contextuality is that inevitably measurements involve some kind of disturbance. I'm not just learning about some definite property the system had prior to the measurement. I can be learning about some property the system had, but only in a way that depends on how I did the measurement."

One of the leading approaches for quantum computing uses a technique called fault-tolerant stabilizer computation. It's a way of correcting errors that occur in quantum computers as the quantum states interact with the environment. By using a process called "magic-state distillation," quantum computers can be made to function dependably despite the noise introduced by the environment.

Emerson's paper shows that the only kinds of "magic states" that will yield quantum computational power are those that rely on contextuality.

"Ultimately this should be a tool for experimentalists, to set the bar for what they have to achieve if they want to build a quantum computer that is useful, perhaps as a litmus test for a quantum computer's viability," Emerson says.

Although the mathematical proof of the power of contextuality is limited for now to a particular kind of quantum computation, Emerson thinks that future work might show that it's a general feature of all quantum computation.

Emerson says that the result builds on earlier work from a collaboration with CIFAR Senior Fellow Daniel Gottesman (Perimeter Institute), which grew out of contact they had through the CIFAR program.

"The CIFAR quantum information network and CIFAR funding were both instrumental to developing this result, which was a collective effort from several members of my research group," Emerson says.