One of the most important classes of problems that all scientists and mathematicians aspire to solve, due to their relevance in both science and real life, is optimization problems. From esoteric computer science puzzles to the more realistic problems of vehicle routing, investment portfolio design, and digital marketing--at the heart of it all lies an optimization problem that needs to be solved.

An appealing technique often used in solving such problems is the technique of "quantum annealing", a framework that tackles optimization problems by using "quantum tunneling"--a quantum physical phenomenon--to pick an optimum solution out of several candidate solutions. Ironically, it is in quantum mechanical problems where the technique has found rather scarce application! "Chemists and materials scientists, who deal with quantum problems, are mostly unfamiliar with quantum annealing and so do not think to use it. Finding applications of this technique is therefore important for increasing its recognition as a useful method in this domain," says Prof. Ryo Maezono from Japan Advanced Institute of Science and Technology (JAIST), who specializes in applying information science to the field of materials science.

To that end, Prof. Maezono explored, in a recent study published in Scientific Reports, the phenomenon of ionic diffusion in solids, a topic of great interest in both pure and applied materials science, along with his colleagues, Keishu Utimula, a Ph.D. graduate in materials science from JAIST (in 2020) and lead author of the study, Prof. Kenta Hongo, and Prof. Kousuke Nakano, by applying a framework that combined quantum annealing with ab initio calculations, a method that calculates physical properties of materials without relying on experimental data. "While current ab initio techniques can provide information about diffusion path networks of the ions, it is difficult to map that information into useful knowledge of the diffusion coefficient, a practically relevant quantity," explains Prof. Maezono. 

Specifically, the team looked to calculate the "correlation factor", a key quantity in the diffusion process, and realized that this could be done by framing the process as a routing optimization problem, which is precisely what the quantum annealing framework is designed to solve! Accordingly, scientists calculated the correlation factor for a simple two-dimensional tetragonal lattice, for which they already knew the exact result, using quantum annealing and a variety of other computational techniques and compared their outputs.

While the evaluated correlation factors were consistent with the analytical result for all the methods employed, all the approaches suffered from limitations due to unrealistic computational costs for large system sizes. However, scientists noted that the computational expense for quantum annealing grew much more slowly in a linear fashion compared to the other techniques, which showed rapid exponential growth.

Prof. Maezono is excited by the finding and is confident that, with sufficient technological advancement, quantum annealing would present itself as the best possible choice for solving problems in materials science. "The problem of ion diffusion in solids is of central importance in building smaller batteries with higher capacity or improving the strength of steel. Our work shows that quantum annealing is effective in solving this problem and can expand the scope of materials science as a whole," he concludes.

In 2018, Kang-Kuen Ni and her lab earned the cover of Science with an impressive feat: They took two individual atoms, sodium and cesium, and forged them into a single dipolar molecule, sodium cesium.

Sodium and cesium normally ignore each other in the wild; but in the Ni lab's carefully calibrated vacuum chamber, she and her team captured each atom using lasers and then forced them to react, a capability that gifted scientists with a new method to study one of the most basic and ubiquitous processes on Earth: the formation of a chemical bond. With Ni's invention, scientists could not only discover more about our chemical underpinnings, but they could also start creating bespoke molecules for novel uses like qubits for quantum supercomputers.

But there was one flaw in their original sodium cesium molecule: "That molecule was lost soon after it's made," said Ni, the Morris Kahn associate professor of chemistry and chemical biology and of physics. Now, in a new study published in Physics Review Letters, Ni and her team report a new feat: They granted their molecule an extended lifetime of up to almost three and a half seconds--a luxury of time in the quantum realm--by controlling all the degrees of freedom (including its motion) of an individual dipolar molecule for the first time. During those precious seconds, the researchers can maintain the full quantum control necessary for stable qubits, the building blocks for a wide variety of exciting quantum applications.

According to the paper, "These long-lived, fully quantum state-controlled individual dipolar molecules provide a key resource for molecule-based quantum simulation and information processing." For example, such molecules could accelerate progress toward the quantum simulation of new phases of matter (faster than any known computer), high-fidelity quantum information processing, precision measurements, and basic research in the field of cold chemistry (one of Ni's specialties). 

And, by forming obedient molecules in their quantum ground states (basically, their simplest, most pliant form), the researchers created more reliable qubits with electric handles, which, like the magnetic handles of a magnet, allow researchers to interact with them in new ways (for example, with microwaves and electric fields).

Next, the team is working on scaling their process: They plan to assemble not just one molecule from two atoms but force larger collections of atoms to interact and form molecules in parallel. In so doing, they can also start to perform long-range entanglement interactions between molecules, the basis for information transfer in quantum computing.

"With the addition of a microwave and electric field control," said Ni, "molecular qubits for quantum computing applications and simulations that further our understanding of quantum phases of matter are within experimental reach."