Gaurang Agrawal

Categorical quantum mechanics

Higher order quantum theory

Indefinite causal order

Quantum resource theories

Applied category theory

Surveyed the existing literature on quantum combs, memory channels, Indefinite causal order, quantum operations with indefinite input-output direction, and coherent control of quantum channels.

Derived the advantages of quantum operations with indefinite input-output direction in metrology. We show Heisenberg scaling in estimating arbitrary parameters in vast number of channels in the absence of entanglement, and compare our strategy to quantum switch and standard cascade strategies. A preprint is under preparation.

Learned the theory and applications of semi definite programming in quantum information theory. Learned the process matrix framework and derived many of the result using diagrammatic formulation.

Going forward I plan to extend the above results by optimizing over strategies via semi definite programming. I also seek applications of these operations in discrimination and capacity enhancement tasks, while also trying to further develop their theory using linear algebraic and category-theoretic formalisms.

We are trying to derive the generalized Born rule in symmetric monoidal categories as an outcome of some minimal constraints on a ’good’ probability function over state-effect pairs.

We show that with a number of physically well-motivated constraints there exist a functor between the composition of the state effect pair and the corresponding probability

Devised a procedure to construct resource breaking channels from a given set of free states and free channels for any convex resource theory, giving a sufficient criterion for breaking channels.

Derived the necessary conditions for convex combination of unitaries to be non absolute separability (NAS)breaking. Identified extremal points of such breaking channels and verified that they satisfy our conditions.

Learned various static and dynamical resource theories and the process theoretic framework.

Conducted a literature survey in higher-order quantum theory, definite and indefinite causal structures, and the use of category theory to these domains, with an emphasis on diagrammatic methods.

Studied the classification of quantum types, Choi-like characterization of higher-order quantum maps, and explored concepts like quantum uncurrying, and generalized combs.

Studied category theoretic models of causal structures, including precausal and Caus[C] categories, mathematical characterization of one way signalling, non-signalling, bipartite second-order causal and general higher order processes. Read about realization theorems e.g. realization of quantum combs as memory channels etc.

Learned applied category theory and its uses in the study of preorders, resource theories, databases, and more prominently in quantum physics. Presented my work at the end of the programme and submitted a report.

○ learned the use of symmetric monoidal categories in developing a diagrammatic formalism for quantum physics. Showed the relation between local and global Choi matrices as a minute application of the theory.

Analyzed Fourier transform-based quantum adder circuits on qudits, demonstrating trade-offs between noise and defects. Led to a first author preprint under review for publication.

Identified coherence as a crucial resource for the performance of the circuit and showed the advantages of using higher-dimensional qudits in fidelity.

○Demonstrated that constant-depth approximating circuits yield better results in noisy conditions compared to exact circuits, promising subsequent additions in constant time.

Wrote more than 10,000 lines of code in Qiskit and QuTiP, and developed my own set of modules to simulate quantum circuits on qudits to produce the numerical results which I later derive analytically

In my first semester long project I studied the basic principles of quantum information, quantum computing, and cryptography under the mentorship of Prof. Deepak Dhar.

I devised a quantum ripple carry adder circuit using IBM’s Qiskit SDK imitating the classical full adder and half adder approach. I took part in weekly presentations and submitted a report at the end.

○ With Prof. M.S. Santhanam I simulated the dynamics of classical and quantum kicked top systems. I characterized their chaotic behavior using level spacing distributions, concurrence, and symmetry classes of the Floquet operators. I presented my work at the end of the semester and submitted a report.

At HRI and IISER Pune as part of Mid-Year thesis presentations: I gave a brief introduction of metrology, quantum combs framework, process matrix framework, quantum operations with indefinite input output directions and their applications. I present our original results on metrology using quantum time flip (not shown here) and mention the need of optimization over strategies using semi-definite programming. Here is the link for the slides.

At ICTS Bengaluru under the S. N. Bhatt memorial excellence fellowship and at the QIC group, HRI as part of group's weekly presentations: I presented the diagrammatic method of doing quantum physics and the mathematics of category theory underpinning it. I also presented the diagrammatic description of teleportation and Choi theorem. Here is the link for the slides and the associated report.

At the Wolfram winter school 2024: I presented the theory of magic, its implication on classical simulability of quantum circuits and the mathematica function which I have implemented to calculate the same. I introduce ZX calculus and how it can be used to analyze simulability. The presentation ends by analyzing the ZX diagrams of QFT based quantum adders. Here is the link of the mathematica notebook.

Project presentations to HRI QIC group: Throughout the senior year of my undergraduate I presented the findings of various research projects which I have pursued.

Presentations and reports as part of IISER Pune semester projects: Presentations made as a part of semester projects at IISER Pune and their associated project reports. First project (Quantum Information and Foundation) and second project (Chaos in Quantum Kicked Tops)