Quantum simulation
The properties of quantum computers open up a new world of simulation possibilities.
Since the 1980s researchers have predicted quantum computers will be invaluable tools to study individual molecules, chemical reactions, and special materials like superconductors. Typically, scientists in these fields need to resort to expensive and time-consuming trial and error processes. Think of the pharmaceutical industry, where lengthy studies must be taken to evaluate the performance of new drugs and examine their side-effects on human health. Surely it would be cheaper and easier to simulate the drugs and their effects.
Classical computers can simulate small molecules or chemical processes, but as the number of particles grows, so too does the required computational power. This severely limits the size of the simulations and thus the study of interesting applications. Quantum computers, on the other hand, behave according to the same laws of nature as molecules and materials, namely quantum mechanics! Therefore, it can be much more efficient to use a quantum computer for such simulations.
Here, we introduce some of the leading ideas researchers are using to think about quantum modeling. We also describe one of the “low-hanging fruits” for obtaining a practical quantum advantage, and briefly list some of the big ideas that quantum computers might be able to tackle in the future.
Analog Quantum Simulation
One approach to quantum simulation is to program a quantum computer to behave mathematically equivalent (or extremely close) to how some real system works. Typically, this requires the quantum computer to be built out of components that are similar to what you would like to simulate. For example, magnetism is easier to simulate on computers that are built out of tiny magnets themselves. Analog quantum simulation is attractive, as it generally requires fewer resources than a digital quantum simulation. However, it is less universal and may only extend to studying small and very specific problems.
Hybrid Quantum Simulation
In a hybrid quantum-classical algorithm, a quantum processor is used to try to prepare a quantum state for study, such as the state of a small molecule. This is done by guessing an initial quantum circuit that may be adjusted with some parameters. By running, measuring, and analyzing the output of this circuit, the parameters can be optimized on a classical computer. The goal is to obtain an optimal circuit that creates a quantum state out of reach for a classical computer alone. Such hybrid algorithms are heavily researched because they can run on smaller NISQ processors without costly quantum error correction. However, they are still affected by noise, so the extent of their usefulness is limited by the quality of quantum hardware.
Digital Quantum Simulation
Quantum computers can also be digitally programmed to simulate a system by breaking down the simulation into a series of short time-steps – similar to how classical computers solve many interesting problems, like the airflow through an airplane’s engine. In digital quantum simulation, it doesn’t matter if the quantum computer behaves anything like the system it is simulating – just like a classical computer behaves nothing like a jet engine. Therefore, digital quantum simulation is viewed as more universal, but it also requires more resources including a much larger number of qubits as well as quantum error correction. For the most ambitious quantum simulation problems, including the examples listed here, this kind of approach will be necessary.
High-Tc Superconductors
Quantum computers are expected to provide insight into the behavior of materials that exhibit particularly quantum properties by studying models such as the Fermi-Hubbard model. One example of this are so-called high-temperature superconductors. Many metals will exhibit superconductivity – a phenomenon where electrical resistance vanishes – at extremely low temperatures. Certain materials, however, become superconducting at “high” (or rather, less cold) temperatures that can be achieved more economically, but the physics behind this is not clearly understood. High-temperature superconductors could be used for extremely efficient power transfer over long distances, reducing the cost of moving energy from where it is produced to where it is consumed.
The Fermi-Hubbard Model
The Fermi-Hubbard model is believed to be one of the first practical use cases of a quantum computer, because it is applicable to problems in science that are difficult for classical computers. The Fermi-Hubbard model describes how electrons move in a solid, carrying electricity. They are pulled towards “sites” and may also “hop” between neighboring locations. The quantum nature of electrons means that this simple picture can be challenging to tackle classically, but quantum computers “speak the same language”.
This application serves as a good benchmark for how powerful a quantum computer needs to be to achieve a practical quantum advantage. Current estimates suggest that a quantum computer with 50-100 good quality qubits on a NISQ processor could beat a classical computer. However, these qubits must be accurate 99.99% of the time, about 10 times the quality we have today. Furthermore, such an algorithm could require hundreds of quantum computers running at once, with a total computation time of a couple days. Quantum engineers still have much work to do, both improving qubit quality and quantity, but this goal is in sight. It also puts into perspective what “soon” means when discussing the timeline of practical quantum algorithms.
Catalysts
The field of quantum chemistry is concerned with explaining the behavior of molecules using the underlying theory of quantum mechanics. A central concept is that of the electronic structure – the configuration of electrons in a molecule in a given state. The electronic structure determines how different molecules interact, how quickly a reaction takes place, and what products are yielded. Because of their complicated electronic structure, some of the most industrially important molecules are also the most difficult to model with a classical computer. This includes catalysts and enzymes, which facilitate reactions from fertilizer production to photosynthesis.
Batteries
As the world transitions away from fossil fuels and towards electric vehicles, the demand for high-quality batteries will continue to surge. The goal is to maximize energy storage and reliability while minimizing cost. In order to do this, researchers try to model the electronic properties of materials as precisely as possible, and this becomes more difficult as the systems become more complex. For instance, many major car companies have taken an interest in the potential of quantum computers, and several exploratory studies are already underway to find out if today’s NISQ processors can accurately investigate the industrially relevant chemistry, such as lithium compounds.
Drug Discovery
New pharmaceutical drugs typically cost over a billion dollars and take ten years to reach a commercial market. This is a reflection of the technical complexity required to ensure drug efficacy and safety. Although simulating a drug on a computer is cheaper than running a clinical trial, this is limited by the power of classical computers to accurately model the chemical behavior. Quantum computing has the potential to disrupt the costly drug discovery process by allowing drugs to be thoroughly simulated in less time with less money. Although the general concept is exciting, much more research is needed to understand the applicability of quantum computers to specific problems in this field.
Fertilizer Manufacturing
The industrial process used to create modern fertilizer is called the Haber-Bosch process. It requires high temperatures and energies in order to convert atmospheric nitrogen into a form that is usable by plants. By one estimate, the Haber-Bosch process consumes 2% of the world’s total energy consumption. Bacteria, however, can perform this nitrogen fixation process at atmospheric conditions thanks to the use of the enzyme nitrogenase. Due to its difficult electronic structure, many questions about nitrogenase have not been answered, including whether a similar chemical reaction could be used to supplant the Haber-Bosch process with a less energy-intensive procedure. A very large quantum computer would be needed to tackle such a problem, but quantum computational chemistry may help provide scientists with an answer in the long run.
The Fine Print
Much is still uncertain about which quantum algorithms will perform the best when they move from ideas on paper to real quantum hardware. Only very recently have small quantum computers become available for proof-of-concept ideas to be explored. As an example, algorithms that can run on NISQ hardware, like hybrid quantum algorithms, are very exciting due to their near-term usability. However, their ability to achieve quantum advantage is still an open question. Their performance can depend on heuristic guesses, much like classical optimization algorithms. Optimization routines can get stuck or require so much time that any quantum advantage may disappear.
In addition, physics applications that can be implemented soon, such as the Fermi-Hubbard model, and much more complicated tasks envisioned for a universal quantum computer, like investigating chemical reactions in drugs, have vastly different resource requirements. In the short term, quantum computers will therefore be used to study specific problems primarily of interest to small groups of scientists. The world-changing problems require far bigger and better quantum computers, and it will be some time before the opportunity here can be accurately known.