In a recent *Physical Review Research* article, U.S. Naval Research Laboratory (NRL) scientists published what they are calling the Cascaded Variational Quantum Eigensolver (CVQE) algorithm. According to NRL, this can become a powerful tool to investigate the physical properties of electronic systems.

The CVQE algorithm is a variant of the Variational Quantum Eigensolver (VQE) algorithm. This algorithm only requires the execution of a set of quantum circuits once, rather than at every iteration during the parameter optimization process. This thereby increases the computational throughput.

“Both algorithms produce a quantum state close to the ground state of a system, which is used to determine many of the system’s physical properties,” says John Stenger, Ph.D., a research physicist in theoretical chemistry. “Calculations that previously took months can now be performed in hours.”

The CVQE algorithm uses a quantum computer to probe the needed probability mass functions and a classical computer to perform the remaining calculations, including the energy minimization.

“Finding the minimum energy is computationally hard as the size of the state space grows exponentially with the system size,” says Steve Hellberg, Ph.D., a research physicist in the theory of advanced functional materials. “Except for very small systems, even the world’s most powerful supercomputers are unable to find the exact ground state.”

### Advantages of the New Method

To address this challenge, scientists use a quantum computer with a qubit register. Its state space also increases exponentially, in this case with qubits. By representing the states of a physical system on the state space of the register, a quantum computer can be used to simulate the states in the exponentially large representation space of the system.

Data can subsequently be extracted by quantum measurements. As quantum measurements are not deterministic, the quantum circuit executions must be repeated multiple times to estimate probability distributions describing the states. This process is known as sampling.

Variational quantum algorithms, including the CVQE algorithm, identify trial states by a set of parameters that are optimized to minimize energy.

“The key difference between the original VQE method and the new CVQE method is that the sampling and optimization processes have been decoupled in the latter… such that the sampling can be performed exclusively on the quantum computer and the parameters processed exclusively on a classical computer,” says Dan Gunlycke, D.Phil., section head of theoretical chemistry.

Gunlycke also leads the NRL quantum computing effort.

“The new approach also has other benefits,” Gunlycke adds. “The form of the solution space does not have to comport with the symmetry requirements of the qubit register, and therefore, it is much easier to shape the solution space and implement symmetries of the system and other physically motivated constraints, which will ultimately lead to more accurate predictions of electronic system properties.”

### Addressing Corrosion Concerns

Quantum computing is a component of quantum science, which has been designated as a critical technology area within the Office of the Under Secretary of Defense for Research and Engineering.

“Understanding the properties of quantum-mechanical systems is essential in the development of new materials and chemistry for the Navy and Marine Corps,” Gunlycke says. “Corrosion, for instance, is an omnipresent challenge costing the Department of Defense billions every year. The CVQE algorithm can be used to study the chemical reactions causing corrosion and provide critical information to our existing anticorrosion teams in their quest to develop better coatings and additives.”

For decades, NRL has been conducting fundamental research in quantum science. They say this has the potential to yield disruptive technologies for precision, navigation, and timing; quantum sensing; quantum computing; and quantum networking.

### About the Naval Research Laboratory (NRL)

NRL is a scientific and engineering command dedicated to research driving innovative advances for the U.S. Navy and Marine Corps. These initiatives range from the seafloor to space, as well as in the information domain.

NRL is located in Washington, DC, USA, with major field sites in Stennis Space Center, Mississippi; Key West, Florida; and Monterey, California. It employs approximately 3,000 civilian scientists, engineers and support personnel.

*Source: U.S. Defense Visual Information Distribution Service, www.dvidshub.net. *