One night last July, IQIM postdoc Ning Bao emailed me a photo. Heâd found a soda can that read, âShare a Coke with Patrick.â
Ning and I were co-mentoring two Summer Undergraduate Research Fellows, or SURFers. One mentee received Ningâs photo: Caltech physics major Patrick Rall.
âHaha,â Patrick emailed back. âIâll share a Coke.â
Patrick, Ning, and I shared the intellectual equivalent of a six-pack last summer. We shared papers, meals, frustrations, hopes, late-night emails (from Patrick and Ning), 7-AM emails (from me), and webcomic strips. Now a senior, Patrick is co-authoring a paper about his SURF project.
The project grew from the question âWhat would happen if we quantized Conwayâs Game of Life?â (For readers unfamiliar with the game, Iâll explain below.) Lessons we learned about the Game of Life overlapped with lessons I learned about life, as a first-time mentor. The soda fountain of topics containedÂ the following flavors.
Update rules: Till last spring, Iâd been burrowing into two models for out-of-equilibrium physics. PhD students burrow as no prairie dogs can. But, given five years in Caltechâs grassland, I wanted to explore. I wanted an update.
Ning and I had trespassed upon quantum game theory months earlier. Consider a nonquantum game, such as the Prisonerâs Dilemma or an election. Suppose that players have physical systems, such as photons (particles of light), that occupy superposed or entangled states. These quantum resources can change the landscape of the gameâs possible outcomes. These changes clarify how we can harness quantum mechanics to process, transmit, and secure information.
How might quantum resources change Conwayâs Game of Life, or GoL? British mathematician John Conway invented the game in 1970. Imagine a square board divided into smaller squares, or cells. On each cell sits a white or a black tile. BlackÂ represents a living organism; whiteÂ represents a lack thereof.
Conway modeled population dynamics with an update rule. If prairie dogs overpopulate a field, some die from overcrowding. If a blackÂ cell borders more than three blackÂ neighbors, a whiteÂ tile replaces the black. If separated from its pack, a prairie dog dies from isolation. If a blackÂ tile borders too few blackÂ neighbors, we exchangeÂ the black for a white. Mathematics columnist Martin Gardner detailed the rest of Conwayâs update rule in this 1970 article.
Updating the board repeatedly evolves the population. Black and white shapes might flicker and undulate. Space-ship-like shapes can glide across the board. A simple update rule can generate complex outcomes—including, I found, frustrations, hopes, responsibility for another humanâs contentment, and more meetings than Iâd realized could fit in one summer.
Initial conditions: The evolution depends on the initial state, on how you distribute white and black tiles when preparing the board. Imagine choosing the initial state randomly from all the possibilities. White likely mingles with about as much black. The random initial condition might not generate eye-catchers such as gliders. The board might fade to, and remain, one color.*
Enthusiasm can fade as research drags onward. Project Quantum GoL has continued gliding due to its initial condition: The spring afternoon on which Ning, Patrick, and I observed the firmness of each otherâs handshakes; Patrick walked Ning and me through a CV that could have intimidated a postdoc; and everyone tried to soothe everyone elseâs nerves but occasionally avoided eye contact.
I donât mean that awkwardness sustained the project. The awkwardnessÂ faded, as exclamation points and smiley faces crept into our emails. I mean that Ning and I had the fortune to entice Patrick. We signed up a bundle of enthusiasm, creativity, programming skills, and determination. That determination perpetuated the project through the summer and beyond. Initial conditions can determine a systemâs evolution.
Long-distance correlations:Â âSure, I’d love to have dinner with you both! Thank you for the invitation!â
Lincoln Carr, a Colorado School of Mines professor, visited in June. Lincolnâs group, Iâd heard, was exploring quantum GoLs.** He studies entanglement (quantum correlations) in many-particle systems. When I reached out, Lincoln welcomed our SURF group to collaborate.
I relished coordinating his visit with the mentees. How many SURFers could say that a professor had visited for his or her sake? When I invited Patrick to dinner with Lincoln, Patrick lit up like a sunrise over grasslands.
Our SURF group began skyping with Mines every Wednesday. We brainstorm, analyze, trade code, and kvetch with Mines student Logan Hillberry and colleagues.Â TheyÂ offer insights about condensed matter; Patrick, about data processing and efficiency; I, about entanglement theory; and Ning, about entropy and time evolution.
Weâve learned together about long-range entanglement, about correlations between far-apart quantum systems. Thank goodness for skype and email that correlate far-apart research groups. Everyone would have learned less alone.
Time evolution: Logan and Patrick simulated quantum systems inspired by Conwayâs GoL. Each researcher coded a simulation, or mathematical model, of a quantum system. They agreed onÂ a nonquantum update rule; Logan quantized it in one way (constructed one quantum analog of the rule); and Patrick quantized the rule another way. TheyÂ choseÂ initial conditions, let their systems evolve, and waited.
In July, I noticed that Patrick brought a hand-sized green spiral notepad to meetings. He would synopsize his progress, and brainstorm questions, on the notepad before arriving. He jotted suggestions as we talked.
The notepad began guiding meetings in July. Patrick now steers discussions, ticking items off his agenda. The agenda Iâve typed remains minimized on my laptop till he finishes. My agenda contains few points absent from his, and his contains pointsÂ not in mine.
Patrick and Logan are comparing their results. Behaviors of their simulations, theyâve found, depend on how they quantized their update rule. One might expect the update rule to determine a systemâs evolution. One might expect the SURF programâs template to determine how research and mentoring skills evolve. But how we implement update rules matters.
Life: Iâve learned, during the past six months, about Conwayâs Game of Life, simulations, and many-body entanglement. Iâve learned how to suggest references and experts when I can’tÂ answer a question. Iâve learned that editing SURF reports by hand costs me less time than editing electronically. Iâve learned where Patrick and his family vacation, that he’s studyingÂ Chinese, and how undergrads regard on-campus dining. Conwayâs Game of Life has expanded this prairie dogâs view of the grassland more than expected.
Iâll drink a Coke to that.
Glossary: Conway’s GoL is aÂ cellular automaton.Â A cellular automaton consists of a board whose tiles change according to some update rule. Different cellular automata correspond to different board shapes, to boards of different dimensions, to different types of tiles, and to different update rules.
*Reversible cellular automata have greater probabilities (than the GoL has) of updatingÂ random initial statesÂ through dull-looking evolutions.
**Others have pondered quantum variations on Conway’s GoL.