The challenge we addressed: To determine the efficacy of 5 alternative approaches for the simulation, compilation, and verification of quantum circuits.Actions taken:• Learnt the fundamentals of the 5 alternative design tools used in quantum computing.• Conducted a literature review on tensor networks, decision diagrams, and ZX-calculus. • Analyzed each design tool carefully while evaluating its merits and demerits, and learnt how to construct them using specialized diagramming software like Dia. Results:• We successfully understood the specific use case of each alternative design tool.• We concluded that the ZX-calculus is the the most efficient design tool, providing upto 50% workflow efficiency.

The challenge we addressed: To architect a method to reduce the time and space complexity of the state-of-the-art quantum string matching algorithm. Actions taken:• Learnt the fundamentals of quantum computing under the mentorship of Dr. Amit Saha. • Conducted a literature review on Grover's search algorithm and various string & pattern-matching algorithms. • Developed quantum algorithms using myQLM.• Successfully implemented the quantum circuit from the paper titled – ‘A quantum algorithm for string matching’ (by Pradeep Niroula and Yunseong Nam) in myQLM.• Assisted in developing an improved quantum circuit implementation for the string-matching problem with the help of higher-dimensional intermediate temporary qudits.Results:• We successfully reduced the time complexity, query complexity, and the ancilla count of the state-of-the-art quantum algorithm for string matching. • We have exhibited an improved gate cost and depth over the circuit.• The primary use cases of the matching algorithm, such as a quick text search in a big file or spotting patterns in an image, can now be carried out more effectively.