Imagine trying to use a computer that looks and acts like no computer you've ever seen. There is no keyboard or screen. Code designed for a normal computer is useless. The components don't even follow the laws of classical physics. Quantum computing would be radically new and fundamentally different from the classical computers we're used to.

“It's a brand-new technology,” said Bert de Jong, a scientist at the Department of Energy's (DOE) Lawrence Berkeley National Laboratory (LBNL). “It's where we were with conventional computing 40, 50 years ago.”

Quantum computers will use microscopic objects or other extraordinarily tiny entities — including light — to process information. These tiny things don't follow the classical laws that govern the rest of the macroscopic universe. Instead, they follow the laws of quantum physics.

Harnessing the phenomena associated with quantum physics may give scientists a tool to solve certain complex problems that are beyond even the future capabilities of classical computers. For this specific set of problems, experts estimate that a single quantum computer just twice the size of the very early-stage ones today could provide advantages beyond those of every current supercomputer in the world combined.

Fulfilling quantum computers’ potential will be a major challenge. The strange nature of quantum particles conflicts with almost everything we know about computers. Scientists need to rewrite the foundations that underlie all existing computer languages. To harness quantum computers’ power, the DOE Office of Science Advanced Scientific Computing Research program is supporting research to develop the basics for quantum software. Three DOE national laboratory projects — led by Oak Ridge National Laboratory (ORNL), Sandia National Laboratories (SNL), and LBNL — are tackling this problem.

#### More Powerful than the Most Powerful Computers

Quantum computers offer one of the first new ways of computing in more than 60 years. Because there's a limit to how many transistors fit on a chip, there are physical bounds on how powerful even the best classical computers can be. Quantum computers should be able to reach beyond these confines.

In particular, simulations on classical computers cannot efficiently simulate quantum systems. These are systems that are so small that they follow the laws of quantum physics instead of classical physics. One example of this type of system is the relationship between electrons in large molecules. How these large electron systems act determines superconductivity, magnetism, and other important phenomena. As Pavel Lougovski, leader of the ORNL project, said, “I'm interested in understanding how quantum systems behave. To me, there is a no-brainer there.”

Quantum computers may be able to solve other currently unsolvable problems as well. Modeling the process by which enzymes in bacteria “fix” nitrogen involves so many different chemical interactions that it overwhelms classical computers’ capabilities. Solving this problem could lead to major breakthroughs in making ammonia production — which uses a tremendous amount of energy — far more efficient. Quantum computers could potentially reduce the time it takes to run these simulations from billions of years to only a few minutes.

“This kind of physics seems to have the power to do things much, much faster or much, much better than [classical] physics,” said Ojas Parekh, leader of the SNL project.

#### How to Speak Quantum

Just like humans, computers use language to communicate. Instead of letters that form words, computers use algorithms — step-by-step instructions written in a mathematical way. Every computer, whether classical or quantum, relies on them to solve problems. Just as we have 26 letters that create a near infinite number of sentences, algorithms can string individual instructions together into billions of possible calculations. But even some of the most basic mathematical functions don't have quantum algorithms written for them yet.

“Without quantum algorithms, a quantum computer is just a theoretical exercise,” said Stefan Wild, a mathematician at DOE's Argonne National Laboratory and member of the LBNL team. That's part of what DOE is tackling with these three projects.

Quantum algorithms come in two forms: digital and analog. Digital quantum computing somewhat resembles the computers we're used to. Classical computers use electrical currents to store information in bits of electromagnetic materials. They convey that information over miniscule wires. Quantum computers store information in the physical state, such as the locations and energy states, of their quantum objects. Quantum algorithms direct the computer how to move and change those objects’ locations, energy states, and interactions.

But like anything in quantum, it's never that easy. Classical computer algorithms present a set of decisions as to whether an electrical current should move forward or not. For quantum computers, it's not a simple “yes” or “no” answer. “In a classical computer, when we're asking about a particular set of operations, we're assuming we're getting a repeatable, or deterministic, output,” said Wild. “And that's something quantum computing doesn't give us.”

Instead, the answers from quantum computers are drawn from probability distributions. Quantum computers don't give you a specific value for an answer. What they do is tell you how likely it is for a certain value to be the correct solution. In the case of understanding where an electron is in a molecule, the laws of quantum mechanics dictate that we can never pinpoint an electron's exact location. The laws of quantum physics state that the electron is spread out and not in any exact location. But a quantum computer can tell you that the electron is 50 percent likely to be in this location or 30 percent likely to be in another one.

Unfortunately, running a quantum algorithm only once isn't enough. To get as close as possible to the “right” answer, computer scientists run these calculations multiple times. Each sample reduces uncertainty. The computer may need to run the algorithm thousands of times — or even more — to get as close as possible to the most accurate distribution; however, quantum computers run these algorithms so quickly that they still have the potential to produce results much, much faster than classical ones.

If digital quantum computing seems strange, analog quantum computing takes bizarre to a whole new level. In fact, analog quantum computing is more like a laboratory physics experiment than a classical computer. But the field of quantum computing as a whole wouldn't exist without it. In 1982, physicist Richard Feynman theorized that to accurately model a quantum system, scientists would need to build another quantum system. The idea that we could build a system using quantum objects was the first seed of quantum computing.

These days, very early analog quantum computers allow scientists to match up quantum objects in natural systems with quantum objects inside the computer. By setting certain parameters and allowing the system to change over time, the hardware models how the natural system evolves. It's like listening to a conversation between two people in one language, setting up two more people with the same topic and guidelines in another language, and then using the second conversation to understand the first.

#### Three Ways of Looking at the Same Problem

All three DOE projects are creating the groundwork to solve scientific problems using quantum computers. The ORNL project is developing algorithms for three systems involving quantum objects: correlated electron systems, nuclear physics, and quantum field theory. The problem sets for all three are too large for classical computers to handle.

Correlated electron systems describe how electrons interact in solid materials. This process could hold the key to developing high-temperature superconductors or new batteries. Nuclear physicists seek to describe how protons and neutrons behave in atoms. Quantum field theorists want to explain how quarks and gluons that make up protons interact.

The team is combining multiple technologies. First, they're creating algorithms that split up the problems between high-performance classical computers and quantum computers. That allows them to create much simpler quantum algorithms. Simpler algorithms reduce the potential for errors and use the quantum computers as efficiently as possible. The team is also combining analog and digital quantum computing. By arranging some particles to mimic quantum systems and programming others, they limit the number of digital operations the system needs to run.

The project's most unique characteristic may be that it's using a computer thousands of miles away from the programmers. The ORNL team relies on quantum computers that IBM and Rigetti are making available to scientists via the Internet — basically, it's quantum computing for the masses.

The LBNL project is taking a similar approach, but tackling a different set of problems. They're also using both classical and quantum computers. After they get initial results from a quantum computer, they're using a classical computer to analyze them. They then use the analysis to tweak the limits they've set for the quantum computer.

They're focusing on quantum chemistry, which uses quantum mechanics to look at interactions between atoms and molecules. While scientists have a number of theories about quantum chemistry, they can't yet apply them. These real-world applications include improving our understanding of how light excites electrons in a material. That could lead to a better way to produce hydrogen.

Computer scientists and applied mathematicians in the LBNL team are also figuring out the best ways to implement algorithms to minimize the errors quantum computers are prone to make. So far, the team has developed and is experimentally testing a protocol on LBNL's quantum computer testbed that distinguishes between the scrambling and loss of quantum information. They're also exploring how they can apply certain types of quantum circuits inspired by tensor networks used in machine learning in the classical context to classify images of handwritten numbers.

SNL's project largely focuses on developing the underlying techniques for new types of algorithms designed to run on quantum computers. They're exploring quantum algorithms for machine learning, where computers can learn through practice. In particular, they're looking into how quantum computers might learn faster or produce more accurate results than conventional computers. They're also creating algorithms to simulate quantum systems in high-energy physics so that scientists can better explore the elementary constituents of matter and energy, the interactions between them, and the nature of space and time.

Lastly, the team is developing quantum algorithms for optimization and linear algebra. Optimization is a process where scientists figure out a maximum or a minimum value within a set of possibilities, such as the minimum number of circuits needed to create an electronic system. The team is expanding optimization techniques originally designed for conventional computers to solve problems in quantum physics. Linear algebra is essential for modeling natural systems. These new quantum algorithms are significantly simpler than existing ones, but expected to be just as fast and accurate. Simple quantum algorithms are important for understanding how quantum computers built in the next five to ten years might benefit scientific problems.

In the world of quantum computing, scientists are just learning to use the computing equivalent of letters to create words. The algorithms researchers create today will be the start of languages that provide new ways to tackle scientific problems.

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