Quantum computers, just like classical computers, are only as good as the instructions that we give them. And although quantum computing is one of the hottest topics in science these days, the instructions, or algorithms, for quantum computers still have a long way to go to become useful. Garnet Chan, Caltech's Bren Professor of Chemistry, is tackling this problem. In a new paper, he describes how he, together with Fernando Brandao, Bren Professor of Theoretical Physics, and Austin Minnich, professor of mechanical engineering and applied physics, developed an algorithm for quantum computers that will help them find use in simulations in the physical sciences.

The algorithm is derived from one already in use in classical computing called imaginary time evolution. Chan's new algorithm, tailored to run on quantum computers, has been fittingly dubbed quantum imaginary time evolution and allows a user to find the lowest energy of a given molecule or material.

We sat down with Chan to talk about his research and what it means for quantum computing.

### In lay terms, what have you achieved with your new research?

There has been a lot of interest in what kind of problems a quantum computer can potentially help to solve in the physical sciences. One problem that many people are interested in is how to simulate the ground states of molecules and materials. Our new paper proposes a way to calculate ground states of Hamiltonians that runs on near-term quantum computers with very few resources.

### What is a Hamiltonian, and why would you want to know its ground state?

The Hamiltonian represents the energy of the system, and the ground state of the Hamiltonian is the most stable state of the problem. Most physical systems, under ordinary conditions, are not too excited, and thus live close to their ground states.

For example, if we want to do a simulation of water, we could look at how water behaves after it has been blasted into a plasma—an electrically charged gas—but that's not the state water is usually found in; it is not the ground state of water. Ground states are of special interest in understanding the world under ordinary conditions.

### Why is it challenging to perform these calculations on a quantum computer?

Quantum devices currently decohere after a short period of time, which means that the computer needs to be recalibrated and cannot be used for calculations until it is set up again. That means we need to find a way to perform calculations on them very efficiently so we solve our problem before decoherence occurs.

### What does your algorithm do?

There have been many proposals for how to obtain ground states on quantum computers. One of the first was by Alexei Kitaev [Caltech's Ronald and Maxine Linde Professor of Theoretical Physics and Mathematics], but unfortunately that algorithm, known as phase estimation, requires too many instructions and cannot be implemented before current quantum computers decohere. Another way, called the variational approach, is very simple to implement but in practice turns out not to be so accurate. We wanted to find a way that could be potentially as accurate as phase estimation but which could also be practically programmed on today's quantum computers

### What does the development of this algorithm mean for quantum computing?

Quantum computers are still very new, and we still need to learn what they will be useful for. Because we can barely use them right now, part of the answer lies in developing efficient programs that can be run on them in very little time. Our work provides a basis for assessing the capabilities of quantum computers as they are now, which will help tell us what we can expect in the future.

Written by Emily Velasco