Symmetric Phases of Universal Quantum Computation

Jacob Miller and Akimasa Miyake have recently published a paper in Physical Review Letters giving strong evidence that certain forms of symmetric topological quantum matter can be utilized ubiquitously to power quantum computation. Their work is carried out within measurement-based quantum computation, where computation is extracted from a fixed quantum “resource state” using local measurements. In this setting, the power of computation attributes the physical properties of the resource state, but the properties which guarantee a state can carry out universal quantum computation are still unknown.
In their work, the authors study a model of symmetric topological matter and identify special states in each phase which enable universal quantum computation precisely when they possess nontrivial quantum order. This gives an infinite family of new universal resource states whose structure perfectly mirrors a recent classification of symmetric quantum order coming from condensed matter physics. These special resource states are distinguished by their “fractional symmetry”, a property already noticed in previous universal resource states, but which hadn’t been investigated systematically. Overall, the work provides a concrete research program for identifying phases of universal quantum computation within the setting of symmetric quantum matter.
The full article can be found online at Phys. Rev. Lett. 120, 170503 (2018).
Classification of special resource states with fractional symmetry.

Chair’s Award of Best Dissertation in Physics

Jacob Miller completed his PhD under Akimasa Miyake about a year ago, with a dissertation entitled Measurement-Based Quantum Computation and Symmetry-Protected Topological Order.  In his thesis, Jacob made fundamental contributions to understanding the kind of many-body entanglement that can enable universal quantum computation within the framework of measurement-based quantum computation.  CQuIC’ers were reminded of Jacob’s outstanding research at the 2018 Physics and Astronomy Convocation on May 12, when he was awarded the Chair’s Award for Best Dissertation in Physics for the preceding year.   Notable not just for outstanding research, Jacob’s dissertation also contained a full-page paean to CQuIC’s TACLA Coffee Club, for which Jacob was Coffee Commander for several years.  Recognizing fully the mutual relationship between coffee and research, Jacob wrote: “For there is no question that in the face of tough research puzzles, prickly conundrums, and flummoxes of every type, we can find solace in the words of noted abolitionist Henry Ward Beecher that, `A cup of coffee—real coffee—homebrowned, home ground, home made, that comes to you dark as a hazel-eye . . .  neither lumpy nor frothing on the Java: such a cup of coffee is a match for twenty blue devils and will exorcise them all.’ ’’


Topological quantum matters are useful for sensing

Akimasa Miyake has recently published in a new journal Quantum Science and Technology in collaboration with Stephen Bartlett (University of Sydney) and Gavin Brennen (Macquarie University), presenting a scheme of robust quantum sensing using one-dimensional strongly-interacting spin chains. It takes advantage of passive error-preventing properties of a symmetry-protected topologically ordered phase, to measure the direction and strength of an unknown electronic field.

The full article can be found online at Quantum Sci. Technol. 3, 014010 (2018) .

How can one verify the performance of a near-term quantum device?

Jacob Miller, Keith Sanders, and Akimasa Miyake have recently published a paper in Physical Review A presenting a distinctive means of demonstrating the unique computational power inherent in quantum mechanics. Their work follows other proposals in the growing topic of “quantum computational supremacy”, which aims to construct a realistic device implementing a sampling-based computational task which is otherwise impossible with any modern digital computer. Such sampling tasks must achieve a careful balance, where they are both easier to implement in a laboratory than full quantum computation, but must also be hard enough to require genuinely quantum effects to solve.
The proposal put forward by Miller, Sanders, and Miyake has several desirable features. First, it can carry out its computational task in a constant amount of time, helping to mitigate the harmful effects of experimental noise. Secondly, it is capable of seamlessly verifying the correct operation of the difficult sampling task with exactly the same resources required to perform the sampling itself. This latter property is important, since the difficulty of the sampling generally makes it extremely hard to check whether or not a realistic device is actually achieving quantum supremacy. While previous works had satisfied one or the other of these properties, the current proposal uses the framework of measurement-based quantum computation and insights from the study of quantum phases of matter to simultaneously achieve both.
The full article can be found online at Phys. Rev. A 96, 062320 (2017).

(a) Quantum circuit to sample probability distributions related to certain Boolean functions. The task is expected to be intractable to modern computers. (b) Our measurement-based implementation, which realizes a sampling task and its verification procedure under the same resource requirement.