## Quantum coherence and entanglement for complex chemical and biological systems

The objective is to understand the role of quantum coherence and entanglement in complex systems such as photosynthesis, avian compass, solar cells, and complex chemical reactions.

### Adiabatic Quantum Computing

The exact solution of Schrodinger equation for atoms, molecules and extended systems continues to be a "Holy Grail" problem that the entire field has been striving to solve since its inception.

### Quantum Algorithms for Quantum Chemistry

Quantum simulation is one of the most promising near term applications for quantum computation that could demonstrate significant advantage over classical algorithms.

### Dimensional Scaling and Finite Size Scaling for Quantum Phase Transitions and Critical Phenomena in atomic and molecular systems

We have established an analogy between symmetry breaking of electronic structure configurations and quantum phase transitions at the large dimensional limit.

A talk on finite scaling and stability of atomic and molecular systems in super intense laser fields. View PDF

### Maximal Entropy Approach For Quantum State Tomography

### Entanglement as Measure of Electron-Electron Correlation in Quantum Chemistry Calculations

In quantum chemistry calculations, the correlation energy is defined as the difference between the Hartree–Fock limit energy and the exact solution of the nonrelativistic Schrodinger equation. We have shown that the entanglement can be used as an alternative measure of the electron correlation in quantum chemistry calculations. Entanglement is directly observable and is one of the most striking properties of quantum mechanics.

### Quantum Computing Using Polar Molecules

We investigate several aspects of realizing quantum computation using entangled polar molecules. We develop methods for realizing quantum computation in the gate model, the measurement-based model and the adiabatic model using polar molecules. Moreover, we explore the possibility of a novel quantum computing model built with coupled 2-level systems. The quantum coherent states formed by coupled 2-level systems have unique properties that have inspired numerous ideas in excitonic systems and spin systems.

### Quantum Machine Learning

*Developing game-changing quantum algorithms to perform machine learning tasks on large-scale scientific datasets for various industrial and technological applications.*

Quantum machine learning — a hybridization of classical machine learning techniques with quantum computation – is emerging as a powerful approach both allowing speed-ups and improving classical machine learning algorithms. This program will leverage our expertise in developing quantum algorithms to fully realize the tremendous promise of combining quantum algorithms with machine learning to solve important and challenging problems in quantum chemistry. The first part of the project focuses on combining quantum computing with machine learning techniques for the intent of performing electronic structure calculations. Our initial results for small molecules indicate the feasibility of this combined approach. The second part of the project focuses on developing quantum machine learning techniques for quantum coherence and dynamics for controlling the outcome of chemical reactions. The final part will be On developing hybrid quantum-classical machine learning algorithms for data classifications, particularly for quantum phases.

### Measuring Quantum Entanglement in Chemical Reactions

Since its development in 1964, Bell’s Inequality has been validated as the go-to test that scientists use to identify entanglement in particles. The theorem uses discrete measurements of properties of particles such as the orientation their spin to find if the particles are correlated. The problem is, discovering entanglement in chemical reactions requires that measurements are continuous. This means measuring aspects such as the angles of beams which scatter reactants forcing them into contact and transform into products. We have generalised Bell’s Inequality to include continuous measurements in chemical reactions, in a similar way to how the theorem had previously been generalised to examine photonic systems.

For more details see “Entanglement Classifier in Chemical Reactions” by Junxu Li and Sabre Kais, Science, Advances 5: 5283 (2019) pdf

### Quantum Simulation in Qudit Space

In Collaboration with the Weiner group at Purdue, we have successfully demonstrated the first implementation of the Phase Estimation Algorithm (PEA) on a qudit‐based photonic platform. This experiment utilized the high dimensionality of the time and frequency DoFs on a single photon to realize the 2‐qudit multi‐value‐controlled‐gate (MVCG) gate, circumventing the inherently probabilistic photon-photon interactions. Although limited to a proof‐of‐principle model with arbitrary‐phase diagonal unitaries, this work is a first physical demonstration of a qudit‐based PEA. Future improvements to our PEA include higher‐dimensional qudits ( >3 ), arbitrary (non‐diagonal) unitaries, and statistical estimation of the phase via large ensemble measurements.

For more details, see Quantum Phase Estimation with Time-Frequency Qudits in a Single Photon, Advanced Quantum Technologies, 1900074, (2019).

Link to PDF

### Characterization of Quantum States Based on Creation Complexity

### Using Quantum Games to Teach Quantum Mechanics

The learning of quantum mechanics is contingent upon an understanding of the physical significance of the mathematics that one must perform. Concepts such as normalization, superposition, interference, probability amplitude, and entanglement can prove challenging for the beginning student. Several class activities that use a nonclassical version of tic-tac-toe are described to introduce several topics in an undergraduate quantum mechanics course. Quantum tic-tac-toe is a quantum analogue of classical tic-tac-toe and can be used to demonstrate the use of superposition in movement, qualitative (and later quantitative) displays of entanglement, and state collapse due to observation.