# research

The laws of quantum mechanics govern the microscopic world of atoms and electrons. The field of condensed matter physics attempts to understand how simple interactions between these tiny particles can collectively give rise to rather complex behavior. Such an understanding paves the way to tame the materials found in nature to the benefit of humankind.

Major strides in our theoretical understanding of materials along with experimental techniques were made in the last century making Feynman’s grand dream of simulating quantum mechanics using quantum computers finally possible. The qubits (quantum analogue of classical bits) need to protected from any uncontrolled interaction with their surroundings; otherwise, the quantum information is lost. Hence, we are currently in the noisy intermediate scale quantum (NISQ) era. Noisy quantum computers with around 100 qubits have been available lately and scientific efforts are already in place to improve noise tolerance and increase the number of qubits. Although noisy, these devices are still powerful and techniques such as variational quantum eigensolver(VQE) and quantum machine learning are being rapidly tested to harness their power.

The long term vision is to reach fault tolerant quantum computing, and this can be achieved via quantum error correction. The idea is to construct a logical qubit by using a combination of relatively noisy physical qubits, whose errors are periodically detected through measurement of stabilizer operators and then corrected.

My research interest lies at the intersection of quantum computing and condensed matter physics. My current main areas of focus are highlighted below:

## Quantum algorithms

I am interested best utilizing the NISQ as well as future fault tolerant devices to understand how the complex and exotic behaviors in condensed matter systems emerge from simple interactions among the electrons. I have been working on variational algorithms to efficiently prepare the ground as well as excited states of the strongly correlated electron systems such as the Fermi-Hubbard model. One of my current projects also includes how to extract information about entanglement from the NISQ computers using VQE + classical machine learning i.e. quantum machine learning!

## Quantum Error Correction (QEC)

Insights from theoretical condensed matter has immensely helped the field of QEC. Certain QEC codes, including the most ubiquitous Kitaev’s toric code, also serve as a model for some exotic condensed matter systems. I am interested in QEC from the perspectives of both quantum computing and condensed matter.

## Measurement induced quantum phase transition

A many-body system that undergoes a random unitary dynamics interspersed with frequent, random measurements is found to undergo a measurement induced phase transition between two qualitatively different, stable dynamic phases with distinct entanglement properties. Random unitary applied to a many-body system creates entanglement among its constituent particles, and in the absence of measurement, we can expect the entanglement to keep growing in time whereas a measurement reduces the entanglement due to the wave-function collapse. An extreme case involves performing measurements in all the qubits of a quantum system, which destroys all of the entanglement and yields a product-state, a qualitatively different phase than the entangled phase that is obtained by performing measurements with finite probability. I am interested in studying these entanglement phase transitions to understand strongly correlated systems from the perspective of entanglement and also seek insights into quantum error correction.