I am a first year PhD student at the Centre for Research in String Theory, Queen Mary University of London working under the supervision of Dr. Matthew Buican. I am interested in the relationships between topological and conformal field theories. I am also interested in the growing connections between quantum information theory and quantum gravity.
Nov 2016 - Dec 2016
TIFR Centre for Interdisciplinary Sciences
- Hyderabad, Telangana, India
- Visiting Student
Research Items (13)
In this dissertation, we will define a Topological Quantum Field Theory (TQFT) and discuss some of its properties. We will emphasise on anyonic models, and explore how the algebraic data in an anyonic model is contained in a Modular Tensor Category (MTC). We will define Hopf algebras, and discuss two series of anyonic models obtained from Hopf algebras. Namely, those obtained from the quantum double of a finite group, and quantum groups. We will study how 3D TQFTs and 2D Conformal Field Theories are related to each other, and explore the relationships between Chern-Simons-Witten theory and Wess-Zumino-Witten Models. We will motivate how TQFTs are 'simpler' compared to general quantum field theories, and how they could be used to do explicit computation to learn about the subtle properties of QFTs in general. Keeping this goal in mind, we discuss a recent development in defining topological entanglement entropy in Chern-Simons-Witten theories.
In an earlier publication we had given an exhaustive analysis of the criteria for weak value measurements of pure states to be optimal in the sense considered by Wootters and Fields. We had proved, for arbitrary spin cases, that the measurements are optimal when the post-selected state is mutually unbiased wrt the eigenstates of the observable being measured.Here we extend the discussion to mixed states. For these, weak value measurements have several problems which we illustrate with the protocol proposed by Shengjun Wu. We discuss tomography of mixed states based on weak measurements and show that while the principal results of Wootters and Fields hold, namely, the set of observables needed for complete tomography are such that their eigenstates form a mutually unbiased bases, weak tomography removes a serious lacuna from the Wootters and Fields analysis i.e the need to consider only state averaged error volumes or information. We also consider another proposal for weak tomography of mixed states by Lundeen and Bamber, and reach similar conclusions about MUB.
We apply the notion of optimality of measurements for state determination( tomography) as originally given by Wootters and Fields to weak value tomography. They defined measurements to be optimal, if the corresponding 'error volumes' in state space were minimal(for technical reasons they actually maximised a certain informationtheoretic quantity). In this paper, we first focus on weak value tomography of pure states. We prove, for Hilbert spaces of arbitrary (finite) dimensionality, that varieties of weak value measurements are optimal when the post-selected bases are mutually unbiased with respect to the eigenvectors of the observable being measured. We prove a number of important results about the geometry of state spaces when expressed through the weak values as coordinates. We derive an expression for the Kahler potential for the N-dimensional case from which the full metric and other relevant geometrical entities can be straightforwardly computed.
A quantum algorithm to solve the parity problem is better than its most efficient classical counter- part with a separation that is polynomial in the number of queries. This was shown by E. Bernstein and U. Vazirani and was one of the earliest indications that the quantum information processing can outperform the classical one by a significant margin. The problem and its solution both is usually stated for a 2-level system since we generally work with bits/qubits. However, many works have been done generalizing known quantum computing techniques to higher level systems. Following this, we look at a generalization of the Bernstein-Vazirani algorithm implemented on a general qudit system.
This article gives a brief overview of the newly found relationships between concepts in Quantum Information Theory and Quantum Gravity which were realized through the AdS-CFT correspondence.
Knots are deceivingly simple mathematical objects. Showing whether two knots are the same or not is a hard problem. While it can be done easily by inspection for simple knots, the problem becomes hard very quickly. Ideally, to distinguish between inequivalent knots we have to define knot invariants. At first sight, this may not have anything to do with quantum computation or field theories. However, it turns out that these subjects are intimately related to each other through an algebraic object called a modular tensor category (MTC). In this talk, I will describe an MTC and explain how it forms the bridge between the aforementioned topics.
A general quantum search algorithm is described using quantum state tomography. The error associated with a weak value measurement is used to estimate the query complexity. The query complexity depends on the details of the quantum tomography method employed. Query complexity of two algorithms differing in the tomography procedure employed is analyzed and it is shown that the algorithms are not efficient.
Two-level systems are one of the most important quantum systems and they form the basis of quantum computers. We briefly look at the traditional approach to two-level systems with an external driving field as well as those subjected to noise. This project is aimed at studying two specific methods for obtaining analytic solutions for two-level systems. One of the methods enables us to obtain analytic solutions for driven time-dependent two-level systems while the other attempts to give exact solution of qubit decoherence using a transfer matrix method. A thorough study of both papers is done and results are reproduced. The latter method is generalized for a qutrit system as well as a two qubit system subjected to noise. A general method is formally derived for an N-dimensional quantum system and the difficulties in applying the method in real life systems is discussed.
The equations giving energy eigenvalues for the bounding step potential is obtained using Bohr-Sommerfeld Quantisation and using Schr¨odinger’s equation. The transcendental equations obtained are solved graphically. The deviation of results obtained using Bohr-Sommerfeld Quantisation from that of Schr¨odinger’s equation is explained.
Two-level systems are one of the most important quantum systems. It is the basis of quantum computers. We briefly look at the traditional approach to two-level systems with an external driving field as well as those subjected to noise. This project is aimed at studying two specific methods for obtaining analytic solutions for two-level systems. One of the methods enables us to obtain analytic solutions for driven time-dependent two-level systems while the other attempts to give exact solution of qubit decoherence using a transfer matrix method. A thorough study of both the papers is done and results are reproduced. The latter method is generalized for a qutrit system as well as a two qubit system subjected to noise. A general method is formally derived for an N-dimensional quantum system and the difficulties in applying the method to real life systems is discussed.
Decoherence problems are usually solved by coupling the system concerned with an environment. Then, a master equation for the reduced density matrix is formed which can take care of the effect of the system on the environment too.In certain cases, this back-action is not important and we can model environment as a source of noise. A transfer matrix method can be used to obtain exact solution for such systems. This method was first described in the paper ’Exact solution of qubit decoherence models by a transfer matrix method’ by Diu Nghiem and Robert Joynt. This presentation was delivered during the discussion of the paper.
In 2012, Edwin Barnes and S. Das Sarma developed a completely new theoretical approach towards obtaining analytic solutions for driven two-state systems in their paper ’Analytically solvable driven time-dependent two-level quantum systems’. This new method gives an unbounded set of analytically solvable driven-two level systems which are driven by a single axis field. It is shown that the driving field and the evolution operator of such a system can be obtained from a single real-function satisfying some conditions. This presentation was delivered during the discussion of the paper.
Quantum mechanical systems get affected by observation. One of the classic example of this is losing interference pattern in a Young's double slit experimental setup while trying to get the '"which-path" information. The phenomenon of entanglement has shown its weirdness in various ways and the same has been used in the Quantum Eraser experiment which gives a clear picture of the nature of loss of interference while trying to get the "which-path" information. The article describes a simple experiment using a laser and polarizes to set-up a classical version of the Quantum Eraser experiment. Though the system is classical and we can no longer talk about individual photons the results are very similar to what happens in a quantum eraser experiment. Such experiments which mimic the results observed in an experiment on quantum systems play an important role in physics pedagogy.
Awards & Achievements (3)
Scholarship · Apr 2016
Summer Research Fellowship-2016 (JNCASR)
Award · Jan 2016
National Graduate Physics Examination 2016:State Topper
Award · Jan 2015
National Graduate Physics Examination 2015: State Topper