March 17, 2014
Nippon Telegraph and Telephone Corp. (NTT; Head Office: Chiyodaku, Tokyo; President: Hiroo Unoura) proposed a method for generating a largescale entangled quantum state^{(*1)} of ultracold atoms in an optical lattice^{(*2)} with high fidelity and short operation time, which becomes a resource for quantum computers^{(*3)}. This result solves important problems toward the realization of a quantum computer, such as scalability of quantum bits and decreasing the errors. This result paves the way for realizing a millionbitscale quantum computing.
This will be published online in the US science journal “Physical Review Letters” on March 17, 2014. This research was supported in part by Japan Science and Technology Agency, CREST.
The biggest challenges for realizing a quantum computer (Fig. 1 ) are obtaining a scalability of quantum bits and decreasing the errors. An optical lattice recently gets attention as a good candidate for solving these problems. In an optical lattice (Fig. 2 ), single atom can be periodically confined in each site of the lattice with a distance of about light wavelength (< 1 μm). Compared to the other physical systems, an optical lattice is expected to be a great technology that can store many atoms in a very small volume and in a highly ordered manner, where atoms can serve as uniform and ideal quantum bits. An optical lattice clock^{(*4)} (Fig. 3 ) is a promising application of this technology and has already been experimentally demonstrated. If one can make a special largescale entangled quantum state (Fig. 4 ) among huge number of atoms, then one can realize measurementbased quantum computation by performing individual atom measurements on it, which are more simple operations compared to quantum gates (Fig. 5 ). An optical lattice can compactly array many atoms, however, we have not yet established any method that can generate a largescale entangled quantum state with high fidelity and short operation time, which are necessary for the realization of a quantum computer.
NTT basic research laboratories and NTT secure platform laboratories have collaborated to exploit their advanced techniques on ultracold atoms and quantum information processing to this achievement. They, for the first time, successfully proposed a method for generating a largescale entangled quantum state of atoms confined in optical lattice with high fidelity (>99%) and short operation time (~1ms), which can be used as a computational resource for quantum computing. The existing methods have tradeoffs such that highfidelity gate operations work slowly or fast gate operations offer low fidelity. Moreover, the existing methods have a problem that multibit operation makes a crosstalk and causes a serious error. In this research, NTT proposes a new entanglement generation method with high fidelity, short operation time and scalability, which solves the above tradeoffs by ingeniously controlling several laser lights for designing the optical lattice. This result opens up a possibility of the realization of quantum computer with a million scale quantum bits.
An optical lattice is an artificial crystal made by lasers and an ideal crystal without defects and impurities. This crystal has a periodic structure with a distance of about light wavelength (< 1 μm) and can stably confine an atom in each lattice site. With the present technology, one can confine about a million atoms within a 3dimensional space with 100 μm on a side. We can use the huge number of atoms as homogeneous and ideal quantum bits.
In order to decrease the errors of quantum bits, they should not interact with each other. However, when one tries to make entanglement between quantum bits, they have to interact with each other and this results in producing unwanted errors (Fig. 6 ). In this research, NTT proposes a method to utilize only one physical state for mediating quantum bits and actively use it as an ancillary state, then we succeed to make highfidelity quantum entangling gates (Fig. 7 ). We propose a “phasetuning method” (Fig. 8 ) for solving the tradeoff between fidelity and operation time, a “pairwise control method” (Fig. 9 ) for generating entanglement in parallel without producing a crosstalk, and an “error removal method” (Fig. 10 ) for obtaining a better errortolerance by converting errors to losses. The great advantage is that this method can be simply implemented by combining the currently established technologies such as controlling the wavelength and strength of laser (microwave) lights. The present limit of the scale (about a million atoms) only depends on the atom trap technology. If much greater number of atoms can be trapped in future, this method can be applied in the same way.
We verified the performance of this method by abinitio physical modeling and exact numerical simulations ^{(*5)}. Ultracold atoms in an optical lattice are considered to be a clean and ideal physical system, which makes a theoretical evaluation highly realistic. Therefore this method will be faithfully realized in an experiment.
We plan to study the detailed conditions for experimentally demonstrating the generation of largescale entangled quantum state based on the present method. In parallel, we plan to develop an essential experimental technique for measuring the quantum state of individual atoms. Moreover, we try to generate the entangled quantum state in a twodimensional optical lattice, where the individual atom measurement is easier to perform in contrast to the three dimensional case, and try to demonstrate the measurementbased quantum computation in a scale of 10,000 quantum bits within five years. Our goal is to realize a largescale quantum computation using one million quantum bits in a threedimensional optical lattice.
Nippon Telegraph and Telephone CorporationScience and Core Technology Laboratory Group, Public Relationsainfo@lab.ntt.co.jp 

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