Welcome to my blog! I’m Shounak Das, an undergraduate student in Computer Science and Engineering at Jadavpur University in Kolkata, India. I am deeply interested in Quantum Information Processing and Decision Making. I’m thrilled to have the chance to contribute to Red Hen Lab as a participant in Google Summer of Code (GSoC) 2024. I’m eager to advance the study of Quantum Wave Function in the realm of information processing.

I am grateful for my experience with Google Summer of Code (GSoC). Through this program, I was paired with Red Hen Lab, an international, interdisciplinary research consortium focused on multi-modal communication and machine learning. Under the guidance of experienced mentors, I had the opportunity to contribute to real-world projects and gain valuable software development experience while benefiting the open-source community. Red Hen Lab brings together scholars and researchers from various fields, including computer science, linguistics, cognitive science, and media studies, to analyze and understand human communication across different media formats.

I am very happy to have Prof. Francis Steen from the University of California, Los Angeles and Prof. Paavo Pylkkanen from Helsinki University as my mentors. We had discussions on every weekend, and their detailed emails and clear, tireless explanations helped me grasp the subject and translate ideas into computational code. They also introduced me to Prof. B. Hiley at Birkbeck College, University of London, allowing me to deepen my understanding of the subject. I am grateful to Prof. Steen and his colleagues for their invaluable support.

This blog is for a weekly document of progress for the Quantum Wave Function in the realm of information processing project of Red Hen Lab, GSoC 2024.

Abstract

McCulloch and Pitts first proposed a mathematical model of a neuron in 1943, which served as the foundation for Rosenblatt’s development of the Perceptron model in 1957. The Perceptron model, however, assumed that information is digital in nature, which can be considered a drawback since unicellular organisms actually receive analog signals. Initially, these models were based on the functioning of multicellular organisms, and at the time, a simple logic gate model of the neuron seemed plausible. However, subsequent significant advancements in microbiology have revealed the limitations of these models, rendering them no longer credible. It has become evident through these advancements that information processing and harvesting capabilities are not exclusive to multicellular organisms but are also present in unicellular organisms. In fact, it is believed that during the evolutionary process, unicellular organisms aggregated to form multicellular organisms. For instance, the work of Jennings demonstrated complex decision-making abilities in a single-celled organism, Stentor, which is equipped with beating hairs known as cilia. In his experiments, Jennings observed that when Stentor was subjected to an irritant, such as carmine powder directed at its mouth, it would first bend away, then reverse the beating of its cilia to expel the powder, contract, and finally detach. This behavior showcased Stentor’s ability to confront a stimulus with one response and adapt to a more costly approach if the irritant persisted. Such observations challenge the notion that a network of neurons is necessary for rudimentary information processing.

Biological processes like photosynthesis in unicellular organisms occur at the nano scale. Fleming’s experiment, published in Nature, illustrates that during photosynthesis, energy transfer within the FMO (Fenna–Matthews–Olson) complex is optimized by quantum phenomenon. When viewed in this way, the system is essentially performing a single quantum computation, sensing many states simultaneously and selecting the correct answer, as indicated by the efficiency of the energy transfer writes “while cognitive scientists for many years have tried to draw principled distinctions between ‘metabolic’ and ‘cognitive’ function (even in microbes …), this dividing line is increasingly difficult to defend even in human beings”
This suggests optimizing metabolic activities lead to optimal decision making too. This highlights how information harvesting can lead to near-perfect decision-making. We believe that modeling these quantum phenomena into neurons could lead to the next step in the evolution of neural networks.

Community Bonding (May 2024):

During the community bonding period, I began interacting with Prof. F. Steen, who provided a detailed explanation of the project. I started coding on the Schrödinger equation in one dimension. He recommended that I read “The Undivided Universe” by David Bohm. Through this, I learnt about the Pilot Wave Theory, a novel approach in quantum mechanics that could potentially be applied to wayfinding or decision-making using quantum information processing.

May 27 — June 2:

I developed Python code to solve the Time-Dependent Schrödinger Equation using the Crank-Nicolson method. Initially, I wrote a monolithic piece of code to ensure its functionality. For the Crank-Nicolson method, I used the CuPy library to leverage GPU acceleration. With the solution to the Schrödinger Equation in hand, I was able to easily calculate the probability density.

June 3 — June 9:

I wrote code to calculate the Quantum Potential from the estimated wave function, assuming no gauge field interaction among the particles. This allowed me to determine the velocity of the particle guided by the pilot wave. Finally, I derived the particle trajectory in three dimensions for the non-gauge field scenario.

June 10 — June 16:

I tested and validated the wave function’s acceptability, as outlined below.

The wave function provides complete description of all properties of matter at the atomic and molecular level. Wave Function is a function of position and time. Time dependent ψ(r, t) carries dynamical observable (experimentally measured/ observed viz., position, momentum, energy, etc.) but it is not directly observable in the experiment. Experimental observable depend on ψψ∗ = |ψ|2. If ψ is normalized then Probability Density is

I listed the test cases

a) ψψ∗ must be single valued. b) Value of ψ should not blow-up for all x, y, z, t c) First derivative of ψ finite and continuous d) Normalizable e) ψ Continuous everywhere f) Probability Density is integration ψψ∗ and analyzed the sub-functional modules. After tuning the parameters, I generated the expected output.

June 17 — June 23:

I was supposed to use MWLS method to solve Time Dependent Schrodinger Equation. But I solved the equation using Crank–Nicolson method.
Finally we can calculate the trajectory of excitons.

But what does this mean?

According to Bohmian mechanics, the motion of the exctions respond to the form of the Quantum wave. The Quantum Potential contains information about its surroundings, such as the slit in our case. Now, consider a single-celled amoeba. Suppose when a food particle comes into contact with the exterior of the amoeba, it changes the shape of the slit. As the slit is influenced by external information, the Quantum Potential is also affected by it. Consequently, the excitons receive this external information and move accordingly — in this case, deciding whether or not to ingest the food particle.

June 24 — June 30:

I tested and validated the system according to Wave Function acceptability. The test cases were met, and all sub-functional modules were ready. I analyzed the sub-functionals and generated the parameters after tuning the expected output.

July 1 — July 7:

I changed the rectangular slit-shape to an annular shape and varied the classical potential wells according to σ and μ. I wrote the code for a system with multiple slits (seven slits) and parallelized the code for improved performance using the CuPy library.

July 8 — July 12:

I completed the midterm evaluation, finalized the model of the first approach, and submitted a report to my Red Hen Lab mentor. I then had a discussion with Prof. Paavo Pylkkänen from Helsinki University and Prof. Prof. Basil Hiley at Birkbeck College, University of London, alongside my mentor Prof. Steen. During this discussion, I gained a detailed understanding of Bohmian Mechanics, which led me to change my approach to the problem by introducing quantum tunneling into the code. Last week, I focused on working with seven slits; this week, I began framing the problem with seven potential barriers.

July 13 — July 21:

This week, I began modeling the Mach–Zehnder interferometer, which uses four potential barriers. The Mach–Zehnder interferometer forms the basic structure of the FMO complex. I wrote the code and simulated the interferometer, focusing on potential barriers and barrier width as the most crucial parameters in the simulation. Next, I plan to extend this simulation to include seven potential barriers.

July 22 — July 28:

I modeled the FMO (Fenna-Matthews-Olson) complex, which plays a critical role in photosynthetic processes, and adapted it for the study of unicellular ingestion. The FMO complex is composed of seven chromophores arranged in a specific, intricate structure. In my approach, I represented these seven chromophores as seven potential barriers within the system.

To capture the dynamic nature of the complex, I wrote code that allows these seven potential barriers to be placed dynamically at different locations within the model. This flexibility is crucial for accurately simulating the complex behavior of the FMO structure in various scenarios.

July 29 — Aug 4:

I introduced quantum entanglement into the system, an essential aspect of quantum mechanics that can significantly influence the interactions between the barriers. By incorporating quantum entanglement, I aimed to simulate the intricate quantum effects that occur within the FMO complex, providing a deeper understanding of how these quantum phenomena might impact unicellular ingestion processes.

Aug 5 — Aug 11 :

I have done some Model tuning and written animation codes. Model tuning means adjusting a) time length of simulation, b)size of simulation space, c) wave vector, k d) location of barriers, e) location of reaction center.

Animation code generated the movie to demonstrate the wave function in the simulation space. The complete code of this project is available in the github free for users. There is no restriction to modify and reuse the code if required.

Aug 12 — Aug 18 :

Results and Analysis: I have conducted simulations under various noise levels within the system, producing numerous simulation movie files to visualize the trajectories of excitons. The analysis reveals that the excitons successfully reach the reaction center when the noise level is up to 90% of the barrier height. Even in such a noisy environment, the quantum potential effectively guides the excitons, ensuring they reach the reaction center consistently. This indicates that the quantum potential remains robust and reliable in directing excitons to their target, even under significant noise conditions.

Example of a simulation video with various noise level is available in this link: https://github.com/ShounakDas101/FMOComplex

Aug 19 — Aug26 :

The final week of GSoC for submitting my work product and completing my final mentor evaluation. All my codes and simulation results are available free in https://github.com/ShounakDas101/FMOComplex

My entire work is open to anyone interested in quantum information processing, and I welcome any suggestions or feedback. I hope you enjoyed reading this blog!