Global symmetry not required for fast quantum search
A quantum particle can search for an item in an unsorted "database" by jumping from one item to another in superposition, and it does so faster than a classical computer ever could.
In a complete graph (left) every node is connected to every other. For other well studied graphs, the Paley graph in the center and the Latin square graph on the right, that is not true. A quantum particle could hop directly to the target position, in red, only from connected nodes, marked in blue.
Credit: Tom Wong, UC San Diego
This assertion assumes, however, that the particle can directly hop from any item to any other. Any restriction on which items the particle can directly hop to could slow down the search.
"Intuition says that a symmetric database allows the particle to hop freely enough to retain the quantum speedup, but our research has shown this intuition to be false," says Tom Wong, a physicist at the University of California, San Diego.
In a paper accepted for publication by Physical Review Letters, the researchers used a technique familiar to physicists called "degenerate perturbation theory" in a novel way to prove that global symmetry is not required for a sped up search.
Information scientists represent the database to be searched as a graph. In globally symmetric graphs, the nodes can be swapped with each other such that the connections between them are preserved. "Strongly regular graphs" don't share this property, but this analysis shows they also support a fast search through local symmetries.
Their finding extends the use of this theory to the field of quantum information science and expands the kinds of data structures on which quantum computing outperforms classical computing.
Jonatan Janmark, KTH Royal Institute of Technology in Stockholm, Sweden and UC San Diego's Department of Mathematics and David Meyer, professor of mathematics at UC San Diego co-authored the work.
The Defense Advanced Research Projects Agency partially supported this work as part of its Quantum Entanglement Science and Technology program. Additional funding came from the Air Force Office of Scientific Research as part of the Transformational Computing in Aerospace Science and Engineering Initiative, and the Achievement Awards for College Scientists Foundation.
Tom Wong | Eurek Alert!
Tiniest Particles Shrink Before Exploding When Hit With SLAC's X-ray Laser
05.02.2016 | Tohoku University
Scientists create new state of matter: Quantum gas, liquid and crystal all-in-one
02.02.2016 | Universität Stuttgart
Automobiles increase the mobility of their users. However, their maneuverability is pushed to the limit by cramped inner city conditions. Those who need to...
Advance in biomedical imaging: The University of Würzburg's Biocenter has enhanced fluorescence microscopy to label and visualise up to nine different cell structures simultaneously.
Fluorescence microscopy allows researchers to visualise biomolecules in cells. They label the molecules using fluorescent probes, excite them with light and...
NASA's follow-on to the successful ICESat mission will employ a never-before-flown technique for determining the topography of ice sheets and the thickness of sea ice, but that won't be the only first for this mission.
Slated for launch in 2018, NASA's Ice, Cloud and land Elevation Satellite-2 (ICESat-2) also will carry a 3-D printed part made of polyetherketoneketone (PEKK),...
In the last decades, sea level has been rising continuously – about 3.3 mm per year. For reef islands such as the Maldives or the Marshall Islands a sinister picture is being painted evoking the demise of the island states and their cultures. Are the effects of sea-level rise already noticeable on reef islands? Scientists from the ZMT have now answered this question for the Takuu Atoll, a group of Pacific islands, located northeast of Papua New Guinea.
In the last decades, sea level has been rising continuously – about 3.3 mm per year. For reef islands such as the Maldives or the Marshall Islands a sinister...
The ‘Internet of Things’ is growing rapidly. Mobile phones, washing machines and the milk bottle in the fridge: the idea is that minicomputers connected to these will be able to process information, receive and send data. This requires electrical power. Transistors that are capable of switching information with a single electron use far less power than field effect transistors that are commonly used in computers. However, these innovative electronic switches do not yet work at room temperature. Scientists working on the new EU research project ‘Ions4Set’ intend to change this. The program will be launched on February 1. It is coordinated by the Helmholtz-Zentrum Dresden-Rossendorf (HZDR).
“Billions of tiny computers will in future communicate with each other via the Internet or locally. Yet power consumption currently remains a great obstacle”,...
02.02.2016 | Event News
26.01.2016 | Event News
26.01.2016 | Event News
05.02.2016 | Life Sciences
05.02.2016 | Materials Sciences
05.02.2016 | Physics and Astronomy