Confusion, Clarity, and Quantum Highs: A Summer at the QED-C

By: Avimita Chatterjee, a fourth-year PhD student in Computer Science and Engineering at Pennsylvania State University, where she focuses on quantum computing and quantum error correction.

Embarking on a Quantum Journey

As a PhD student at Penn State, I have spent the better part of my academic life immersed in the fascinating (and sometimes frustrating) world of Quantum Error Correction (QECC). My background is rooted in computer science, so I was comfortable in my digital domain, wrangling code, algorithms, and the occasional debugging session that turns into an all-nighter, blissfully unaware of the complexities of quantum physics. But this summer, life decided to throw me a curveball. When I joined the QED-C for the summer as a quantum benchmarking intern, I naively thought I would be sticking to my comfort zone. Instead, I found myself navigating the uncharted waters of Quantum Hamiltonians.

Now, I would love to say I embraced this challenge with full confidence, but the truth is, I was confused. Very confused. I mean, Hamiltonian? Sounds more like the name of an indie rock band than a concept in quantum mechanics. For someone who has mostly worked on QECC for my PhD, this summer was like being handed a puzzle with all the pieces, but none of them seemed to fit until they did. It was challenging, it was confusing, and sometimes it was downright mind-bending, but it was also exhilarating. As the weeks went by, that initial confusion started to give way to clarity. The more I learned, the more everything fell into place, and suddenly, I found myself on a new kind of high — a quantum high, if you will. From writing code for the QED-C benchmarking suite to crafting my first-author paper, it all became an exhilarating experience that I would not trade for anything. (Yes, I am still pinching myself.)

Overcoming the Challenges of Quantum Hamiltonians

When I first encountered Hamiltonians in quantum computing, it felt like stepping into a realm where the rules I had known no longer applied. It was as if I had been transported from the familiar terrain of code and algorithms into a world governed by quantum bits and mysterious forces that I struggled to understand. The Hamiltonian, in classical mechanics, represents the total energy of a system, but in quantum mechanics, it became something far more elusive — a key that unlocks the door to understanding how quantum states evolve.

At first, this door felt locked tight. I was overwhelmed by the sheer complexity of the mathematics and the physics. It was not just about learning new concepts; it was about unlearning some of the intuitions I had built up over the years in computer science. The Schrodinger equation, which seemed like an abstract idea at first, started to feel like a giant puzzle that I could not solve. The frustration was real — there were moments when I wondered if I had taken on more than I could handle.

During my internship at QED-C, I worked with various Hamiltonian models, including the Fermi-Hubbard model, the Bose-Hubbard model, the Heisenberg model, and the Transverse Field Ising Model (TFIM). Each of these models brought unique challenges because of their complex interactions and the need for precise simulations to accurately represent their behavior.

For example, the Fermi-Hubbard model, which describes how fermions (particles like electrons) move on lattice sites, is especially challenging. Simulating this model requires extensive computational efforts, particularly in higher dimensions. The Hamiltonian for the Fermi-Hubbard model includes terms that represent the kinetic energy of particles moving between sites and the potential energy from interactions between particles on the same site.

To address these challenges, I needed to deeply understand the physics and mathematics behind these models. This involved studying the interactions between qubits and mapping them to physical phenomena like electron interactions in materials. By deconstructing the Hamiltonians into their fundamental components, I was able to grasp how each part influenced the quantum system’s behavior. Then, piece by piece, the puzzle started to come together. The more I wrestled with the Hamiltonian models, the more the confusion began to lift. I realized that this challenge was not just about quantum mechanics; it was about pushing my limits, about growing into a researcher who could handle this level of complexity. Every breakthrough, no matter how small, felt like a victory, and with each one, my confidence grew. The Fermi-Hubbard model, which had seemed so daunting at first, became a fascinating challenge — something I could conquer with enough persistence and determination.

Elucidating the Confusion through Simulation Techniques

The turning point in my journey came when I began working with simulation techniques like Trotterization. Before this, I had felt like I was constantly playing catch-up, trying to grasp concepts that seemed just out of reach. But Trotterization was different. It was as if I had finally found a tool that made sense to me, something I could use to chip away at the complexity and start making real progress.

Simulating the time evolution of a quantum system is no small feat — it requires approximating the exponential of a Hamiltonian, a task that had initially felt impossible. But as I learned about the Trotter-Suzuki decomposition, I started to see the pieces fall into place. It was still challenging, but now it was a challenge that I felt I could meet. I remember the first time I successfully applied Trotterization to a problem — it was like a light bulb went off in my head. Suddenly, the concepts that had seemed so abstract started to make sense concretely. I could see how the Hamiltonian’s components interacted, and how they drove the evolution of the quantum system. It was a moment of clarity that I had been striving for all summer.

In our research, we used three methods to benchmark quantum Hamiltonian simulations:

1. Hardware Performance (Method 1): We ran the Trotterized Hamiltonian circuit on both a real quantum device and a noiseless classical simulator to compare results and understand the impact of hardware noise. This method helped identify where fidelity loss occurred due to hardware imperfections.
2. Algorithmic Performance (Method 2): This method focused on comparing the Trotterized circuit’s output with results from classical matrix diagonalization, highlighting errors from the Trotterization process itself. It was particularly useful in assessing the accuracy of the simulation in the presence of Trotter errors.
3. A Scalable Performance Metric (Method 3): To evaluate scalability, we used mirror circuits, doubling the circuit depth by appending the inverse of the original circuit. This method tested whether the system could return to its initial state, which is crucial for large-scale quantum systems where traditional simulation methods are computationally challenging.

Each of the methods we used to benchmark quantum Hamiltonian simulations — whether it was assessing hardware performance, algorithmic performance, or scalability — gave me a deeper understanding of the field. But more than that, they gave me confidence. With each successful simulation, I felt like I was not just learning about quantum mechanics; I was becoming a quantum researcher.

Rationalizing the Mind-Bending with Real Applications

One of the most rewarding aspects of my internship was realizing how these theoretical concepts and simulation techniques have direct implications in real-world applications. Quantum Hamiltonian simulations are not just an academic exercise; they have the potential to revolutionize fields ranging from materials science to quantum chemistry.

For example, the Fermi-Hubbard model is crucial for understanding the behavior of electrons in materials, especially in studying high-temperature superconductors. By simulating this model on a quantum computer, we can explore the conditions under which electrons pair up without resistance, potentially leading to the development of new superconducting materials that could transform energy transmission.

Similarly, the Max3SAT problem, which we also simulated, is important in optimization and artificial intelligence. This problem involves finding the maximum number of satisfiable clauses in a Boolean formula. Its corresponding Hamiltonian can be represented in a way that reflects the constraints of the SAT problem. By leveraging quantum simulations, we can potentially solve these problems more efficiently than classical algorithms.

The realization that the work I was doing could contribute to such transformative technologies was both exhilarating and humbling. It underscored the importance of the research we were conducting and motivated me to continue pushing the boundaries of what is possible with quantum computing. This experience not only deepened my understanding of quantum mechanics and computational techniques but also solidified my commitment to exploring the practical applications of quantum technologies in the future.

Embracing the Quantum Experience

Here is the thing: I have always known I love to write. I have written many papers during my PhD, and each time, the writing process has been a joy. Seriously, if you ask me what my favorite part of research is, I will shamelessly tell you it is the writing. I am known for giving my papers creative (sometimes quirky) titles — because why not have a little fun with it? But this summer, writing took on a new meaning. It was not just about documenting research; it was about capturing a journey, from confusion to understanding, from coding to creating something meaningful.

I did not do it alone, of course. I had the incredible support of my fellow interns, Sonny Rappaport and Anish Giri, who quickly became more than just colleagues—they became friends. And then there were Tom Lubinski and Jonathan Felbinger, who went above and beyond the call of duty as our mentors. Tom was the Yoda to my Luke Skywalker, guiding me through the mysterious ways of quantum mechanics. They were there every step of the way, turning what could have been a daunting experience into one of the most rewarding adventures of my academic life.

So, what did I do this summer? I explored, I mastered, and I evolved. I might not have started as a quantum physicist, but thanks to this internship, I got a taste of what it is like. And you know what? I loved it. I would do it all over again in a heartbeat. Here is to more quantum adventures in the future!