Posts by Collection

Lower bound on PPT distillable entanglement from isotropic states

Quantum entanglement is an essential resource in quantum information theory. What is the rate of distillation of entanglement from isotropic states using operations that are positive-partial-transpose-preserving? This project presents a detailed proof of a theorem from the paper A semidefinite program for distillable entanglement by Rains that shows a lower bound for this rate. The problem is equivalent to the rate of transmission through a quantum depolarizing channel assisted by PPTp codes.

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E91 Cryptographic Protocol

E91 protocol proposed by Ekert was one of the first practical applications of quantum entanglement. It achieves the task of quantum key distribution. In this short document I present a step by step proof of the protocol.

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Hypercontractivity Via the Entropy Method

In this project I present a detailed proof of a hypercontractive inequality using basic entropic quantities and their properties. The proof comes from the paper Hypercontractivity Via the Entropy Method by Blais and Tan.

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Classical Machine Learning for Quantum Systems and Quantum Enhanced Machine Learning

What is Quantum Machine Learning? We may use classical machine learning to solve problems in quantum physics or we may use quantum algorithms to develop new, fully quantum machine learning techniques. I chose a paper from both categories and summarized them in my project. The first paper is A Neural Decoder for Topological Codes by Giacomo Torlai, Roger G. Melko which proposes a stochastic neural network to create decoders for topological quantum error-correction codes. The second paper is Quantum Perceptron Models by Nathan Wiebe, Ashish Kapoor, Krysta M Svore which shows how to quantumly represent and train a perceptron.

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Non-additivity of Channel Capacities in the Quantum Shannon Theory

In classical information theory channel capacities are additive. Is it the case in quantum information theory as well? Can we transmit any information by combining quantum channels which alone have no capacity? This project summarizes a paper Quantum Communication With Zero-Capacity Channels by Graeme Smith and Jon Yard that answers these questions.

Download my work here.

Portfolio item number 1

Short description of portfolio item number 1

Portfolio item number 2

Short description of portfolio item number 2

Lower bound on PPT distillable entanglement from isotropic states

Quantum entanglement is an essential resource in quantum information theory. What is the rate of distillation of entanglement from isotropic states using operations that are positive-partial-transpose-preserving? This project presents a detailed proof of a theorem from the paper A semidefinite program for distillable entanglement by Rains that shows a lower bound for this rate. The problem is equivalent to the rate of transmission through a quantum depolarizing channel assisted by PPTp codes.

Download my work here.

Hypercontractivity Via the Entropy Method

In this project I present a detailed proof of a hypercontractive inequality using basic entropic quantities and their properties. The proof comes from the paper Hypercontractivity Via the Entropy Method by Blais and Tan.

Download my work here.

Classical Machine Learning for Quantum Systems and Quantum Enhanced Machine Learning

What is Quantum Machine Learning? We may use classical machine learning to solve problems in quantum physics or we may use quantum algorithms to develop new, fully quantum machine learning techniques. I chose a paper from both categories and summarized them in my project. The first paper is A Neural Decoder for Topological Codes by Giacomo Torlai, Roger G. Melko which proposes a stochastic neural network to create decoders for topological quantum error-correction codes. The second paper is Quantum Perceptron Models by Nathan Wiebe, Ashish Kapoor, Krysta M Svore which shows how to quantumly represent and train a perceptron.

Download my work here.

Non-additivity of Channel Capacities in the Quantum Shannon Theory

In classical information theory channel capacities are additive. Is it the case in quantum information theory as well? Can we transmit any information by combining quantum channels which alone have no capacity? This project summarizes a paper Quantum Communication With Zero-Capacity Channels by Graeme Smith and Jon Yard that answers these questions.

Download my work here.

Implementation of the hybrid Quantum Approximate Optimization Algorithm in Q# and C#

Published: August 11, 2020

QAOA is a quantum algorithm for solving combinatorial optimization problems. Its sucessful execution depends on input parameters that need to be tailored to a specific problem that we are solving. Usually, this choice is challenging for a user and might require a trial and error approach. The problem can be mitigated by using a classical feedback loop that involves a classical optimizer that searches for good input parameters. I will present my implementation of such a hybrid QAOA algorithm in Q# and C# taht uses a gradient-free Cobyla optimizer and I will show how to solve a simple problem using it.

Linear Algebra for Engineers

Linear Algebra for Engineers, University of Waterloo, Department of Combinatorics & Optimization, 2017

Organizing and proctoring weekly quizzes, grading.

Introduction to Optimization (Non-Specialist Level)

Introduction to Optimization (Non-Specialist Level), University of Waterloo, Department of Combinatorics & Optimization, 2018

Holding office hours, grading and proctoring exams.

Portfolio Optimization Models

Portfolio Optimization Models, University of Waterloo, Department of Combinatorics & Optimization, 2018

Tutorials, holding office hours, grading and proctoring exams.

Introduction to Optimization

Introduction to Optimization, University of Waterloo, Department of Combinatorics & Optimization, 2019

Holding office hours, grading and proctoring exams.