Danesh Morales Hashemi

Danesh Morales Hashemi

Quantum Information

University of Waterloo

I am a Master's student at the University of Waterloo and a researcher at the Institute for Quantum Computing, under the supervision of Prof. Graeme Smith. My research focuses on quantum error correction under non-Markovian noise. Using the process tensor framework, I study how QEC codes interact with temporally correlated errors and whether error correction can effectively suppress or Markovianize the noise process.

News

Research Interests

Quantum Error Correction Fault-Tolerant Quantum Computing Non-Markovian Dynamics Open Quantum Systems Quantum Error Mitigation Quantum Error Characterization & Suppression

Education

Master of Mathematics in Applied Mathematics
University of Waterloo
Quantum Information Specialization
May 2025 – Current
Bachelor of Mathematics in Mathematical Physics
University of Waterloo
Co-op Program · Pure Mathematics Minor · Graduated with Distinction and Dean's Honours
September 2020 – April 2025

Publications

Thesis and selected course projects

2025 Course Project

Introduction to Cycle Benchmarking for Quantum Error Diagnostics

Danesh Morales-Hashemi

Theory of Quantum Information — Final Project, University of Waterloo, Fall 2025

Cycle benchmarking is a scalable protocol used to measure the error rate of a specific cycle of quantum gates implemented in parallel. We will introduce the cycle benchmarking protocol, explain how it works, and numerically illustrate its effectiveness. We demonstrate that relaxing the assumptions required to accurately estimate the process fidelity can lead to inaccurate results; in particular, allowing gate-dependent noise on the twirling gates can cause a misestimation of the process fidelity. However, we also show that highly gate-dependent errors can still yield accurate results in certain regimes. Finally, when the gate-independent condition is relaxed, we show that it is possible to reconcile the estimated and theoretical fidelities by measuring in a different basis via a unitary transformation which depends on both the chosen error model on the twirling gates and the targeted gateset.

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2025 Thesis

Demonstrating Circuit Benchmarking for Efficient and Scalable Fidelity Estimation

Danesh Morales-Hashemi

PHYS 437B — Undergraduate Thesis, University of Waterloo, Winter 2025

In this project, we will illustrate the theoretical concept of circuit benchmarking, an efficient and scalable protocol to “lower bound” the process fidelity of a circuit. Finding a lower bound to the process fidelity is crucial because it tells us what is the worst-case error rate in our quantum circuit. We will exhaustively run simulations on quantum circuits with different error models and error strengths to measure the closeness of the theoretical bound imposed by the circuit benchmarking theory with respect to the actual process fidelity. We will find that in several cases there is a minimal or zero gap, and thus not only we have found a lower bound, but rather a good approximation to the process fidelity.

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2024 Course Project

Introduction to Superoperator Representations and Characterization of Completely Positive Maps

Danesh Morales-Hashemi

Open Quantum Systems — Final Project, University of Waterloo, Spring 2024

We introduce the concept of superoperators, which are mathematical constructs used to describe the evolution of quantum states. We will focus on completely positive and trace-preserving maps, which are essential in quantum information theory as they represent the most general form of physical quantum operations. Next, we delve into different representations of superoperators. We define each of these representations in detail and prove several theorems that demonstrate their importance. Then, we prove that all the different representations of a superoperator are equivalent. This equivalence is important because it allows us to convert between representations with ease, depending on which one is more convenient for the problem at hand. Consequently, we analyze the properties of these representations when we add the restrictions that the superoperators are trace-preserving and/or completely positive. Finally, we visualize specific quantum channels using these representations. This analysis provides a new perspective on how the representations depict the channels and allows us to examine their properties in greater detail.

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Blog

Personal notes on quantum information.

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Contact

Feel free to reach out — I'm open to questions about my research, collaboration proposals, and job or research opportunities.

Office

QNC 4203
Quantum Nano Centre
University of Waterloo
Waterloo, ON, Canada

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