Simulation of many body Fermi systems on a universal quantum computer
We provide fast algorithms for simulating many body Fermi systems on a universal quantum computer. Both first and second quantized descriptions are considered, and the relative computational complexities are determined in each case. In order to accommodate fermions using a first quantized Hamiltonian, an efficient quantum algorithm for anti-symmetrization is given. Finally, a simulation of the Hubbard model is discussed in detail.

title: Estimation of the local density of states on a quantum computer
abstract: We report an efficient quantum algorithm for estimating the local density of states (LDOS) on a quantum computer. The LDOS describes the redistribution of energy levels of a quantum system under the influence of a perturbation. Sometimes known as the 'strength function' from nuclear spectroscopy experiments, the shape of the LDOS is directly related to the survivial probability of unperturbed eigenstates, and has recently been related to the fidelity decay (or 'Loschmidt echo') under imperfect motion reversal. For quantum systems that can be simulated efficiently on a quantum computer, the LDOS estimation algorithm enables an exponential speedup over direct classical computation.

title: ANALOG QUANTUM ERROR CORRECTION
abstract: Quantum error-correction routines are developed for continuous quantum variables such as position and momentum. The result of such analog quantum error correction is the construction of composite continuous quantum variables that are largely immune to the effects of noise and decoherence.

title: Quantum Computation over Continuous Variables
abstract: This paper provides necessary and sufficient conditions for constructing a universal quantum computer over continuous variables. As an example, it is shown how a universal quantum computer for the amplitudes of the electromagnetic field might be constructed using simple linear devices such as beam splitters and phase shifters, together with squeezers and nonlinear devices such as Kerr-effect fibers and atoms in optical cavities. Such a device could in principle perform “floating point” computations. Problems of noise, finite precision, and error correction are discussed.

title: Computational capacity of the universe.
abstract: All physical systems register and process information. The laws of physics determine the amount of information that a physical system can register (number of bits) and the number of elementary logic operations that a system can perform (number of ops). The Universe is a physical system. The amount of information that the Universe can register and the number of elementary operations that it can have performed over its history are calculated. The Universe can have performed 10(120) ops on 10(90) bits ( 10(120) bits including gravitational degrees of freedom).

title: Quantum Algorithm Providing Exponential Speed Increase for Finding Eigenvalues and Eigenvectors
abstract: We describe a new polynomial time quantum algorithm that uses the quantum fast Fourier transform to find eigenvalues and eigenvectors of a local Hamiltonian, 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.

title: The effect of a finite mass reservoir on the collapse of spherical isothermal clouds and the evolution of protostellar accretion
abstract: Motivated by recent observations that detect an outer boundary for starless cores, and evidence for time-dependent mass accretion in the Class 0 and Class I protostellar phases, we re-examine the case of spherical isothermal collapse in the case of a finite mass reservoir. The presence of a core boundary, implemented through a constant-volume approximation in our simulation, results in the generation of an inward-propagating rarefaction wave. This steepens the gas density profile from r -2 (self-similar value) to r -3 or steeper. After a protostar forms, the mass accretion rate M evolves through three distinct phases: (1) an early phase of decline in M, which is a non-self-similar effect due to rapid and spatially non-uniform infall in the pre-stellar phase; (2) for large cores, an intermediate phase of near-constant M from the infall of the outer part of the self-similar density profile, which has low (subsonic) infall speed in the pre-stellar phase; and (3) a late phase of rapid decline in M when accretion occurs from the region affected by the inward-propagating rarefaction wave. Our model clouds of small to intermediate size make a direct transition from phase (1) to phase (3) above. Both the first and second phase (if the latter is indeed present) are characterized by a temporally increasing bolometric luminosity L bol , while L bol is decreasing in the third (final) phase. We identify the period of temporally increasing L bol with the Class 0 phase, and the later period of terminal accretion and decreasing L bol with the Class I phase. The peak in L bol corresponds to the evolutionary time when 50 ± 15 per cent of the cloud mass has been accreted by the protostar. This is in agreement with the classification scheme proposed in the early 1990s by Andre et al.; our model adds a physical context to their interpretation. We show how our results can be used to explain tracks of envelope mass M env versus L bol for protostars in Taurus and Ophiuchus. We also develop an analytic formalism that successfully reproduces the protostellar accretion rate from profiles of density and infall speed in the pre-stellar phase. It shows that the spatial gradient of infall speed that develops in the pre-stellar phase is a primary cause of the temporal decline in M during the early phase of protostellar accretion.

title: Comparisons of fully differential exact results for O(α) virtual corrections to single hard bremsstrahlung in e+e− annihilation at high energies
abstract: We present comparisons of the fully differential exact virtual correction to the important single hard bremsstrahlung process in e + e − annihilation at high energies, which is essential for precision studies of the Standard Model from 1 GeV to 1 TeV, as calculated by two completely independent methods and groups. We show that the two sets of results are in excellent agreement. Phenomenological implications are discussed.

title: HERWIRI1.031: New Approach to Parton Shower MC's in Precision QCD Theory
abstract: The new IR-improved Dokshitzer-Gribov-Lipatov-Altarelli-Parisi-Callan-Symanzik (DGLAPCS) kernels recently developed by one of us is implemented in the HERWIG6.5 environment to generate a new MC, HERWIRI1.0(31), for hadron-hadron scattering at high energies. The comparison between the parton shower generated by the standard DGLAP-CS kernels and that generated by the new IR-improved DGLAP-CS kernels is illustrated using MC data. This is done for some of the respective exact O(αs) corrected spectra using the seamless interfaces to MC@NLO while making comparisons with FNAL data. Some discussion of possible implications for LHC phenomenology is also presented.