Chapter 8: Quantum Simulation

While many systems that we would like to simulate are indeed classical, systems on the microscopic scale are intrinsically quantum. As an example, suppose we want to understand the folding dynamics of the RNA embedded in the COVID-19 virus. An RNA can include up to several millions nucleotides, but we'll take the shortest one to be around 200 nucleotides in length. Let’s see why the simulations of quantum systems on classical computers is a very challenging problem. 

For simplicity let’s assume each of the nucleotides can be represented by only a couple of basis functions (i.e. orbitals which we label 0 or 1) that determine their interactions with their neighbors. If our nucleotide sequence is classical, then we can write down the state with 200 numbers (e.g. the first 6 nucelotides are 010110, and we just wrote them down with 6 digits). If instead, we assume our nucleotide sequence is quantum, we can also have superpositions of many states (e.g. a|001000> + b|100111> + c|1110110> + ...). If we want to write the full quantum state, we have to write down the strengths of each of the possible combinations of our state. We have 2^200 possible states (000000..., 100000..., 010000..., ..., 111111...). Then, just to write down the state of this short RNA would require  2^200 coefficients, which equals 200,000,000,000,000,000,000,000,000,000,000,000,000,000,000 Petabytes! Just being able to store such large amounts of information is already an impossible task on any supercomputer, so trying to do any computation with this information is out of the question.

The difficulty of dealing with this amount of data stems from the fact that classical systems are fundamentally not well-suited to capture the properties of quantum objects. As illustrated by our COVID example, it is practically impossible to simulate the various molecules and solid-state systems that are relevant to fields like modern chemistry, medicine, and material science. 

So, is it hopeless to try to simulate quantum systems? Notably, among the early proponents of quantum computing was by physicists Richard Feynman who proposed using quantum objects to simulate quantum dynamics. 

Quantum simulators can take many shapes and sizes, so researchers spend a lot of time thinking about how to build a simulator that can best model the physical system they're interested in. An example of a platform for quantum simulation are quantum gas microscope experiments which can be used to explore models for materials.

In such an experiment, scientists trap and cool a cloud of atoms to extremely low temperatures, close to absolute zero. This creates a state of matter called a quantum gas, where atoms behave according to quantum dynamics. The "microscope" part comes in when researchers use laser light to image the individual atoms in this cold cloud. By shining laser light on the atoms and capturing the scattered light, scientists can take high-resolution pictures of the atom positions. This allows them to directly observe and study the quantum behavior of individual atoms.

By manipulating the potential landscape of atoms in the quantum gas and observing their interactions, scientists can draw a direct parallel between the dynamics of these atoms to physical systems that we care about such as the behavior of an electron in a superconducting material. Therefore, scientists are able to gain valuable insight into the quantum dynamics of a material that would otherwise be impractical to simulate on a classical computer.

As quantum science continue to evolve, quantum simulation has the capability to not only advance our fundamental understanding of quantum dynamics but also holds promise for addressing practical scientific questions.