## Quantum Flow Algorithms for Simulating Many-Body Systems on Quantum Computers

*A new approach uses reduced quantum resources to effectively describe chemical processes*

## The Science

As quantum computing is still in relatively early stages of development, applications are limited by the size of available resources. Current noisy intermediate-scale quantum (NISQ) devices are small and restrict the complexity of problems solvable by pure quantum approaches. Researchers developed a hybrid quantum flow approach, QFlow, to integrate features of both classical and quantum computing to solve chemical problems. The QFlow algorithms take a constant-circuit-depth approach, which bypasses a major sticking point in quantum computing systems. Initial testing showed that QFlow algorithms are practical across a range of problem complexities, with a further extension when combined with other methods.

## The Impact

Quantum computing is an emerging field of interest with broad potential applications, including the modeling of chemical systems. However, current computing resources have limited the use of quantum approaches. By combining different features from classical and quantum computing, QFlow algorithms allow researchers to effectively simulate more types of chemical systems on a quantum computer architecture. Additionally, QFlow captures the sparsity of quantum systems, an essential step in developing distributed quantum computing.

## Summary

Current quantum computing applications are significantly limited by the size of available NISQ devices. To bypass these challenges, researchers developed QFlow—a hybrid quantum flow approach that combines variational problems defined by effective Hamiltonians, which capture the energy of a system using a subset of orbitals and drastically reduce the dimensionality of the problem. The QFlow algorithms use classical computers to store cluster amplitudes and form effective Hamiltonians, which are then optimized by quantum computers to solve coupled active space problems. The QFlow algorithms help explore large subspaces of Hilbert space—critically important to mathematical formulations of quantum mechanics—using simple quantum circuits. It also allows researchers to optimize more variables than previously possible. The QFlow approach can take advantage of currently available NISQ devices and provide a flexible framework to adapt to ever-growing classical and quantum computational resources.

## Contact

Karol Kowalski, Pacific Northwest National Laboratory, karol.kowalski@pnnl.gov

## Funding

This material is based upon work supported by the “Embedding QC into Many-Body Frameworks for Strongly Correlated Molecular and Materials Systems” project, which is funded by the Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences, the Division of Chemical Sciences, Geosciences, and Biosciences (under FWP 72689) and by Quantum Science Center (QSC), a National Quantum Information Science Research Center of the DOE (under FWP 76213). This work used resources from Pacific Northwest National Laboratory.

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Published: March 18, 2024*

K. Kowalski, N.P. Bauman, “Quantum Flow Algorithms for Simulating Many-Body Systems on Quantum Computers,” *Phys. Rev. Lett.* **131**, 200601 (2023). DOI: 10.1103/PhysRevLett.131.200601