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

Efficient Multi-stage Inference on Tabular Data

Many ML applications and products train on medium amounts of input data but get bottlenecked in real-time inference. When implementing ML systems, conventional wisdom favors segregating ML code into services queried by product code via Remote Procedure Call (RPC) APIs. This approach clarifies the overall software architecture and simplifies product code by abstracting away ML internals. However, the separation adds network latency and entails additional CPU overhead. Hence, we simplify inference algorithms and embed them into the product code to reduce network communication. For public datasets and a high-performance real-time platform that deals with tabular data, we show that over half of the inputs are often amenable to such optimization, while the remainder can be handled by the original model. By applying our optimization with AutoML to both training and inference, we reduce inference latency by 1.3x, CPU resources by 30%, and network communication between application front-end and ML back-end by about 50% for a commercial end-to-end ML platform that serves millions of real-time decisions per second

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

Constant-degree graph expansions that preserve the treewidth

Many hard algorithmic problems dealing with graphs, circuits, formulas and constraints admit polynomial-time upper bounds if the underlying graph has small treewidth. The same problems often encourage reducing the maximal degree of vertices to simplify theoretical arguments or address practical concerns. Such degree reduction can be performed through a sequence of splittings of vertices, resulting in an _expansion_ of the original graph. We observe that the treewidth of a graph may increase dramatically if the splittings are not performed carefully. In this context we address the following natural question: is it possible to reduce the maximum degree to a constant without substantially increasing the treewidth? Our work answers the above question affirmatively. We prove that any simple undirected graph G=(V, E) admits an expansion G'=(V', E') with the maximum degree <= 3 and treewidth(G') <= treewidth(G)+1. Furthermore, such an expansion will have no more than 2|E|+|V| vertices and 3|E| edges; it can be computed efficiently from a tree-decomposition of G. We also construct a family of examples for which the increase by 1 in treewidth cannot be avoided.Comment: 12 pages, 6 figures, the main result used by quant-ph/051107

Synthesis and Optimization of Reversible Circuits - A Survey

Reversible logic circuits have been historically motivated by theoretical research in low-power electronics as well as practical improvement of bit-manipulation transforms in cryptography and computer graphics. Recently, reversible circuits have attracted interest as components of quantum algorithms, as well as in photonic and nano-computing technologies where some switching devices offer no signal gain. Research in generating reversible logic distinguishes between circuit synthesis, post-synthesis optimization, and technology mapping. In this survey, we review algorithmic paradigms --- search-based, cycle-based, transformation-based, and BDD-based --- as well as specific algorithms for reversible synthesis, both exact and heuristic. We conclude the survey by outlining key open challenges in synthesis of reversible and quantum logic, as well as most common misconceptions.Comment: 34 pages, 15 figures, 2 table

Screening of antibacterial activity of raspberry (Rubus idaeus L.) fruit and pomace extracts

Antibacterial activity of fruit and pomace extracts (concentration 50 mg/ml) of two raspberry (Rubus idaeus L.) cultivars (Meeker and Willamette) was tested against selected Gram-positive and Gram-negative bacteria (reference and wild strains). Disc diffusion method with 15 μl of extracts and agar-well diffusion method with 50 and 100 μl were used. Antibiotic (cefotaxime/clavulanic acid) was used as a control. Both raspberry fruit extracts showed the strongest antibacterial activity against Pseudomonas aeruginosa (wild strain) and Bacillus cereus, where the largest clear zones (without growth) appeared. Escherichia coli was the most resistant strain, with only zone of reduced growth. The highest antibacterial activity of pomace extracts was against Staphylococcus aureus and Staphylococcus saprophyticus. There were no differences in the antibacterial activity between cultivars for both fruit and pomace extracts. [Projekat Ministarstva nauke Republike Srbije, br. TR 31044

Mechanism of PbSe y S1 - Y film formation in chemical deposition from aqueous solutions

The growth mechanism of PbSe y S1 - y films has been studied upon chemical deposition from aqueous solutions using scanning probe microscopy. A comparative morphological analysis of layers deposited at the initial growth stages and the use of fractal formalism shows that the formation of films of PbS, PbSe, and PbSe y S1 - y substitutional solid solutions involves cluster-cluster aggregation with self-organization elements. © 2013 Pleiades Publishing, Ltd

Physico-chemical characterization and anti- microbial activity of copper(II) complexes with 2-amino and 2-methylbenzimidazole derivatives

Copper(II) chloride, in warm ethanolic solution, reacted with 2-amino and 2-methylbenzimidazole derivatives to give complexes of the formula CuL2Cl2·nH2O, where L=1-benzyl-2-aminobenzimidazole 1-(4-methylbenzyl)-2-aminobenzimidazole, 1-benzyl-2-methylbenzimidazole and 1-(4-methylbenzyl)-2-methylbenzimidazole( n=1 or 2). The complexes were characterized by elemental analysis of the metal, molar conductivity magnetic susceptibility measurements and IR spectra. The molar conductivities of copper(II)complexes in dimethyl formamide (DMF) corresponding to a 1:1 type of electrolyte indicate that in all the complexes one of the coordinated chloride ions has been replaced by DMF molecule. The room temperature effective magnetic moments and IR data of the complexes suggest that all Cu(II) complexes have a tetrahedral configuration, which is realized by participation of the pyridine nitrogen of two organic ligand molecules and two chloride anions. The antimicrobial activity of the ligands and their complexes against Pseudomonas aeruginosa, Bacillus sp. Staphylococcus aureus, Sarcina lutea and Saccharomyces cerevisiae was investigated. The effect of copper complexation on the ligand antimicrobial activity is discussed

The Boltzmann equation for colourless plasmons in hot QCD plasma. Semiclassical approximation

Within the framework of the semiclassical approximation, we derive the Boltzmann equation describing the dynamics of colorless plasmons in a hot QCD plasma. The probability of the plasmon-plasmon scattering at the leading order in the coupling constant is obtained. This probability is gauge-independent at least in the class of the covariant and temporal gauges. It is noted that the structure of the scattering kernel possesses important qualitative difference from the corresponding one in the Abelian plasma, in spite of the fact that we focused our study on the colorless soft excitations. It is shown that four-plasmon decay is suppressed by the power of $g$ relative to the process of nonlinear scattering of plasmons by thermal particles at the soft momentum scale. It is stated that the former process becomes important in going to the ultrasoft region of the momentum scale.Comment: 41, LaTeX, minor changes, identical to published versio