Quantum Computing

A quantum computer is a device in which data can be stored in a network of quantum mechanical two-level systems, such as spin-1/2 particles or two level atoms. The quantum mechanical nature of such systems allows the possibility of a powerful new feature to be incorporated into data processing, namely the capability of performing logical operations upon quantum mechanical superpositions of numbers. In a conventional digital computer each data register is, throughout any computation, always in a definite state "1" or "0"; however in a quantum computer each data register (or "qubit") will be in an undetermined quantum superposition of two states |1> and |0>. Calculations would then be performed by external interactions with the various two-level systems that constitute the device, in such a way that logic gate operations involving two or more different qubits can be realized. The final result would be obtained by measurement of the quantum mechanical probability amplitudes at the conclusion of the calculation. The "killer application" for quantum computers is a quantum algorithm called Shor's algorithm after its inventor, Peter Shor of AT&T Bell Labs. This algorithm allows the determination of the prime factors of large composite numbers efficiently, which has tremendous potential applications. So far, the most promising hardware proposed for implementation of such a device seems to be the cold-trapped ion system devised by Ignacio Cirac and Peter Zoller of the University of Innsbruck, Austria.

Figure 1.

Their design, which is shown schematically in figure 1, consists of a string of ions stored in a linear radio-frequency trap and cooled sufficiently that their motion, which is coupled together due to the Coulomb force between them, is quantum mechanical in nature. Each qubit would be formed by two internal levels of each ion, a laser being used to perform manipulations of the quantum mechanical probability amplitudes of the states; conditional two-qubit logic gates being realized with aid of the excitation or de-excitation of quanta of the ions' collective motion. At Los Alamos we are building a prototype quantum computer based on this scheme. For various reasons, singly ionized Calcium seems to be the best choice of ion. A simplified energy level diagram is shown in figure 2, with transition wavelengths and decay times. The engineering problems associated with making such a device work are formidable. Firstly an ion trap had to be designed and built; in January of 1997, Calcium ions were confined in the ion trap that has been built by the quantum information group here at Los Alamos. Next the ions have to be cooled down to their ground state; we are currently performing numerical simulations of the laser cooling procedure to establish the optimum laser powers and wavelengths to do this job. Once the ions are cooled, the computation will be performed by a series of laser pulses directed at one or other of the ions; each pulse must transfer population from one level of the ion to a different level, without exciting any third level, or affecting any of the adjacent ions. Sometimes the laser will be used to excite a quantum of the ions' oscillations, requiring the that the laser be in a standing wave. Chosing the best combination of lasers and energy level of the ion, and then inventing ways in which these operations can be performed reliably with the available technology is a complicated problem of atomic and optical physics. Of course, it will be impossible to perform all of the operations required to execute a quantum algorithm completely reliably, and so there is also a lot work being done here on the theory of fault tolerant quantum computation.

Figure 2.

Address scientific comments and questions to

Daniel James <dfvj@t4.lanl.gov>

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