Empirical orbit determination using Apollo 14 data

An empirical orbit determination method is shown to yield highly accurate navigation results when applied to lunar orbit tracking data. Regressions and predictions of free flight Apollo 14 tracking data exhibit minimal residual growth, and the solution orbital elements behave in a very consistent manner. Solutions from data acquired during propulsive maneuvers result in degraded predictions. The residual patterns from free flight processing are shown to be consistent from pass to pass and are correlated with lunar topographic features

Synthesis of Quantum Logic Circuits

We discuss efficient quantum logic circuits which perform two tasks: (i) implementing generic quantum computations and (ii) initializing quantum registers. In contrast to conventional computing, the latter task is nontrivial because the state-space of an n-qubit register is not finite and contains exponential superpositions of classical bit strings. Our proposed circuits are asymptotically optimal for respective tasks and improve published results by at least a factor of two. The circuits for generic quantum computation constructed by our algorithms are the most efficient known today in terms of the number of expensive gates (quantum controlled-NOTs). They are based on an analogue of the Shannon decomposition of Boolean functions and a new circuit block, quantum multiplexor, that generalizes several known constructions. A theoretical lower bound implies that our circuits cannot be improved by more than a factor of two. We additionally show how to accommodate the severe architectural limitation of using only nearest-neighbor gates that is representative of current implementation technologies. This increases the number of gates by almost an order of magnitude, but preserves the asymptotic optimality of gate counts.Comment: 18 pages; v5 fixes minor bugs; v4 is a complete rewrite of v3, with 6x more content, a theory of quantum multiplexors and Quantum Shannon Decomposition. A key result on generic circuit synthesis has been improved to ~23/48*4^n CNOTs for n qubit

Merchandising through Use of Lotteries

It has been almost universally held that there must be three elements present for a promotion to constitute a lottery. These elements are consideration, chance, and prize. The absence of any one of these elements is fatal to identifying the transaction as a lottery.Promoters are continually modifying and shading each of these three elements, however, so that the courts and government officials must constantly reappraise their positions to protect both the public and legitimate business

Minimal Universal Two-qubit Quantum Circuits

We give quantum circuits that simulate an arbitrary two-qubit unitary operator up to global phase. For several quantum gate libraries we prove that gate counts are optimal in worst and average cases. Our lower and upper bounds compare favorably to previously published results. Temporary storage is not used because it tends to be expensive in physical implementations. For each gate library, best gate counts can be achieved by a single universal circuit. To compute gate parameters in universal circuits, we only use closed-form algebraic expressions, and in particular do not rely on matrix exponentials. Our algorithm has been coded in C++.Comment: 8 pages, 2 tables and 4 figures. v3 adds a discussion of asymetry between Rx, Ry and Rz gates and describes a subtle circuit design problem arising when Ry gates are not available. v2 sharpens one of the loose bounds in v1. Proof techniques in v2 are noticeably revamped: they now rely less on circuit identities and more on directly-computed invariants of two-qubit operators. This makes proofs more constructive and easier to interpret as algorithm

Higgs Boson Decays to tau-pairs in the s-channel at a Muon Collider

We study the observability of the \tautau decay mode of a Higgs boson produced in the $s$-channel at a muon collider. We find that the spin correlations of the \tautau in $\tau\to \pi\nu_{\tau}, \rho\nu_{\tau}$ decays are discriminative between the Higgs boson signal and the Standard Model background. Observation of the predicted distinctive distribution can confirm the spin-0 nature of the Higgs resonance. The relative coupling strength of the Higgs boson to $b$ and $\tau$ can also be experimentally determined.Comment: to appear in PL