Exponential improvement in precision for simulating sparse Hamiltonians

We provide a quantum algorithm for simulating the dynamics of sparse Hamiltonians with complexity sublogarithmic in the inverse error, an exponential improvement over previous methods. Specifically, we show that a $d$-sparse Hamiltonian $H$ acting on $n$ qubits can be simulated for time $t$ with precision $\epsilon$ using $O\big(\tau \frac{\log(\tau/\epsilon)}{\log\log(\tau/\epsilon)}\big)$ queries and $O\big(\tau \frac{\log^2(\tau/\epsilon)}{\log\log(\tau/\epsilon)}n\big)$ additional 2-qubit gates, where $\tau = d^2 \|{H}\|_{\max} t$. Unlike previous approaches based on product formulas, the query complexity is independent of the number of qubits acted on, and for time-varying Hamiltonians, the gate complexity is logarithmic in the norm of the derivative of the Hamiltonian. Our algorithm is based on a significantly improved simulation of the continuous- and fractional-query models using discrete quantum queries, showing that the former models are not much more powerful than the discrete model even for very small error. We also simplify the analysis of this conversion, avoiding the need for a complex fault correction procedure. Our simplification relies on a new form of "oblivious amplitude amplification" that can be applied even though the reflection about the input state is unavailable. Finally, we prove new lower bounds showing that our algorithms are optimal as a function of the error.Comment: v1: 27 pages; Subsumes and improves upon results in arXiv:1308.5424. v2: 28 pages, minor change

Simulating Hamiltonian dynamics with a truncated Taylor series

We describe a simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator. Our method can simulate the time evolution of a wide variety of physical systems. As in another recent algorithm, the cost of our method depends only logarithmically on the inverse of the desired precision, which is optimal. However, we simplify the algorithm and its analysis by using a method for implementing linear combinations of unitary operations to directly apply the truncated Taylor series.Comment: 5 page

Reduced Intensity Conditioning for Allogeneic Hematopoietic Cell Transplantation: Current Perspectives

AbstractAllogeneic HCT after myeloablative conditioning is an effective therapy for patients with hematologic malignancies. In an attempt to extend this therapy to older patients or those with comorbidities, reduced intensity or truly nonmyeloablative regimens have been developed over the past decade. The principle underlying reduced intensity regimens is to provide some tumor kill with lessened regimen-related morbidity and mortality and then rely on graft-versus-tumor (GVT) effects to eradicate remaining malignant cells, whereas nonmyeloablative regimens rely primarily on GVT effects. In this article, 3 representative approaches are described, demonstrating the clinical application for hematopoietic and nonhematopoietic malignancies. Current challenges include controlling GVHD while allowing GVT to occur. In the future, clinical trials using reduced intensity and nonmyeloablative conditioning will be compared with myeloablative conditioning in selected malignancies to extend the application to standard-risk patients

Federal Income Tax Developments: 1984

FEDERAL INCOME TAX DEVELOPMENTS: 1984 is the twelfth in a series of articles published at The University of Akron School of Law. In keeping with the established format, the scope of this survey is limited to selected substantive developments in the field of income taxation

Effect of combustor-inlet conditions on performance of an annular turbojet combustor

The combustion performance, and particularly the phenomenon of altitude operational limits, was studied by operating the annular combustor of a turbojet engine over a range of conditions of air flow, inlet pressure, inlet temperature, and fuel flow. Information was obtained on the combustion efficiencies, the effect on combustion of inlet variables, the altitude operational limits with two different fuels, the pressure losses in the combustor, the temperature and velocity profiles at the combustor outlet, the extent of afterburning, the fuel-injection characteristics, and the condition of the combustor basket

Efficient quantum algorithms for simulating sparse Hamiltonians

We present an efficient quantum algorithm for simulating the evolution of a sparse Hamiltonian H for a given time t in terms of a procedure for computing the matrix entries of H. In particular, when H acts on n qubits, has at most a constant number of nonzero entries in each row/column, and |H| is bounded by a constant, we may select any positive integer $k$ such that the simulation requires O((\log^*n)t^{1+1/2k}) accesses to matrix entries of H. We show that the temporal scaling cannot be significantly improved beyond this, because sublinear time scaling is not possible.Comment: 9 pages, 2 figures, substantial revision

Current Range in Lightning Return Strokes

In our investigation of breakdown waves, we use a one-dimensional, steady-state, constant velocity fluid model. This investigation involves breakdown waves for which the electric field force on electrons is in the opposite direction of wave propagation. The waves are considered to be shock fronted and the electron gas partial pressure is large enough to sustain the wave propagation. Our basic set of electron fluid-dynamical equations is composed of the equations for conservation of mass, momentum and energy, coupled with Poisson’s equation. This investigation involves breakdown waves for which a large current exists behind the shock front. The current behind the shock front alters the set of electron fluid-dynamical equations as well as the boundary conditions at the shock front. For the range of reported experimental current values (Wang et al. 1999), we have been able to solve the electron fluid dynamical equations within the dynamical transition region of the wave. Wave profile for electric field and electron velocity, number density and temperature within the dynamical transition region of the wave will be presente