**The strange and complex behavior of quantum systems makes them all but impossible to understand with digital simulation. Even relatively simple systems require enormous amounts of computing power to study, and our conventional tools can’t answer the questions we have about the quantum world.** **Researchers have now turned to quantum simulators, programmable quantum devices that can be used to model to quantum mechanics.**

*Image Credit: Billion Photos/Shutterstock.com*

Quantum simulators consist of numerous qubits that can be manipulated to test theories about the evolution of quantum systems. As these simulators improve, new ways of applying them are found. What started out as a method of better understanding physics has been employed in medicine and chemistry and may soon see use in economic simulations.

## Where Classical Simulation Fails

Quantum systems are difficult to study due to their unintuitive nature. At the quantum level, strange phenomena occur which defy conventional logic. For example, particles can tunnel through barriers that would seem impassable or become entangled, causing “spooky action at a distance,” as coined by Einstein.

In classical systems, if all starting conditions are known, the outcome can always be predicted. This is fantastic for computer simulations, where one set of input variables will give a single, definitive answer. However, all elements of a quantum system exist not as definite states but as superpositions or “mixes” of possible states, and this gives rise to the principles of quantum mechanics. Quantum phenomena are probabilistic, with random outcomes that can’t be predicted; only the likelihood of each outcome can be known.

This makes it almost impossible for classical computers to simulate these systems. With each interaction, the number of possible outcomes grows. The complexity of a complex system grows exponentially with each particle that is added to it. For a system of 10 particles, one would need around a thousand values to express the system state; for a system of 40, a trillion values would be needed. 40 particles is a relatively simple system, yet it would take a supercomputer an eternity to model how it changes over time. Quantum systems of interest often have hundreds of particles, so classical study is impossible.

## Quantum Simulation

As the concept of quantum theory was developed, it was quickly realized that only quantum systems were suitable for running quantum simulations. Quantum simulators use the quantum properties of the particles within them to model quantum phenomena, removing the challenge of expressing these strange interactions as code.

Quantum simulators are “programmed” with a range of starting conditions, then allowed to evolve until they give a clear output state. Normal quantum systems are prone to unwanted entanglement, generate a lot of noise, and are difficult to replicate. Modern quantum simulators allow for the precise control of variables, so tests can be run quickly while still being an accurate model.^{ }

It should be noted that quantum simulators and quantum computers are not the same. While a hypothetical “perfected” quantum computer would be able to simulate any given quantum system, quantum computers have not yet reached the qubit count needed for complex simulations. Instead, quantum simulators are built to run specific simulation types and, outside of variable control, can’t be programmed in the manner that quantum computers can. This makes them more powerful than quantum computers but with fewer applications.

**Simulator Types:** Simulators can vary greatly depending on the system they are intended to model, but there are a few key archetypes. Each of these uses a different quantum element for information storage, and each is suited for different phenomena.

**Trapped Ion: **In these systems, atomic ions are trapped in a lattice. The spin of each ion is the variable of interest, as it is easy to measure and vary remotely. Optical fields can be used to “tune” the ions, orienting their spin and changing their energy levels to create the desired starting conditions for the simulation. These ions will then interact via the electromagnetic force, causing the system to evolve.

Spin is one of the simplest particle properties to manipulate and understand, making it easy to design simulation experiments around. All quantum systems depend on particle spin for some interactions, and trapped-ion systems focus on this property. Trapped-ion simulators are particularly good at simulating materials that depend on quantum phenomena, such as superconductors, as these are very similar to the trapped-ion model.

**Ultracold atom simulators: **Ultracold atoms exhibit quantum phenomena on a large scale and become easy to manipulate due to their reduced energy. These atoms are trapped in optical lattices, electromagnetic fields formed by interfering laser beams. The interference creates potential wells that the atoms sit in, and in this state, they are easy to observe. Ultracold atom simulators have been used to study a number of macroscopic quantum phenomena, such as superfluidity and superconductivity.

**Superconducting Qubits: **In both the trapped-ion and ultracold atom simulations, the energy levels of individual atoms are used as qubits. Superconducting qubits instead track the motion of electrons through superconductors, with the energy level of each conduction band being the variable of interest. Superconductors can be incorporated into traditional circuitry, so they can be implemented more easily.

## Applications

The foremost application of quantum simulators is the investigation of quantum mechanics. Simulators have already been used successfully to study phenomena such as superconductivity, and discoveries made with quantum simulators have aided the development of other quantum technology.

The initial motivation for quantum simulation was the need for a new tool to understand quantum mechanics, but they are already seeing use in other fields. Quantum simulators have been used in chemical research, as the interaction of molecules is inherently quantum. This is an application that has been growing in popularity as quantum simulators improve.

Some researchers are also investigating the possibility of employing quantum simulators to solve economic and logistical problems. While these sociological fields seem far removed from physics, their unpredictable nature makes them well-suited for quantum simulation. As simulators improve in reliability and power, commercialization through such applications may become commonplace.

## References and Further Reading

Lloyd, S. *Universal Quantum Simulators. * Science, Vol 273, Iss 5278. (1996) https://www.science.org/doi/10.1126/science.273.5278.1073

Johnson, T.H. Clark, S.R. Jaksch, D. *What is a Quantum Simulator? *Oxford Physics. (Accessed 2023) https://www3.physics.ox.ac.uk/groups/qubit/fetch.asp?url=groupwebsite/papers/paper311.pdf

Monroe, C. et al. *Programmable Quantum Simulations of Spin Systems with Trapped Ions. *Rev. Mod. Phys. 93, 25001 (2021) https://arxiv.org/abs/1912.07845

Gross, C. Bloch, I. *Quantum simulations with ultracold atoms in optical lattices*. Science, Vol 357, Iss 6355. https://www.science.org/doi/10.1126/science.aal3837

Paraoanu, G.S. *Recent progress in quantum simulation using superconducting circuits. *. Low. Temp. Phys. 175, nos. 5/6 (2014) https://arxiv.org/abs/1402.1388

Kassal Group. *Quantum computing for chemistry. *Online. (Accessed 2023)

Quantum Flagship. *Quantum Simulations. *Online. (Accessed 2023)