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Information was stored as quantum phase in an N-state Rydberg atom data register. One or more flipped states stored in an eight-state atomic wave packet could be retrieved in a single operation, in agreement with a recent proposal by Grover.Storage of information as quantum phase was first proposed several years ago in connection with a new class of computational algorithms based on the rules of quantum mechanics rather than classical physics (1). The analog of the binary bit, which is the smallest piece of classical information, is the two-level quantum system, or qubit (2). Introductions to this subject often begin with the observation that a qubit differs from a bit because it can be prepared in more than two different states (3). For example, if the two levels are designated ͉0͘ and ͉1͘, then superpositions such as [͉0͘ ϩ exp(i)͉1͘]/ ͌ 2 are possible states of the qubit. Here, the real number is the quantum phase difference between probability amplitudes of the two levels in the superposition. Thus quantum phase is present in quantum algorithms, and its maintenance, control, and measurement may be essential factors in the performance of quantum computations.One example of an algorithm where quantum phase plays an essential role is the database search problem proposed by Grover (4, 5). Grover's search differs from some other quantum algorithms because it does not require any nonlocal entanglement of different degrees of freedom in the system. If information is stored as phase, then the superposition principle of quantum mechanics provides an efficient method to search the database (6). Superposition is also present in some classical analog data storage media, such as optical holograms, which use the classical phases of interfering electromagnetic waves; however, quantum systems contain the additional nonclassical feature of wave function collapse after a measurement.In his original paper on this subject, Grover asked the following question: When an N-state quantum register (composed of log 2 N qubits) is prepared with one state phase-shifted from all the others, how many operations does it take to find the flipped state (4)? Grover's algorithm takes only order ͌ N steps, whereas classical algorithms require order N/2 steps. The algorithm performs an inversion about the average defined by the following unitary operation D on the N-element state vector:This operation amplifies the flipped state and attenuates the others. There have been several recent demonstrations of this search, using qubit systems based on magnetic resonance (7,8) or photon interference (9). Grover's second paper considers the case when the database is capable of receiving a single query on all of its states simultaneously. This produces a large payoff in parallelism: The search algorithm now takes only a single quantum operation (5).We have investigated the storage and retrieval of information in the quantum phase of a coherent superposition state of energy levels in a highly excited atom. Two situations were examined. First, we prepared a...

We have constructed an automated learning apparatus to control quantum systems. By directing intense shaped ultrafast laser pulses into a variety of samples and using a measurement of the system as a feedback signal, we are able to reshape the laser pulses to direct the system into a desired state. The feedback signal is the input to an adaptive learning algorithm. This algorithm programs a computer-controlled, acousto-optic modulator pulse shaper. The learning algorithm generates new shaped laser pulses based on the success of previous pulses in achieving a predetermined goal.

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