Read-only-memory-based quantum computation: Experimental explorations using nuclear magnetic resonance and future prospects

Read-only-memory-based (ROM-based) quantum computation (QC) is an alternative to oracle-based QC. It has the advantages of being less magical, and being more suited to implementing space-efficient computation (i.e., computation using the minimum number of writable qubits). Here we consider a number of small (one- and two-qubit) quantum algorithms illustrating different aspects of ROM-based QC. They are: (a) a one-qubit algorithm to solve the Deutsch problem; (b) a one-qubit binary multiplication algorithm; (c) a two-qubit controlled binary multiplication algorithm; and (d) a two-qubit ROM-based version of the Deutsch-Jozsa algorithm. For each algorithm we present experimental verification using nuclear magnetic resonance ensemble QC. The average fidelities for the implementation were in the ranges 0.9-0.97 for the one-qubit algorithms, and 0.84-0.94 for the two-qubit algorithms. We conclude with a discussion of future prospects for ROM-based quantum computation. We propose a four-qubit algorithm, using Grover's iterate, for solving a miniature real-world problem relating to the lengths of paths in a network.

An in situ study of photosynthetic oxygen exchange and electron transport rate in the marine macroalga Ulva lactuca (Chlorophyta)

Direct comparisons between photosynthetic O-2 evolution rate and electron transport rate (ETR) were made in situ over 24 h using the benthic macroalga Ulva lactuca (Chlorophyta), growing and measured at a depth of 1.8 m, where the midday irradiance rose to 400-600 mumol photons m(-2) s(-1). O-2 exchange was measured with a 5-chamber data-logging apparatus and ETR with a submersible pulse amplitude modulated (PAM) fluorometer (Diving-PAM). Steady-state quantum yield ((Fm'-Ft)/Fm') decreased from 0.7 during the morning to 0.45 at midday, followed by some recovery in the late afternoon. At low to medium irradiances (0-300 mumol photons m(-2) s(-1)), there was a significant correlation between O-2 evolution and ETR, but at higher irradiances, ETR continued to increase steadily, while O-2 evolution tended towards an asymptote. However at high irradiance levels (600-1200 mumol photons m-(2) s(-1)) ETR was significantly lowered. Two methods of measuring ETR, based on either diel ambient light levels and fluorescence yields or rapid light curves, gave similar results at low to moderate irradiance levels. Nutrient enrichment (increases in [NO3-], [NH4+] and [HPO42-] of 5- to 15-fold over ambient concentrations) resulted in an increase, within hours, in photosynthetic rates measured by both ETR and O-2 evolution techniques. At low irradiances, approximately 6.5 to 8.2 electrons passed through PS II during the evolution of one molecule of O-2, i.e., up to twice the theoretical minimum number of four. However, in nutrient-enriched treatments this ratio dropped to 5.1. The results indicate that PAM fluorescence can be used as a good indication of the photosynthetic rate only at low to medium irradiances.

The damped and coherently-driven Jaynes-Cummings model

We investigate the influence of a single-mode cavity on the Autler-Townes doublet that arises when a three-level atom is strongly driven by a laser field tuned to one of the atomic transitions and probed by a tunable, weak field coupled to the other transition. We assume that the cavity mode is coupled to the driven transition and the cavity and laser frequencies are equal to the atomic transition frequency. We find that the Autler-Townes spectrum can have one, two or three peaks depending on the relative magnitudes of the Rabi frequencies of the cavity and driving fields. We show that, in order to understand the three-peaked spectrum, it is necessary to go beyond the secular approximation, leading to interesting quantum interference effects. We find that the positions and relative intensities of the three spectral components are affected strongly by the atom-cavity coupling strength g and the cavity damping K. For an increasing g and/or decreasing K the triplet evolves into a single peak. This results in 'undressing' of the system such that the atom collapses into its ground state. We interpret the spectral features in terms of the semiclassical dressed-atom model, and also provide complementary views of the cavity effects in terms of quantum Langevin equations and the fully quantized, 'double -dressing' model.

Separating the quantum sidebands of an optical field

In this paper we investigate the quantum optics of a double-ended optical cavity. We show that an impedance matched, far-detuned cavity can be used to separate the positive and negative sidebands of a field. The 'missing' sideband will be replaced by the equivalent sideband incident on the cavity from the other direction. This technique can be used to convert the quantum correlations between the sidebands of the incident fields into quantum correlations between the two spatially distinct output fields. We show that, under certain experimental conditions, the fields emerging from the cavity will display entanglement.

Temperature dependence of polaronic transport through single molecules and quantum dots

Motivated by recent experiments on electric transport through single molecules and quantum dots, we investigate a model for transport that allows for significant coupling between the electrons and a boson mode isolated on the molecule or dot. We focus our attention on the temperature-dependent properties of the transport. In the Holstein picture for polaronic transport in molecular crystals the temperature dependence of the conductivity exhibits a crossover from coherent (band) to incoherent (hopping) transport. Here, the temperature dependence of the differential conductance on resonance does not show such a crossover, but is mostly determined by the lifetime of the resonant level on the molecule or dot.

Lower Bounds on the State Complexity of Geometric Goppa Codes

We reinterpret the state space dimension equations for geometric Goppa codes. An easy consequence is that if deg G less than or equal to n-2/2 or deg G greater than or equal to n-2/2 + 2g then the state complexity of C-L(D, G) is equal to the Wolf bound. For deg G is an element of [n-1/2, n-3/2 + 2g], we use Clifford's theorem to give a simple lower bound on the state complexity of C-L(D, G). We then derive two further lower bounds on the state space dimensions of C-L(D, G) in terms of the gonality sequence of F/F-q. (The gonality sequence is known for many of the function fields of interest for defining geometric Goppa codes.) One of the gonality bounds uses previous results on the generalised weight hierarchy of C-L(D, G) and one follows in a straightforward way from first principles; often they are equal. For Hermitian codes both gonality bounds are equal to the DLP lower bound on state space dimensions. We conclude by using these results to calculate the DLP lower bound on state complexity for Hermitian codes.

Quantum correlated twin atomic beams via photodissociation of a molecular Bose-Einstein condensate

We study the process of photodissociation of a molecular Bose-Einstein condensate as a potential source of strongly correlated twin atomic beams. We show that the two beams can possess nearly perfect quantum squeezing in their relative numbers.