An efficient quantum algorithm for preparation of uniform quantum superposition states

Quantum state preparation involving a uniform superposition over a non-empty subset of $n$-qubit computational basis states is an important and challenging step in many quantum computation algorithms and applications. In this work, we address the problem of preparation of a uniform superposition state of the form $\ket{\Psi} = \frac{1}{\sqrt{M}}\sum_{j = 0}^{M - 1} \ket{j}$, where $M$ denotes the number of distinct states in the superposition state and $2 \leq M \leq 2^n$. We show that the superposition state $\ket{\Psi}$ can be efficiently prepared with a gate complexity and circuit depth of only $O(\log_2~M)$ for all $M$. This demonstrates an exponential reduction in gate complexity in comparison to other existing approaches in the literature for the general case of this problem. Another advantage of the proposed approach is that it requires only n=\ceil{\log_2~M} qubits. Furthermore, neither ancilla qubits nor any quantum gates with multiple controls are needed in our approach for creating the uniform superposition state $\ket{\Psi}$. It is also shown that a broad class of nonuniform superposition states that involve a mixture of uniform superposition states can also be efficiently created with the same circuit configuration that is used for creating the uniform superposition state $\ket{\Psi}$ described earlier, but with modified parameters.Comment: 26 page

A hybrid classical-quantum algorithm for solution of nonlinear ordinary differential equations

A hybrid classical-quantum approach for the solution of nonlinear ordinary differential equations using Walsh-Hadamard basis functions is proposed. Central to this hybrid approach is the computation of the Walsh-Hadamard transform of arbitrary vectors, which is enabled in our framework using quantum Hadamard gates along with state preparation, shifting, scaling, and measurement operations. It is estimated that the proposed hybrid classical-quantum approach for the Walsh-Hadamard transform of an input vector of size N results in a considerably lower computational complexity (O(N) operations) compared to the Fast Walsh-Hadamard transform (O(N log2(N)) operations). This benefit will also be relevant in the context of the proposed hybrid classical-quantum approach for the solution of nonlinear differential equations. Comparisons of results corresponding to the proposed hybrid classical-quantum approach and a purely classical approach for the solution of nonlinear differential equations (for cases involving one and two dependent variables) were found to be satisfactory. Some new perspectives relevant to the natural ordering of Walsh functions (in the context of both classical and hybrid approaches for the solution of nonlinear differential equations) and representation theory of finite groups are also presented here.Comment: 29 pages, 10 figure

A quantum approach for digital signal processing

We propose a novel quantum approach to signal processing, including a quantum algorithm for low-pass and high-pass filtering, based on the sequency-ordered Walsh-Hadamard transform. We present quantum circuits for performing the sequency-ordered Walsh-Hadamard transform, as well as quantum circuits for low-pass, high-pass, and band-pass filtering. Additionally, we provide a proof of correctness for the quantum circuit designed to perform the sequency-ordered Walsh-Hadamard transform. The performance and accuracy of the proposed approach for signal filtering were illustrated using computational examples, along with corresponding quantum circuits, for DC, low-pass, high-pass, and band-pass filtering. Our proposed algorithm for signal filtering has a reduced gate complexity and circuit depth of $O (\log_2 N)$, compared to at least $O ((\log_2 N )^2)$ associated with Quantum Fourier Transform (QFT) based filtering (excluding state preparation and measurement costs). In contrast, classical Fast Fourier Transform (FFT) based filtering approaches have a complexity of $O (N \log_2 N )$. This shows that our proposed approach offers a significant improvement over QFT-based filtering methods and classical FFT-based filtering methods. Such enhanced efficiency of our proposed approach holds substantial promise across several signal processing applications by ensuring faster computations and efficient use of resources via reduced circuit depth and lower gate complexity.Comment: 29 page

A Method for Dynamic Characterization and Response Prediction Using Ground Vibration Test(GVT)Data for Unknown Structures.

The Objective Of This Proposed Work Is To Develop A Reliable Method For Dynamic Characterization And Prediction Of Dynamic Response Of Structures Of Known/Unknown Configurations, By Processing The Free Vibration Data Generated Experimentally From The Ground Vibration Tests (GVT)Of The Prototype Vehicles. The Methodology Would Make Use Of The Measured Dynamic Data In Terms Of Mode Shapes, Natural Frequencies, Modal Damping, Point Impedances Etc.And Generate Modal (Scaled) Stiffness And Inertia Information That Will Be Used For Prediction Of Response Characteristics Of The Prototype Structure . With These Objectives, The Present Work Develops The Mathematical Formulation Of The Method, And Demonstrates Its Reliability By Performing The Experiment On A Simple Cantilever Beam To Determine Its Dynamic Characteristics. Results On Scaled Modal Stiffness And Inertia, Generated Through The Method Using Experimental (GVT) Data Show Excellent Agreement With Those Generated By FE And Analytical Models .It Must Be Noted That A Valid Benchmarking Is Performed With The Condition That The Experimental Procedure Is 'Blind' To The Actual Stiffness And Inertia Distributions As Used In FEM Or Analytical Models . Agreement Of The Predicted Response Of The Structure With That From Direct Experiment And Those From The FE And Analytical Models Indicates That This Method Will Be A Promising Tool To Predict The Dynamic And Aeroelastic Characteristics Of Any Prototype Vehicle In The Future. Once The Reliability Of The Method Is Established,It Can Be Extended To Determine The Dynamic And Aeroelastic Characteristics Of All Aircraft For Which Dynamic Characteristics Are Available From A Ground -; Vibration Test (GVT)

Boron in crop production from soil to plant system: A review

The deficiency of boron is spreading rapidly in Indian soils. Boron deficiency in crops is more widespread than deficiency of any other essential micronutrient. However, imbalanced or excess use of boron fertilizers found to impose negative impact on crops due to very narrow range of boron deficiency and toxicity in soil and plants which increases production cost also. Therefore, optimized boron fertilizer supply in boron deficient soils is important in order to attain normal crop growth, yield and high-quality produce.  It this review the role of boron in crop production, its deficiency in crop plants has been discussed

PRA Techniques in Agriculture: Common Diagraming and Mapping Tools

PRA techniques and tools commands paramount importance in bottom up approach of planning and implementation of agricultural programmes. The following paper describes the various PRA techniques used in the study such as Transect, Mobility map, Timeline and Time trend. Apart from PRA, other methods of data collection such as use of semi-structured interview schedule, direct observation and focus group methods were also used to elicit information from the villagers

Matrix Ranking- An important PRA tool to assess farmers preferences and priorities

Matrix ranking is an important PRA tool to assess and study the preferences of farmers for a particular technology over others, with respect to crop or animal based technologies. The preferences and criteria for the same are also studied in the process. The following study gives a first-hand idea of farmers’ relative preferences for different varieties of rice, mustard, tomato, chilli, garden pea, fish and lac hosts. The results of the matrix ranking for different varieties of rice revealed that, the variety “Arize 6444” was the most preferred one followed by “Abhishek”. “Pusa Mahak” was the leading variety of mustard followed by Pusa Bold. Swarna Sampada is more preferred tomato variety among the farmers. Among fish, “Rohu” was widely preferred by the respondents due to its higher yield, more market demand, resistance to water quality and higher market price