At the 1981 Physics of Computation conference, Richard Feynman proposed the idea of a machine—the quantum computer—that could efficiently simulate the physical world. Today, there are several research groups around the world working on the field of quantum simulations, and I am very excited to be part of one at Rice University led by professor Guido Pagano. The focus of our lab is the simulation of reaction dynamics, open quantum systems, and phase transitions of interacting spin systems. To perform a quantum simulation, we start with an apparatus in the lab that we can control well according to the laws of quantum physics—the quantum simulator (for this discussion, quantum simulator = quantum computer). A theorist, next, proposes a mapping between this system and a system in nature that we don’t fully understand. In the quantum simulator we prepare an initial state resembling one that the natural system might assume, let it evolve under a Hamiltonian of interest, and measure the final state. Results we obtain after a large number of repetitions of (initialization, evolution, measurement) give us a glimpse into the innerworkings of the system of interest. 

The core of our quantum simulator consists of an array of 171Yb+ ions trapped by RF electric fields inside a vacuum chamber at 10−14 𝑎𝑡𝑚. The hyperfine interaction in the ground state of the valence electron of ¹⁷¹Yb⁺ produces two long-lived levels that are first-order insensitive to external magnetic fields, making it a very stable two-level (spin-1/2) system that we use as our qubit. The qubit is the fundamental carrier of information in a quantum simulator. Its state can be any linear combination of the two levels comprising it: |𝜓⟩=𝛼|0⟩+𝛽|1⟩, |𝛼|2+|𝛽|2=1 . Depending on the setting of the trapping fields, multiple ions can assume different crystal configurations where the trapping forces are counteracted by the Coulomb repulsion among the ions. In this harmonic trapping potential, 𝑁 ions experience collective motion at 3𝑁 normal modes. Fig. 1: Vacuum chamber with the ion trap and ion array (see left). This collective motion allows for connectivity among qubits, and can be quantized, with associated creation and annihilation operators for motional quanta. Therefore, we work in a Hilbert space that is the tensor product of the 2D qubit space and the motional Hilbert space. While the latter is theoretically infinite-dimensional, in practice the anharmonicity of the trap restricts us to ~100D. The state of the system is a tensor product of a spin state and a number state: |Ψ⟩=|𝜓⟩⊗|𝑛⟩.

To slow down—cool—the ions, control their quantum state, and mediate interactions among them, we use electromagnetic radiation from UV to MW. The electric or magnetic field of the incident radiation couples to the electric or magnetic dipole (primarily) moment of the qubits, as well as their motion. As a result, we can prepare the system in simple spin-1/2 states, more complex motional Fock or coherentstates, but also entangle two qubits, the latter being a necessary characteristic of a quantum processor, computer or simulator. In addition, real-time manipulations of the trapping potential combined with light pulses of different durations and frequencies allow for engineered Hamiltonians. And voila! Our quantum simulator is ready! The only limit is our imagination and ingenuity in establishing mappings to nature.                              Fig. 2: Ion-laser interaction

When people ask me what I do, I usually say “kindergarten, but with very expensive and dangerous toys.”  To some significant degree, this is what research is: you don’t know whether the direction you are going will produce fruit, but you enjoy the journey most of the time. In this journey, one becomes more skilled in problem-solving and analytic thinking, more knowledgeable about all sorts of weird physics, wiser, but more importantly, if pay enough attention, one understands people. And this individual development not toward becoming an expert in a small area of science as most people describe a PhD, but toward becoming a master learner for life.

I am encouraging anyone not sure about their next steps in physics to reach out through the professors in the physics department to CSU alumni who are continuing their education or career in physics and get an idea of what each path might look like. I am grateful to the department of physics at CSU for their guidance, support, and equipping me with the skills necessary to be able to pursue a PhD in the beautiful field of quantum simulations.