Quantum Mechanics helps in searching for a needle in a haystack

Quantum mechanics can speed up a range of search applications over unsorted data. For example imagine a phone directory containing N names arranged in completely random order. To find someone's phone number with a probability of 50%, any classical algorithm (whether deterministic or probabilistic) will need to access the database a minimum of O(N) times. Quantum mechanical systems can be in a superposition of states and simultaneously examine multiple names. By properly adjusting the phases of various operations, successful computations reinforce each other while others interfere randomly. As a result, the desired phone number can be obtained in only O(sqrt(N)) accesses to the database.Comment: Postscript, 4 pages. This is a modified version of the STOC paper (quant-ph/9605043) and is modified to make it more comprehensible to physicists. It appeared in Phys. Rev. Letters on July 14, 1997. (This paper was originally put out on quant-ph on June 13, 1997, the present version has some minor typographical changes

The Kinematics of the Ionized and Molecular Hydrogen in the Starburst Galaxy NGC 253

Near-infrared H_2 1-0 S(1) and Br_gamma velocity curves along the major axis of NGC 253 have revealed a central velocity gradient that is seven times steeper than that shown by the optical velocity curve. This is interpreted as an optical depth effect due to dust. Approximately 35 mag of visual extinction in the center is required to match the SW side of the optical velocity curve. The spatial variation of the ratio of these lines to the CO (J=1-0) line is compared among starburst galaxies NGC 253, M82, and NGC 4945 to investigate the excitation mechanism responsible for the H_2 1-0 S(1) line.Comment: Uuencoded postscript file, 10 pages (4 tables included), 8 figures available on request to [email protected], Ap.J. (in press

Observations of the J = 2→1 transitions of ¹²C¹⁶O and ¹²C¹⁸O towards galactic H II regions

Observations are reported of the J = 2→1 transitions of CO and 12C18O at 230 and 219 GHz respectively from a number of galactic sources. A map of the central 1/2° × 1/2° of the Orion A molecular cloud is presented. The spectra are interpreted to derive molecular densities and abundance ratios in the molecular clouds observed

Structure and Star Formation in NGC 925

We present the results from an optical study of the stellar & star formation properties of NGC 925 using the WIYN 3.5m telescope. Images in B,V,R, & H-alpha reveal a galaxy that is fraught with asymmetries. From isophote fits we discover that the bar center is not coincident with the center of the outer isophotes nor with the dynamical center (from Pisano et al. 1998). Cuts across the spiral arms reveal that the northern arms are distinctly different from the southern arm. The southern arm not only appears more coherent, but the peaks in stellar and H-alpha emission are found to be coincident with those of the HI distribution, while no such consistency is present in the northern disk. We also examine the gas surface density criterion for massive star formation in NGC 925, and find that its behavior is more consistent with that for irregular galaxies, than with late-type spirals. In particular, star formation persists beyond the radius at which the gas surface density falls below the predicted critical value for star formation for late-type spirals. Such properties are characteristic of Magellanic spirals, but are present at a less dramatic level in NGC 925, a late-type spiral.Comment: accepted for publication in the August 2000 Astronomical Journal 12 pages, 3 tables, 14 figure

Efficient Scheme for Initializing a Quantum Register with an Arbitrary Superposed State

Preparation of a quantum register is an important step in quantum computation and quantum information processing. It is straightforward to build a simple quantum state such as |i_1 i_2 ... i_n\ket with $i_j$ being either 0 or 1, but is a non-trivial task to construct an {\it arbitrary} superposed quantum state. In this Paper, we present a scheme that can most generally initialize a quantum register with an arbitrary superposition of basis states. Implementation of this scheme requires $O(Nn^2)$ standard 1- and 2-bit gate operations, {\it without introducing additional quantum bits}. Application of the scheme in some special cases is discussed.Comment: 4 pages, 4 figures, accepted by Phys. Rev.

The structure, energy, and electronic states of vacancies in Ge nanocrystals

The atomic structure, energy of formation, and electronic states of vacancies in H-passivated Ge nanocrystals are studied by density functional theory (DFT) methods. The competition between quantum self-purification and the free surface relaxations is investigated. The free surfaces of crystals smaller than 2 nm distort the Jahn-Teller relaxation and enhance the reconstruction bonds. This increases the energy splitting of the quantum states and reduces the energy of formation to as low as 1 eV per defect in the smallest nanocrystals. In crystals larger than 2 nm the observed symmetry of the Jahn-Teller distortion matches the symmetry expected for bulk Ge crystals. Near the nanocrystal's surface the vacancy is found to have an energy of formation no larger than 0.5 to 1.4 eV per defect, but a vacancy more than 0.7 nm inside the surface has an energy of formation that is the same as in bulk Ge. No evidence of the self-purification effect is observed; the dominant effect is the free surface relaxations, which allow for the enhanced reconstruction. From the evidence in this paper, it is predicted that for moderate sized Ge nanocrystals a vacancy inside the crystal will behave bulk-like and not interact strongly with the surface, except when it is within 0.7 nm of the surface.Comment: In Press at Phys. Rev.

Semicausal operations are semilocalizable

We prove a conjecture by DiVincenzo, which in the terminology of Preskill et al. [quant-ph/0102043] states that ``semicausal operations are semilocalizable''. That is, we show that any operation on the combined system of Alice and Bob, which does not allow Bob to send messages to Alice, can be represented as an operation by Alice, transmitting a quantum particle to Bob, and a local operation by Bob. The proof is based on the uniqueness of the Stinespring representation for a completely positive map. We sketch some of the problems in transferring these concepts to the context of relativistic quantum field theory.Comment: 4 pages, 1 figure, revte