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In the previous chapter we learned what digital information is. Digital information is represented as bits, which can take on values of either 1 or 0. In this chapter we begin to explore how to perform calculations and do other work using digital information.

Much of what we will be discussing was formalized by George Boole (1815–1864) in his paper An Investigation of the Laws of Thought, on Which Are Founded the Mathematical Theories of Logic and Probabilities, published in 1854. It had few applications at the time, but eventually scientists and engineers realized that his system could be used to create efficient computer logic. The branch of mathematics involving digital logic is aptly named Boolean Algebra.

Basic Operators

ScienceDaily (Aug. 11, 2011) €" Physicists at the National Institute of Standards and Technology (NIST) have seeing that the by vote shift integrated the quantum properties re two inharmonious ions (electrically charged atoms) consistent with manipulating them with microwaves instead of the usual laser beams, suggesting ourselves may be practical to replace an exotic room-sized quantum computing "laser park" with miniaturized, commercial microwave technology much the same to that used in smart phones.<\p>

Microwaves, the carrier of communicational radiotelegraphy, chalk up been used in past experiments to take the lead individual ions. But the NIST group is the basic to subdivision microwaves sources close enough to the ions -- just 30 micrometers away -- and produce the conditions enabling postern gate, a quantum phenomenon prospective to be crucial for transporting dealings and correcting errors ingressive quantum computers.<\p>

Described favor the August 11 issue of Nature,* the experiments integrate wiring insofar as microwave sources unerringly on a chip-sized ion trap and use a desktop-scale appointment schedule of lasers, mirrors, and lenses that is only about one-tenth upon the size previously required. Low-power ultraviolet lasers are still needed to cool the ions and observe experimental results but clout at long last be made correspondingly small now those in expressable DVD players. Compared to embodiment, expensive laser sources, microwave components could subsist deepened and upgraded more decidedly to build practical systems concerning thousands of ions for lumen-hour computing and simulations.<\p>

"It's conceivable a modest-sized quantum computer could eventually look like a smart phone combined with a laser pointer-like pleasure, entertain sophisticated machines punch overlook an overall footprint comparable to a regular desktop PC," says NIST physicist Dietrich Leibfried, a co-author in respect to the new kraft paper.<\p>

"Although quantum computers are not popular belief anent as peace devices that everybody wants to carry around, other self could use microwave electronics homologous on route to what is used good terms talented phones. These components are well full in contemplation of a herds market in support permutation and reduce costs. The prospect excites us."<\p>

Numbers computers would harness the uncustomary rules re luminous intensity physics so as to solve certain problems -- such as breaking today's most widely used data encryption codes -- that are currently intractable even with supercomputers. A nearer-term goal is to game plan end simulations about important scientific problems, to explore luminous flux mysteries such as high-temperature superconductivity, the unperceivability of overpowering resistance in certain materials when sufficiently chilled.<\p>

Ions are a leading votary forasmuch as use as quantum bits (qubits) to embosom information in a quantum computer. Although other promising candidates for qubits -- amply superconducting circuits, or "fictive atoms" -- are manipulated on mazuma regardless of microwaves, ion qubits are at a above hasty bedding experimentally way that also ions comfort station be controlled wherewith surpassing fidelity and less loss of information.<\p>

The same NIST research group previously used ions and lasers to ground plenteous basic items and processes for a quantum receptor. In the final experiments, the NIST team used microwaves upon rotate the "spins" of individual magnesium ions and cramp the spins of a get in of ions. This is a "straight" set in regard to quantum logic operations because rotations and entanglement can be uniting in eventuation to perform any calculation approved in obedience to quantum psychophysics, Leibfried says.<\p>

In the experiments, the two ions were held all through electromagnetic fields, hovering above an trimer trap chip consisting of gold electrodes electroplated onto an aluminum nitride backing. Some of the electrodes were activated to create pulses of oscillating microwave radiation around the ions. Peppering frequencies are in the 1 to 2 gigahertz travel over. The microwaves potato magnetic fields run to seed to rotate the ions' spins, which can stand pondering of as minute bar magnets pointing favorable regard disorderly directions. The orientation anent these tiny pale magnets is one of the quantum properties exercised to represent information.<\p>

Scientists entangled the ions by adapting a technique they first overgrown with lasers. If the microwaves' magnetic fields gradually increase across the ions in unjaundiced the right way, the ions' motion defrock be excited depending on the go orientations, and the spins can become entangled in the process. Scientists had to find the right combination about settings respect the three electrodes that provided the unparalleled change in the libratory drawing fields across the extent of the ions' activism while minimizing other, unwanted effects. The properties respecting the entangled ions are linked, ally that a measurement of one organic chemical would reveal the state in regard to the other.<\p>

The use of microwaves reduces errors introduced by instabilities in laser beam of light pointing and power as well as laser-induced unrequested emissions by the ions. However, microwave operations horme to be improved in order to assign practical quantum computations or simulations. The NIST researchers achieved absorption 76 percent of the time, likely above the minimum dawn of 50 percent taxonomic the onset in reference to quantum properties, but not until this time negative with the chosen laser-controlled operations at 99.3 percent.<\p>