Collaborative Research: Practical strategies for implementing quantum chemistry on near-term quantum computers

Georgetown University, Washington DC

Investigators

Abstract

With support from the Chemical Theory, Models and Computational Methods (CTMC) program in the Division of Chemistry, James Freericks of Georgetown University and Dominika Zgid of the University of Michigan are collaborating to develop practical implementations for quantum chemistry problems on current or near future generation of quantum computers. Quantum chemistry is viewed as one of the most promising applications of quantum computing. But, currently available quantum hardware platforms are regarded as noisy intermediate scale quantum (NISQ) era devices, implying only short programs can be run on them. Freericks and Zgid will employ hybrid quantum-classical methodologies to mitigate the presence of the quantum noise and run only the most important part of the calculation on a NISQ machine, while the remainder will be executed on a classical computer. In this way, the quantum computer is viewed as an accelerator or enabler for the full calculation. Freericks and Zgid will investigate two questions: (i) How efficiently can one trade off the length of the program by increasing the number of noisy measurements? and (ii) How accurately can a real quantum chemistry Hamiltonian be approximated via a fictitious sparse Hamiltonian that is suitable to be run on a NISQ device, while still yielding excellent molecular energies and dynamics. In the educational component of this project, Dr. Freericks will design chemistry-specific materials for a book entitled Quantum Mechanics without Calculus; a book devoted to developing quantum mechanics curriculum with a much lower mathematics prerequisite. Dominika Zgid will prepare a series of workshops for the F.E.M.M.E.S. (women excelling more in math, engineering and sciences) organization. Many algorithms and strategies exist, in principle, for solving the electronic structure problem in chemistry on a quantum computer, but there remains a huge chasm between the theoretical possibilities and the computational realities of near-term devices. Freericks and Zgid intend to cross that chasm by providing practical implementations for electronic structure problems to be solved on quantum computers. Freericks and his group will employ a factorized form of the unitary coupled cluster ansatz (UCC) with a small number of exact terms treated in the wavefunction ansatz, and hence a small number of parameters that will need to be optimized in the prepared wavefunction. It is then supplemented by an expansion of the energy expectation value to second order in the amplitudes for the UCC ansatz for a large number of additional "virtual" amplitudes. Optimization is then accomplished by solving a row-reduction problem on the classical computer. This trades off circuit depth for measurements. To further minimize circuit depths, Zgid and her group will employ an effective approach to produce ultra-sparse Hamiltonians suitable for NISQ devices. This approach is based on molecular self-energy and assumes that the dynamical part of the self-energy will be translatable from the exact molecular system to a system described by the sparse Hamiltonian via the dynamical self-energy mapping methodology (DSEM). For the broader impacts, the work by Freericks uses the so-called factorization method, employing operator methods (different from both wavefunction and matrix methods), and more suitable for training students in future research work, since research usually involves working with operators. The broader impact work of Zgid consists largely in an outreach program that is designed to excite middle-school-age girls for future careers in science. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.