Research

Machine learning has been used to amazing effect in classification, regression, and generative modeling problems. We are using deep neural networks to navigate our everyday life. However, in recent years, it has been shown that classical machine learning models can also help in quantum many-body systems and quantum computing research.  Quantum computing devices in current era are noisy and has scalability problems. We often need to calculate quantities of physical interest using these noisy devices. By using noisy experimental data, machine learning models can extract such meaningful information, e.g., phases of quantum matter, ground state of many-body system, optimal parameters for metrology, and reconstruction of quantum states (tomography). 

My current project involves devising a protocol using large language models like Transformers (used in GPT) to accurately predict the quantum state and use that to find expectation value of observables that cannot be directly measured from the quantum device efficiently.

Lattice gauge theories have been immensely informative in predicting some properties of quantum chromodynamics (QCD). QCD is a theory of strong interactions for which a perturbative treatment like QED is not helpful. Classical simulations using the Euclidean action of lattice QCD encounters the sign-problem for Fermions, which are one of the fundamental particles that make up matter. Quantum computers can circumvent these problems and, in principle, for a powerful enough quantum computer, we should be able to simulate QCD with fermions at finite temperature and chemical potential.

However, for the Noisy Intermediate Scale Quantum (NISQ) devices currently available, it is extremely difficult to simulate gauge theories due to non-scalability, large gate depths, infidelity of entangling gates, and noisy readouts. In our group, we are currently inventing ways to use variational quantum algorithms to predict some properties of non-abelian gauge theories in current quantum devices as proof-of-concept of the quantum advantage in simulating fundamental physics.

Quantum information theory (QI) has been a hotbed of research for the past couple of decades. One very interesting aspect of it is the application of the theory to relativistic problems. For example, one can ask what happens to two initially entangled objects as they move through curved spacetime. It turns out that entanglement can be generated or degraded depending upon the initial state and the interaction of the system with the background. These results are relatively new and use the theory of open quantum system dynamics to model the evolution of the entangled system. The master equation in general is very hard to solve exactly, and usually, different approximations are made to obtain results.

Our group at UH recently started working on applications of relativistic quantum information for the specific case of a causal diamond. A causal diamond is a region in flat-spacetime causally connected with a finite lifetime observer. Our interest lies in the fact that the causal diamonds have a close connection with the SO(2,1) algebra of CQM. We discuss some of these issues in our recent paper: arxiv:2207.08086.

We are looking forward to advancing our understanding of the causal diamond temperature and its relation to quantum chaos. It has been established in recent papers that the black hole thermal effects can be described as the scrambling rate of information near the horizon of a black hole. In many-body systems, such scrambling is quantified by the out-of-time order correlators, Loschmidt echoes, and geometric circuit complexity. We want to apply some of these methods to other quantum mechanical systems with instabilities to find if it leads to thermal effects.

A black hole is a classical solution to Einstein's field equation in general relativity with a gravitational pull so immense that no physical signal can escape from within the spacetime region to an outside observer. However, Hawking’s seminal works (1975) showed that black holes can radiate, as was soon corroborated by a series of papers by Unruh, Davies, Fulling, and many others. It was shown that this radiation is caused by quantum effects in curved spacetime and is closely related to black hole thermodynamics. Even though it has already been almost half a century after Hawking's discovery, the thermodynamical aspects of black holes are not fully understood yet.  

A more recent development in understanding Hawking radiation is the use of quantum optics to model the accelerated detector by a two-state atom. This model was applied by Scully et al. in a more recent (PNAS, 2019) to show that an atom freely falling through a Boulware vacuum of a Schwarzschild black hole experiences thermal radiation. We, at UH, showed that this effect is related to the conformal invariance of field equations near the event horizon of the black hole that is governed by the Hamiltonian of conformal quantum mechanics (CQM). The radial part of the field waves starts to pile up near the horizon (in a scale-invariant way) and it is this behavior that gives rise to the thermal effect.  We also generalized the result to more general backgrounds including the rotating Kerr black holes to show that this thermal effect is quite robust. Note that this effect is a bit different than the usual radiation because here the atoms are in free fall (inertial) and the field modes are accelerating.

For more details please check out our papers: arxiv:2009.06580, arxiv:2011.08368.

Now we are focusing on understanding the relationship between the group structure of CQM and the thermal aspects of the acceleration radiation, specifically the entropy associated with this radiation. For recent results on this topic please check out our papers: arxiv:2108.07570, arxiv:2108.07572. 

A part of this work is done in collaboration with Marlan Scully's group at Texas A&M University. This work is partially funded by AFOSR grant FA9550-21-1-0017.  

There are many systems in nature which exhibit scaling symmetry classically. For example, the conformal quantum mechanics (CQM) Hamiltonian in 1D, or the delta function in 2D. However, when these systems are quantized, due to the singular nature of these Hamiltonians, one needs to renormalize the theory which in general leads to a dimensionful parameter. This breaks the classical scale invariance and gives rise to what is known as the quantum anomaly. 

We work with ultracold atoms that exhibit this kind of anomaly, for example with 2D 2-body and 1D 3-body point interactions.  We have shown that a system with antisymmetric derivative delta potential in 1D  also falls within this class of interactions which exhibits anomaly. The relation of this anomaly with Tan's contact, Beth-Uhlenbeck formula, and Levinson's theorem are also explored in our research.

For more details, please check the following papers and citations therein: arXiv:1908.05210, arXiv:1910.00052. 

It is essential to gain insight into how information can propagate within the cortical networks (neural networks in our cortex region of the brain) to understand the neural dynamics and computation in complex networks. In this regard, correlated dynamics resulting from clustered connections in the networks have been extensively studied and have significant importance in neural coding, pathological firing conditions of the brain, and many other neural activities.  On the other hand, another important feature of most cortical networks is the excitation-inhibition balance which prevents unphysical firing in the network. In our research, we explored the effect of structural heterogeneity in the cluster connections and its effect on the balance condition. We introduced a notion of partial balance which keeps the network away from unnatural firing statistics while also creating correlated firing dynamics.

In recent years, it has been proved that the universe is currently in a phase of accelerated expansion. General theory of relativity as proposed by Einstein cannot model this phenomenon. For this purpose, a kind of exotic matter with negative pressure density called Dark Energy is speculated to exist which is driving the accelerated expansion. As of yet, its existence is not established beyond doubt. Nonetheless, there are several theoretical models of dark energy that may mimic the behavior of the universe. While there is not a direct way to determine observationally which model is correct, there are other methods we can use to check the viability of certain models and match it with existing data. 

We used the dynamical system stability method to check the viability of two of the most used dark energy models: Quintessence and K-essence. We found that Quintessence models are more likely to be preferred to K-essence models according to their stability in response to perturbations. However, the dynamical stability analysis could not choose between the two most used Quintessence models, viz. tracking and thawing model.

For more details please check out our papers:  arxiv:1811.00736,  arxiv:1904.10149.