# A few projects

### Quantum Message passing:

Quantum Message passing:

### My PhD thesis built a diagrammatic language for quantum processes based on linearly distributive categories. Cockett and Pastro introduced the Message Passing Logic in order to develop a formal type theory for concurrent programs with message passing as the communication primitive. The proof theory of the message passing logic is given by linear actegories which are also built from linearly distributive categories. By combining these two lines of work, one can possibly construct a formal framework to describe quantum concurrent processes which use message passing as its communication primitive.

My PhD thesis built a diagrammatic language for quantum processes based on linearly distributive categories. Cockett and Pastro introduced the Message Passing Logic in order to develop a formal type theory for concurrent programs with message passing as the communication primitive. The proof theory of the message passing logic is given by linear actegories which are also built from linearly distributive categories. By combining these two lines of work, one can possibly construct a formal framework to describe quantum concurrent processes which use message passing as its communication primitive.

[ Postdoctoral, work in progress ]

### Resistor networks:

Resistor networks:

### Star to mesh transformations are well-known in electrical engineering, and are reminiscent of local complementation for graph states in qudit stabilizer quantum mechanics. In this project, we described a rewriting system for resistor circuits over any positive division rig using general star to mesh transformations and showed how these transformations can be organized into a confluent and terminating rewriting system on the category of resistor circuits. This project is a step forward in the quest for approachable normal forms for stabilizer quantum circuits and has lots more to be explored ...

Star to mesh transformations are well-known in electrical engineering, and are reminiscent of local complementation for graph states in qudit stabilizer quantum mechanics. In this project, we described a rewriting system for resistor circuits over any positive division rig using general star to mesh transformations and showed how these transformations can be organized into a confluent and terminating rewriting system on the category of resistor circuits. This project is a step forward in the quest for approachable normal forms for stabilizer quantum circuits and has lots more to be explored ...

[ Postdoctoral, work in progress ]

### Ph.D. Thesis:

Ph.D. Thesis:

### Monoidal categories are the diagrammatic mathematics to describe and reason about process theories. Dagger monoidal categories are diagrammatic formal language to describe and reason about quantum process theories. The language consists of wires, boxes connected and juxtaposed to describe a specific process. Moreover, the language also specifies rules to manipulate the diagrams. However, dagger monoidal categories are quite restrictive in describing infinite dimensional processes. In my thesis, we developed mixed unitary categories a richer diagrammatic language based on linearly distributive categories to address the dimensionality issue and explored the applications of this new langauge.

Monoidal categories are the diagrammatic mathematics to describe and reason about process theories. Dagger monoidal categories are diagrammatic formal language to describe and reason about quantum process theories. The language consists of wires, boxes connected and juxtaposed to describe a specific process. Moreover, the language also specifies rules to manipulate the diagrams. However, dagger monoidal categories are quite restrictive in describing infinite dimensional processes. In my thesis, we developed mixed unitary categories a richer diagrammatic language based on linearly distributive categories to address the dimensionality issue and explored the applications of this new langauge.

[ PhD ]

### CNot circuits:

CNot circuits:

### The controlled NOT gate belongs the Clifford set of logic gates and the Clifford set along with the T gate is universal for quantum computation. This work provided a finite presentation (in terms of generators and a finite set of identities satisfied by the generators) of CNot circuits with ancillary bits, and proves that such circuits form discrete inverse categories.

The controlled NOT gate belongs the Clifford set of logic gates and the Clifford set along with the T gate is universal for quantum computation. This work provided a finite presentation (in terms of generators and a finite set of identities satisfied by the generators) of CNot circuits with ancillary bits, and proves that such circuits form discrete inverse categories.

[ PhD ]

### Masters Thesis:

Masters Thesis:

### My masters thesis is a systematic analysis of the message passing versus shared memory modes of synchronization on the efficiency of the concurrent software applications. Operating systems were originally designed to run on single core computers. With the advent of multicore computers, hardware support was added for shared memory synchronization of concurrent processes. This study showed that as the number of cores in a computer increases, synchronization via message passing surpasses the throughput of shared memory synchronization by preserving data locality.

My masters thesis is a systematic analysis of the message passing versus shared memory modes of synchronization on the efficiency of the concurrent software applications. Operating systems were originally designed to run on single core computers. With the advent of multicore computers, hardware support was added for shared memory synchronization of concurrent processes. This study showed that as the number of cores in a computer increases, synchronization via message passing surpasses the throughput of shared memory synchronization by preserving data locality.

[ Masters ]

### Quantum RAM:

Quantum RAM:

### A quantum Random Access Memory (qRAM) is a device which can address memory cells in quantum superposition. Since quantum data is extremely prone to decoherence, Lloyd et. al. proposed the Bucket Brigade architecture to build qRAMs. This project was an analysis of the robustness of this architecture for quantum search algorithms.

A quantum Random Access Memory (qRAM) is a device which can address memory cells in quantum superposition. Since quantum data is extremely prone to decoherence, Lloyd et. al. proposed the Bucket Brigade architecture to build qRAMs. This project was an analysis of the robustness of this architecture for quantum search algorithms.

[ Masters ]