Researchers create new algorithm to solve quantum chemistry problem

September 13, 2022 – A team of researchers from the US Department of Energy’s (DOE) Brookhaven National Laboratory and Stony Brook University have devised a new quantum algorithm to calculate the lowest energies of molecules in specific configurations during chemical reactions, including when bonds are broken. As shown in Physics review researchcompared to similar existing algorithms, including team algorithms Previous methodThe new algorithm will greatly improve scientists’ ability to accurately and reliably calculate surface potential energy in the interaction of molecules.

When calculating the surface potential energy of the chemical reaction of H2; +D2 → 2HD, the new algorithm (green diamonds) outperforms the previous algorithm (orange squares) in finding the most accurate solution (blue line).

For this work, Dio Lo, a Center for Functional Nanomaterials (CFN) A physicist at Brookhaven Lab, who has worked with Tzu-Chieh Wei, associate professor specializing in quantum information science at CN Yang Institute of Theoretical Physics at Stony Brook University, Ken Wu, CNN theorist, and Hongye Yu, Ph.D. Student at Stony Brook.

“Understanding the quantum mechanics of a molecule, and how it behaves at the atomic level, can provide key insight into its chemical properties, such as its stability and reactivity,” Lu said.

One particular property that has been difficult to determine is the ground state of the molecule: the point at which the molecule’s total electronic energy (including kinetic and potential energy) is lowest and nothing outside this “molecular system” excites or charges the molecule’s electrons. When the atomic structure of a chemical system becomes more complex, as in a large molecule, many electrons can interact. These interactions make it very difficult to calculate the ground state of complex molecules.

The new quantum algorithm improves on the previous algorithm to creatively address this problem. It exploits a smooth geometric distortion caused by constantly changing bond lengths or bond angles in the molecule structure. With this approach, scientists say they can very accurately calculate the ground state of the molecules, even when chemical bonds are broken and improved during chemical reactions.

foundation construction

“When relying solely on traditional computing methods, this ground-state problem has many variables to solve — even on the most powerful supercomputers,” Lu said.

You can think of an algorithm as a set of steps to solve a particular problem. Classic computers can run complex algorithms, but as they get larger and more involved, they can become very difficult or time-consuming to solve on classic computers. Quantum computers can speed up the process by taking advantage of the rules of quantum mechanics.

In classical computing, data is stored in bits with a value of 1 or 0. A quantum bit, known as a qubit, can only have a value beyond 0 or 1, it can even have a value of 0 And the 1, in what is called quantum superposition. In principle, these more “flexible” qubits can store more information than conventional qubits. If scientists can find ways to harness the information transmission capacity of qubits, computing power could expand exponentially with each additional qubit.

Qubits, however, are very fragile. It can often crash when extracting information. When a quantum device interacts with the surrounding environment, it can generate noise or interference that destroys the quantum state. Temperature changes, vibrations, electromagnetic interference, and even material defects can also cause qubits to lose information.

To compensate for these pitfalls, scientists have developed a hybrid solution that takes advantage of both classical computing algorithms, which are more stable and practical.

Funded by an initial grant from Stony Brook University, Lu and Wei began research on hybrid quantum and classical computing approaches in 2019. This annual grant promotes collaboration between Brookhaven National Laboratory and Stony Brook University by funding joint research initiatives aligned with the missions of both institutions. With this initial work, Lu and Wei first focused on solving the base state problem by replacing more “expensive” classical algorithms—those that were more complex and required more steps (and more computing time) to complete—with quantum algorithms.

Stretching links, creating new paths

The researchers note that all current quantum algorithms come with flaws to solve the ground-state problem, including those developed by Wei and Yu in 2019. While some popular algorithms are accurate when a molecule is in its geometric equilibrium — its natural arrangement of atoms in three dimensions — they can These algorithms become unreliable when chemical bonds are broken at large atomic distances. Bond formation and dissociation play a role in many applications, such as predicting how much energy is needed to start a chemical reaction, so scientists need a way to address this problem when molecules interact. They needed new quantum algorithms that could describe the bond breaking.

For this new version of the algorithm, the team worked with Brookhaven-Lab Co-design center for quantum advantage (C .).2Question and Answer), which was formed in 2020. Wei contributes to the programmatic orientation of the center, which specializes in quantum algorithms. The team’s new algorithm uses a static static approach — one that makes incremental changes — but with some tweaks that ensure it remains reliable when chemical bonds are broken.

“The thermodynamic process works by gradually adapting the conditions of a quantum mechanical system,” Lu explained. “In a way, you reach a solution in very small steps. You develop the system from a simple solvable model to the end goal, usually a more difficult model. In addition to the base case, the multiple electronic system has many excited states at higher energies.” These excited states can present a challenge when using this method to calculate the ground state.”

Wei compared an adiabatic algorithm to driving along a highway, “If you travel from one city to another, there are several ways to get there, but you want to find the safest and most efficient way.”

At a certain distance from the OH inside the H2O molecule, there are several energy crossing points (a). This is the reason for the failure of the initial Adiabatic algorithm. In contrast, the new algorithm, where the distance starts from a point closer and moves more gradually, has smoothly connected energy levels without any intersection (B).

In the case of quantum chemistry, the key is to find a large enough “energy gap” between the ground state and excited states where there are no electronic states. With a large enough gap, vehicles in the highway metaphor won’t “cross lanes,” so their tracks can be accurately traced.

“The big gap means you can go faster, so, in a sense, you’re trying to find a highway that’s less crowded to drive faster without hitting anything,” Wei said.

“By using these algorithms, the path entry is a simple and straightforward solution from classical computing,” Wei noted. “We also know where the outlet is – the base state of the molecule – and we’ve been trying to find a way to connect it to the outlet in the most natural way, which is a straight line.

“We did it in our first paper, but the straight line has hurdles due to the power gap bridging and the intersection of paths. Now we have a better solution.”

When the scientists tested the algorithm, they showed that even with finite bond length changes, the optimized version still worked accurately for the base state.

“We’re out of our comfort zone, because chemistry isn’t our focus,” Wei said. “But it was good to find an application like this and to promote this kind of cooperation with CFN. It is important to have different perspectives in the research.”

He recalled the accumulated efforts of many people. “In the grand scheme, I think we are making a small contribution, but this could be the basis for further work in these areas,” he said. “This research is not only foundational, but a wonderful illustration of how different institutions and facilities can come together to benefit from their areas of expertise.”

Research on quantum algorithm development in this work was supported by the US Department of Energy, Office of Science, National Quantum Information Science Research Centers, and the Quantum Feature Co-Design Center (CDC).2QA), while applications of theoretical quantum chemistry and computational resources were used by the Center for Functional Nanomaterials (CFN), a user facility in the US Department of Energy’s Office of Science at Brookhaven National Laboratory. Additional funding was provided by the National Science Foundation.

About Brookhaven National Laboratory

Brookhaven National Laboratory is supported by the US Department of Energy’s Office of Science. The Office of Science is the largest supporter of basic research in the physical sciences in the United States and works to address some of the most pressing challenges of our time. For more information, please visit the website

source: Dennis Yazak, BNL