Cellular metabolism involved thousands of reactions that determine how cells behave in the real world. These reactions under equilibrium can be modelled as a linear programming problem, which can be analyzed mathematically to understand and predict the behaviour of cells. However, linear programming problems can get computationally prohibitive for large matrices (in our case number of reactions). Recent developments in quantum linear system algorithms offer fault-tolerant quantum computing algrorithms with better scaling than the current state-of-the-art classical algorithms. In this work, we modified the quantum interior point algorithm to analyze metabolic networks. Taking the glycolysis + TCA cycle as a representative example, we tested our algorithm on quantum simulators and found that it converges to the correct solution. 

Skyrmions are topologically protected magnetic structures with vortex-like configurations. Recently, skyrmions with sizes a few times the atomic lattice spacing were experimentally observed. At this scale, quantum effects cannot be ignored. I study the ground state and dynamical properties of quantum skyrmions using numerical methods. We found that the spins in quantum skyrmion ground states are entangled with each other. An external magnetic field can move these quantum skyrmions, during which they can merge and decay. The entanglement increases strongly due to the interaction of quantum skyrmions, a property absent in classical skyrmions.

In quantum many-body systems, like quantum skyrmions, the Hilbert space increases exponentially with the system size. This means that we can study these systems exactly for only a small number of particles before we run out of computer memory. We can study larger systems only approximately. Over many decades physicists have devised clever numerical techniques to approximate the quantum many-body problem. A recent innovation came in the form of neural network quantum states, which uses an artificial neural network to represent the variational wave function. Neural networks have some advantages over traditional variational states and can be used to study systems that were inaccessible before.

1. Quantum algorithm for metabolic network analysis.
   A. Joshi, T. Koyama, (2025) bioRxiv.

2. Quantum skyrmion dynamics studied by neural network quantum states quantum states.
   A. Joshi, R. Peters, T. Posske, Physical Review B 110, 104411 (2024), arxiv.

3. Ground state properties of quantum skyrmions described by neural network quantum states.
   A. Joshi, R. Peters, T. Posske, Physical Review B 108, 094410 (2023), arxiv.

4. Mott transition and magnetism in a fragile topological insulator.
   A. Joshi, R. Peters, Physical Review B 103, 165130 (2021), arxiv.

5. Microwave derived monoclinic Ba1-xSnxNb2O6 materials as an alternative of ITO.
   A. Joshi, V. Shrivastava and A. Pritam, Journal of Alloys and Compounds 828, 153096 (2020), arxiv.

6. Integrating third phase transition and CO/CO2 contamination in microwave tailored Bi2Mo1−xWxO6 nano materials.
   V. Shrivastava, A. Pritam and A. Joshi, Journal of Materials Science: Materials in Electronics 29, 17388-17396 (2018).