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Wednesday, July 28, 2010

[1007.3624] Unbounded-error quantum computation with small space bounds

 

 

Authors: Abuzer Yakaryilmaz, A. C. Cem Say

(Submitted on 21 Jul 2010)

Abstract: We prove the following facts about the language recognition power of quantum Turing machines (QTMs) in the unbounded error setting: QTMs are strictly more powerful than probabilistic Turing machines for any common space bound $ s $ satisfying $ s(n)=o(\log \log n) $. For "1.5-way" Turing machines, where the input tape head is not allowed to move left, the above result holds for $s(n)=o(\log n) $. We also give a characterization for the class of languages recognized with unbounded error by one-way quantum finite automata (QFAs) with restricted measurements. It turns out that these automata are equal in power to their probabilistic counterparts, and this fact does not change when the QFA model is augmented to allow general measurements and mixed states. Unlike the case with classical finite automata, when the QFA tape head is allowed even 1.5-way movement, more languages become recognizable. We define and use a QTM model that generalizes the other variants introduced earlier in the study of quantum space complexity.

Comments:
A preliminary version of this paper appeared in the Proceedings of the Fourth International Computer Science Symposium in Russia, pages 356--367, 2009

[1007.3624] Unbounded-error quantum computation with small space bounds

 

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Monday, July 12, 2010

This remarkable "ion trap" turns charged atoms into quantum information carriers

 

This remarkable "ion trap" turns charged atoms into quantum information carriersA new device uses optical fibers to measure light from individual ions. Since these charged atoms store quantum information, this ion trap could allow us to build practical quantum computers and to link light and matter at the quantum level.

The real stumbling block for quantum computers is finding something that can practically be used to house a qubit, the building blocks of quantum information. This ion trap makes the electrically charged atoms a genuine possibility by isolating each one and making possible the extraction of individual qubits of information. In fact, the researchers were able to use them in some very rudimentary experimental quantum computing.

This remarkable "ion trap" turns charged atoms into quantum information carriers

So how does it work? The device is just one square millimeter in size and has a built-in optical fiber. Tiny electrodes are used to trap the ions that pass through it within 30 to 50 micrometers below the surface of the device. The ion is then within reading distance of the optical fiber, which detects the ion's fluorescence signals and uses that data to figure out the ion's quantum information content.

Previous attempts to read the fluorescence of ions have depended on external lenses located about 5 centimeters away. That may not sound like much, but it's a full 500 times further away from the ions than the fiber needs to be, which means the detection system can be miniaturized and packed in on a level never before imagined. A huge number of these fibers could be put on a single quantum computer chip, which just wouldn't be possible with the older lens system. The fiber method isn't as efficient as its lens counterpart, although its developers are confident they can improve the light absorption of the device. Either way, since ions give off millions of photos per second, they are plenty bright enough for the fibers to detect and read.

For this particular trap design, the researchers ultimately hope to pair individual photons with individual ions. That would allow information to be swapped from matter qubits to photon qubits. Matter qubits, like those using ions, are currently the preferred foundation of quantum computers, while photon qubits are used for quantum communications, which is thought to be the most secure form of communication possible. By linking data between the two types of qubits, the developers could set up a system that would bring together quantum computers and quantum communications networks.

Monday, July 5, 2010

Unusual quantum states may shake up quantum computing

 

 

Researchers have found a new method of controlling the quantum states of solid particles, and the research could enable a different approach to quantum computing, according to a paper published in Nature.

Using doped silicon, scientists found that they were able to exert control over the solid atoms using terahertz frequency radiation, getting the atoms to oscillate between states normally found in hydrogen atoms. While the equipment they used was very specialized, the authors hope that this new level of coherent control will allow for a different style of entanglement, as well as finer manipulation of quantum information held in excited atoms.

Scientists have had a field day using lasers to perform all manner of quantum manipulations on various particles: trapping  photons, entangling them, and sending them over long distances, even using this to perform simple quantum calculations. However, these quantum states are often unstable and hard to control, creating errors and unreliability in their information and in the calculations they perform.

To help fix this, a group of researchers are pursuing the use of well-known quantum states, called Rydberg states, using atoms in a solid. These states follow the rules of a formula that was designed to explain free hydroden atoms, but a special physical loophole allows larger atoms to be obey the formula, too.

Atoms that can be manipulated in Rydberg states have an interesting property: their ground states are too compact to interact with each other. If two such atoms were used for quantum computing, they could be entangled only in their excited states, leaving their ground states independent. This could provide a new quantum information relay method.

A material's impurities can occupy Rydberg states if they have exactly one more valence electron than the host material. Phosphorus-doped silicon, a common type of semiconductor, fits the bill perfectly. The researchers behind the new paper decided they would use radiation in the terahertz range on the phosphorus impurities, hoping that the fine oscillations would let them switch the atoms between two closely spaced Rydberg states.

In order to prove they were actually exerting control over the phosphorus at a quantum level, the researchers had to look for two kinds of activity in the atoms. One was Rabi oscillations, a set of waves that indicate the atom is being driven between a ground and an excited state by the laser. If the laser was set to the right frequency, it would create a superposition of the ground and excited wavefunctions that emits a simple, easily detected wavepacket that oscillates over time.

The other thing they needed to find was photon echoes from the particles. An echo comes from putting a set of particles into a coherent state by zapping them with a laser, then letting their wave functions evolve over time. A second laser pulse would reverse the evolution and cause the particles to send out an extra "echo" of energy.

Packed into the echo is a record of the environment's effects on the atom—a sort of "while you were away" note to would-be observers. Reading the echo would allow researchers to figure out exactly how long the wavefunctions of the atoms would take to "dephase," or get all confused by environmental effects. That length of time is a stand-in measure for how resilient the wavefunctions are, and how long they could be used to hold or transfer quantum information.

Using the Free Electron Laser for Infrared Experiments (FELIX) in the Netherlands, the researchers were able to create laser pulses that exerted remarkable, and remarkably fast, control over the phosphorus atoms. At terahertz frequencies, they were able to stimulate both Rabi oscillations and photon echoes. The Rabi oscillations indicated a superposition of the atoms' ground and first excited states, and had energies that corresponded to the Rydberg series they were looking for.

The photon echoes that the atoms generated indicated that they had a dephasing time of 160 picoseconds. This sounds too short to get much of anything accomplished, but the electrons in the phosphorus atoms were oscillating between states every 100 femtoseconds. If the atom were carrying information, theoretically this means users have over a thousand opportunities to read the atom before its wavefunction gets too distorted to use.

Going forward, the authors of the paper seemed most interested in the prospects for entangling pairs of Rydberg-capable impurities. A Bell state where each atom's ground state is entangled with the other's excited state sounds particularly interesting, since reading one of the atoms has only a chance of setting the other. Aside from that, the researchers hope their new method for exerting coherent control over the quantum states of a solid, widely used material will introduce a bit more versatility to the field of quantum computing.

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