Jaideep Mulherkar

My research work is in the area of Quantum computing. I am currently working on theoretical aspects and implementations of quantum walks. I am also interested in quantum optimization and quantum machine learning algorithms. My other interest is in Computational Finance, particularly, I am interested in fast numerical and Monte Carlo methods for pricing of financial option contracts. In the past I have worked on the applications of quantum spin systems, in quantum information theory.

Quantum Computing

Quantum computing is computing based on the principles of quantum mechanics. One can harness quantum mechanical principles such as superposition and entanglement to develop novel algorithms that give a significant speed up for certain computational tasks. The most famous among quantum algorithms are Shor's factoring algorithm and the Grover's search algorithm. My recent work in quantum mechanical analogues of random walks called quantum walks. I am interested in both discrete and continuous time quantum walks and their applications. Quantum walks can be used for modeling quantum mechanical phenomenon and speed up using quantum Monte Carlo techniques and developing quantum algorithms.

Publications

Quantum simulation of perfect state transfer on weighted cubelike graphs (with R. Rajdeepak and V. Sunitha) Book Chapter: Springer Proceedings in Mathematics and Statistics (2023), Proceedings of International Conference on Mathematics and Computing (ICMC) Vellore Jan 6th – Jan 8th 2022 , vol. 12, (2023).
Implementation of quantum hitting times of cubelike graphs on ibm’s qiskit platform, (with R. Rajdeepak and V. Sunitha) International Journal of Quantum information, World Scientific vol. 2250020, (2022)
Perfect state transfer in weighted cubelike graphs (with R. Rajdeepak and V. Sunitha) ICDM 2021 ISBN 978-93-91077-53-2 Editors: R. Kala, S. Monikandan, K. Selvakumar and T. Tamizh Chelvam, 2021, Manonmaniam Sundaranar University 2021.
Capacity of a quantum memory channel correlated by matrix product states (with V. Sunitha), Quantum Information Processing, 17 (4), 80 (2018).
Classical and entanglement assisted capacity of a qubit depolarizing channel, International Journal of Quantum Information, 1650017 (2016) .
Classical capacity of a qubit depolarizing quantum memory channel with Markovian correlated noise, Proceedings of Asian quantum information science conference (AQIS), Seoul, South Korea (2015).
Implementing Quantum Gates using the Ferromagnetic Spin-J XXZ Chain with Kink Boundary Conditions (with T. Michoel, B. Nachtergaele), New Journal of Physics, Focus issue on Quantum Information and many body theory (2010)
Isolated eigen values in the ferromagmagnetic XXZ model with kink boundary conditions (with S. Starr, R. Sims, B. Nachergaele), Journal of Statistical Mechanics:Theory and Experiment P01016, (2008)
Some properties of the ferromagnetic XXZ model and their applications to quantum computing, PhD thesis, Department of Mathematics, U.C. Davis, (2009)

PhD thesis guidance

Rajdeepak, Rishikant Title: Study of cubelike graphs for parallel and quantum computation, 2022 (Jointly with V. Sunitha)
Dey, Biswajyoti Title: Multiparticle quantum walks (Ongoing)
Makwana, Bhavin Title: Quantum machine learning algorithms (Ongoing)

Undergraduate projects

Parikh Manan, Kevadiya Prathav Title: Quantum optimization algorithms

Asnani Dhruvesh Title: Implementation of a quantum algorithm for the discrete log problem

Rayvadera Meet Title:Hitting time of quantum walks on a hypercube

Computational Finance

My interest in mathematical and computationl finance is in the theory of options pricing. Options are financial contracts that give the right to buy/sell a certain asset at a future date (expiry date) at a fixed price (Strike price). The options buyer has the right but no obligation to honor the contract in return they have to pay the option seller a certain fee or premium. The option pricing theory is nice from both the mathematical, financial and computational perspective. From the mathematical point it is an interesting application of probability theory and ideas such such as random walks, Brownian motion, Markov chains, martingales and the Black Scholes model. From the financial perspective there are many interesting ideas such as efficiency of markets, arbitrage, hedging, replicating portfolio, risk free interest rate etc. From the computational perspective there are ideas such as Monte Carlo simulations and their efficiency and finite difference methods. The field is a nice coming together of these mathematical ideas from probablility theory, financial ideas and computational techniques. I have had success in generating the interest of undergraduate students by offering them capstone projects in various aspects of computational finance. Some of my them have followed up with a career on wall street.

Undergraduate projects

Sharma, Smriti Title: Applications of time series analysis for GDP data.
Mashruwala, Narmit and Parikh, Samarth Title: Pricing American options using least squares Monte Carlo.
Jain, Aadarsh Title: American options Title: Pricing American options using finite difference methods.

Nigam, Parth Title: Financial Mathematics, Interest rate derivatives.

Mehta, Devanshi Title: Proposing the usage of Markov Models and Hidden Markov Models for improvising the option price calculation using Binomial Model.

Jain, Rishabh and Navada, Numrata Title: Bond and bond-option pricing using the Black, Derman and Toy model.
Maheshwari, Chinmay Title: Modern portfolio theory with efficient frontier implementation.
Shah, Harsh Title: Trading strategies involving options
Agarwal, Hitesh and Vadera, Parth Title: Value at risk for a portfolio of bonds
Vatyani, Gaurav and Somani Mudit Title: Credit risk: analysis, modelling and derivatives

Panjabi, Karan and Patel, Parth Title: Credit Derivatives and Valuation of Credit Risk.
Singhal, Ankur and Dhamija, Karan Title: Value at Risk for a Portfolio of Stocks.

Chaudhary, Sahil and Gudsoorkar, Aditya Title: Evaluating the Effectiveness of Delta Hedging Technique for Indian Markets.