An absorption image of the expanding Bose-Einstein condensate, demonstrating the diffraction pattern which constitutes the factoring signal. Image credit: Mark Sadgrove, et al.
By Lisa Zyga, Physics / Physics
(PhysOrg.com) -- Theoretically, quantum computing has the potential to work more efficiently and accurately than classical computing for certain processes, such as factoring. But quantum methods are experimentally challenging, since they often require tiny, fragile systems that are difficult to handle.
Recently, some approaches have suggested “rediscovering” old techniques such as analog computing, which usually lie outside the usual qubit architecture, in the hope of finding new pathways to experimentally realize quantum computation. For instance, using analog techniques and the quantum properties of atomic clusters called Bose-Einstein condensates, a team of researchers from Japan has recently improved upon a classical factoring algorithm.
“Any algorithm where the output is continuous rather than divided into bits (as on a digital computer) is analog,” Mark Sadgrove of the Japan Science and Technology Agency (JSTA) told PhysOrg.com. “In our case, we measure quantities which are continuous in principle. By this I mean that the energy or the probability to find an atom with a given momentum are continuous variables, in theory. In practice, we use a finite number of atoms, so in some sense the final outputs are discrete, but theoretically the result of the computation is analog in nature.”
Sadgrove and his colleagues Sanjay Kumar of the University of Electro Communications (UEC) in Chofushi, Chofugaoka, and Ken’ichi Nakagawa, who has affiliations with both JSTA and UEC, have demonstrated that, compared with the classical implementation, their method can distinguish more accurately between factors and non-factors of large numbers. Specifically, their quantum system could increase the accuracy of a classical algorithm called the Gauss sum algorithm, a technique pioneered by Wolfgang Shleich of Ulm University in Germany.
Their quantum system consists of thousands of rubidium-87 atoms that are cooled to near absolute zero to form a Bose-Einstein condensate (BEC). At such a low temperature, the atoms’ wavelengths increase and overlap, so that the cluster becomes a single quantum state and obeys quantum laws, yet has a relatively large size.
The physicists zapped the BEC with a brief light pulse composed of two counter-propagating beams. They programmed one beam to have phase jumps (to displace the beam’s wavelength), while the second beam had no phase jumps. Programming the first beam served as the input method, representing an integer to be factored.
The dynamics of the atoms subject to the pulse could then be used to perform factoring calculations. After applying the pulse, the researchers allowed the BEC to expand freely for 14 ms. They then took an absorption image of the BEC, which showed that the pulse had separated the atoms in the BEC into different momentum orders. The atoms formed a diffraction pattern, based on the relative number of atoms in each momentum order, which the physicists could interpret as the “factoring signal.” Specifically, high-momentum atoms represented factors, and low-momentum atoms represented non-factors.
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