A quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors

We describe a new polynomial time quantum algorithm that uses the quantum fast fourier transform to find eigenvalues and eigenvectors of a Hamiltonian operator, and that can be applied in cases (commonly found in ab initio physics and chemistry problems) for which all known classical algorithms require exponential time. Applications of the algorithm to specific problems are considered, and we find that classically intractable and interesting problems from atomic physics may be solved with between 50 and 100 quantum bits.Comment: 10 page

Evaluation of LANDSAT MSS vs TM simulated data for distinguishing hydrothermal alteration

The LANDSAT Follow-On (LFO) data was simulated to demonstrate the mineral exploration capability of this system for segregating different types of hydrothermal alteration and to compare this capability with that of the existing LANDSAT system. Multispectral data were acquired for several test sites with the Bendix 24-channel MSDS scanner. Contrast enhancements, band ratioing, and principal component transformations were used to process the simulated LFO data for analysis. For Red Mountain, Arizona, the LFO data allowed identification of silicified areas, not identifiable with LANDSAT 1 and 2 data. The improved LFO resolution allowed detection of small silicic outcrops and of a narrow silicified dike. For Cuprite - Ralston, Nevada, the LFO spectral bands allowed discrimination of argillic and opalized altered areas; these could not be spectrally discriminated using LANDSAT 1 and 2 data. Addition of data from the 1.3- and 2.2- micrometer regions allowed better discriminations of hydrothermal alteration types

Singlet states and the estimation of eigenstates and eigenvalues of an unknown Controlled-U gate

We consider several problems that involve finding the eigenvalues and generating the eigenstates of unknown unitary gates. We first examine Controlled-U gates that act on qubits, and assume that we know the eigenvalues. It is then shown how to use singlet states to produce qubits in the eigenstates of the gate. We then remove the assumption that we know the eigenvalues and show how to both find the eigenvalues and produce qubits in the eigenstates. Finally, we look at the case where the unitary operator acts on qutrits and has eigenvalues of 1 and -1, where the eigenvalue 1 is doubly degenerate. The eigenstates are unknown. We are able to use a singlet state to produce a qutrit in the eigenstate corresponding to the -1 eigenvalue.Comment: Latex, 10 pages, no figure

Higher Order Methods for Simulations on Quantum Computers

To efficiently implement many-qubit gates for use in quantum simulations on quantum computers we develop and present methods reexpressing exp[-i (H_1 + H_2 + ...) \Delta t] as a product of factors exp[-i H_1 \Delta t], exp[-i H_2 \Delta t], ... which is accurate to 3rd or 4th order in \Delta t. The methods we derive are an extended form of symplectic method and can also be used for the integration of classical Hamiltonians on classical computers. We derive both integral and irrational methods, and find the most efficient methods in both cases.Comment: 21 pages, Latex, one figur

Tunable Oscillations in the Purkinje Neuron

In this paper, we study the dynamics of slow oscillations in Purkinje neurons in vitro, and derive a strong association with a forced parametric oscillator model. We demonstrate the precise rhythmicity of the oscillations in Purkinje neurons, as well as a dynamic tunability of this oscillation using a photo-switchable compound. We show that this slow oscillation can be induced in every Purkinje neuron, having periods ranging between 10-25 seconds. Starting from a Hodgkin-Huxley model, we also demonstrate that this oscillation can be externally modulated, and that the neurons will return to their intrinsic firing frequency after the forced oscillation is concluded. These results signify an additional functional role of tunable oscillations within the cerebellum, as well as a dynamic control of a time scale in the brain in the range of seconds.Comment: 12 pages, 5 figure

Low zinc status and absorption exist in infants with jejunostomies or ileostomies which persists after intestinal repair.

There is very little data regarding trace mineral nutrition in infants with small intestinal ostomies. Here we evaluated 14 infants with jejunal or ileal ostomies to measure their zinc absorption and retention and biochemical zinc and copper status. Zinc absorption was measured using a dual-tracer stable isotope technique at two different time points when possible. The first study was conducted when the subject was receiving maximal tolerated feeds enterally while the ostomy remained in place. A second study was performed as soon as feasible after full feeds were achieved after intestinal repair. We found biochemical evidence of deficiencies of both zinc and copper in infants with small intestinal ostomies at both time points. Fractional zinc absorption with an ostomy in place was 10.9% ± 5.3%. After reanastamosis, fractional zinc absorption was 9.4% ± 5.7%. Net zinc balance was negative prior to reanastamosis. In conclusion, our data demonstrate that infants with a jejunostomy or ileostomy are at high risk for zinc and copper deficiency before and after intestinal reanastamosis. Additional supplementation, especially of zinc, should be considered during this time period

Classical simulation of noninteracting-fermion quantum circuits

We show that a class of quantum computations that was recently shown to be efficiently simulatable on a classical computer by Valiant corresponds to a physical model of noninteracting fermions in one dimension. We give an alternative proof of his result using the language of fermions and extend the result to noninteracting fermions with arbitrary pairwise interactions, where gates can be conditioned on outcomes of complete von Neumann measurements in the computational basis on other fermionic modes in the circuit. This last result is in remarkable contrast with the case of noninteracting bosons where universal quantum computation can be achieved by allowing gates to be conditioned on classical bits (quant-ph/0006088).Comment: 26 pages, 1 figure, uses wick.sty; references added to recent results by E. Knil

Evaluation of thermal data for geologic applications

Sensitivity studies using thermal models indicated sources of errors in the determination of thermal inertia from HCMM data. Apparent thermal inertia, with only simple atmospheric radiance corrections to the measured surface temperature, would be sufficient for most operational requirements for surface thermal inertia. Thermal data does have additional information about the nature of surface material that is not available in visible and near infrared reflectance data. Color composites of daytime temperature, nighttime temperature, and albedo were often more useful than thermal inertia images alone for discrimination of lithologic boundaries. A modeling study, using the annual heating cycle, indicated the feasibility of looking for geologic features buried under as much as a meter of alluvial material. The spatial resolution of HCMM data is a major limiting factor in the usefulness of the data for geologic applications. Future thermal infrared satellite sensors should provide spatial resolution comparable to that of the LANDSAT data