Optimizing Quantum Adiabatic Algorithm

In quantum adiabatic algorithm, as the adiabatic parameter $s(t)$ changes slowly from zero to one with finite rate, a transition to excited states inevitably occurs and this induces an intrinsic computational error. We show that this computational error depends not only on the total computation time $T$ but also on the time derivatives of the adiabatic parameter $s(t)$ at the beginning and the end of evolution. Previous work (Phys. Rev. A \textbf{82}, 052305) also suggested this result. With six typical paths, we systematically demonstrate how to optimally design an adiabatic path to reduce the computational errors. Our method has a clear physical picture and also explains the pattern of computational error. In this paper we focus on quantum adiabatic search algorithm although our results are general.Comment: 8 pages, 9 figure

Evolution of structural and physical properties of transition metal oxide Sr₃(Ru₁₋xMnx)₂O₇ (0 \u3c̲ x \u3e̲ 0.7) with Mn concentration

Correlated Electron Materials (CEMs) have attracted the attention of the materials community because the strong coupling between charge, lattice, orbital, and spin degrees of freedom produces exotic phenomena. Transition metal oxide series Srn+1RunO3n+1 (n = 1 to ∞) is a prototype of CEMs. The n = 2 member of this family Sr3Ru2O7 is the subject of this dissertation. It has a paramagnetic (PM) metallic ground state, which can be driven into an antiferromagnetic (AFM) insulator with a partial substitution of Ru by Mn. The focus of this research is to understand the role of chemical doping as the driving force for the structural, electrical and magnetic properties in Mn-doped Sr3Ru2O7. A key to achieving this goal is contained in the understanding of different magnetic ordering in the system. High quality single crystals Sr3(Ru1-xMnx)2O7 (0 ≤ x ≤ 0.7) have been grown by the floating zone technique in an image furnace. A phase diagram of Sr3(Ru1-xMnx)2O7 is presented, which is divided into five different regions. The structural, electrical and magnetic properties of Sr3(Ru1-xMnx)2O7 reveal a turning point around x = 0.2. Two characteristic temperatures TMIT and TM are determined from electrical and magnetic properties measurements, where TMIT represents the temperature of a metallic-to-insulating crossover while TM corresponds to a peak in magnetic susceptibility. TMIT monotonically increases with increasing x while TM shows a cusp at x = 0.16 (TMIT \u3e TM) and the difference between TMIT and TM becomes much larger above x = 0.2. Elastic neutron scattering experiment on x = 0.16 crystal confirms a long-range AFM ordering below its TM and suggests short-range magnetic correlations between TMIT and TM

Resonant Quantum Search with Monitor Qubits

We present an algorithm for the generalized search problem (searching $k$ marked items among $N$ items) based on a continuous Hamiltonian and exploiting resonance. This resonant algorithm has the same time complexity $O(\sqrt{N/k})$ as the Grover algorithm. A natural extension of the algorithm, incorporating auxiliary "monitor" qubits, can determine $k$ precisely, if it is unknown. The time complexity of our counting algorithm is $O(\sqrt{N})$, similar to the best quantum approximate counting algorithm, or better, given appropriate physical resources.Comment: 12 pages, 1 figur

Excitation of high frequency voices from intermediate-mass-ratio inspirals with large eccentricity

The coalescence of a stellar-mass compact object together with an intermediate-mass black hole, also known as intermediate-mass-ratio inspiral, is usually not expected to be a viable gravitational wave source for the current ground-based gravitational wave detectors, due to the generally lower frequency of such source. In this paper, we adopt the effective-one-body formalism as the equation of motion, and obtain the accurately calculated gravitational waveforms by solving the Teukolsky equation in frequency-domain. We point out that high frequency modes of gravitational waves can be excited by large eccentricities of intermediate-mass-ratio inspirals. These high frequency modes can extend to more than 10 Hz, and enter the designed sensitive band of Advanced LIGO and Advanced Virgo. We propose that such kind of highly eccentric intermediate-mass-ratio inspirals could be feasible sources and potentially observable by the ground-based gravitational wave detectors, like the Advanced LIGO and Advanced Virgo.Comment: 16 pages, 16 figures. Class. Quant. Gravity, accepte

Manipulating Highly Deformable Materials Using a Visual Feedback Dictionary

The complex physical properties of highly deformable materials such as clothes pose significant challenges fanipulation systems. We present a novel visual feedback dictionary-based method for manipulating defoor autonomous robotic mrmable objects towards a desired configuration. Our approach is based on visual servoing and we use an efficient technique to extract key features from the RGB sensor stream in the form of a histogram of deformable model features. These histogram features serve as high-level representations of the state of the deformable material. Next, we collect manipulation data and use a visual feedback dictionary that maps the velocity in the high-dimensional feature space to the velocity of the robotic end-effectors for manipulation. We have evaluated our approach on a set of complex manipulation tasks and human-robot manipulation tasks on different cloth pieces with varying material characteristics.Comment: The video is available at goo.gl/mDSC4