Reducing the runtime of fault-tolerant quantum simulations in chemistry through symmetry-compressed double factorization

Reducing the runtime of fault-tolerant quantum simulations in chemistry through symmetry-compressed double factorization

6 Mar 2024 | Dario Rocca, Cristian L. Cortes, Jerome Gonthier, Pauline J. Ollitrault, Robert M. Parrish, Gian-Luca Anselmetti, Matthias Degroote, Nikolaj Moll, Raffaele Santagati, Michael Streif
The paper introduces the symmetry-compressed double factorization (SCDF) approach, which combines a compressed double factorization of the Hamiltonian with the symmetry shift technique to significantly reduce the 1-norm value, thereby reducing the number of Toffoli gates and computational cost in quantum phase estimation (QPE) for chemical applications. The effectiveness of SCDF is demonstrated through numerical simulations on various benchmark systems, including the FeMoco molecule, cytochrome P450, and hydrogen chains of different sizes. SCDF is compared to other methods, such as tensor hypercontraction (THC), in terms of Toffoli gate requirements, showing a substantial reduction in the Toffoli gate count for the systems considered. The SCDF approach is shown to provide more systematic accuracy for ground state energies, making it suitable for large systems and thermodynamic limit calculations. The method is based on optimizing a cost function that combines the benefits of compressed double factorization (CDF) and symmetry shift, leading to a more compact representation of the Hamiltonian and a smaller 1-norm. The numerical results for the FeMoco molecule and cytochrome P450 active space models demonstrate the efficiency and accuracy of SCDF, achieving significant speed-ups and excellent balance between Toffoli gates and logical qubits.The paper introduces the symmetry-compressed double factorization (SCDF) approach, which combines a compressed double factorization of the Hamiltonian with the symmetry shift technique to significantly reduce the 1-norm value, thereby reducing the number of Toffoli gates and computational cost in quantum phase estimation (QPE) for chemical applications. The effectiveness of SCDF is demonstrated through numerical simulations on various benchmark systems, including the FeMoco molecule, cytochrome P450, and hydrogen chains of different sizes. SCDF is compared to other methods, such as tensor hypercontraction (THC), in terms of Toffoli gate requirements, showing a substantial reduction in the Toffoli gate count for the systems considered. The SCDF approach is shown to provide more systematic accuracy for ground state energies, making it suitable for large systems and thermodynamic limit calculations. The method is based on optimizing a cost function that combines the benefits of compressed double factorization (CDF) and symmetry shift, leading to a more compact representation of the Hamiltonian and a smaller 1-norm. The numerical results for the FeMoco molecule and cytochrome P450 active space models demonstrate the efficiency and accuracy of SCDF, achieving significant speed-ups and excellent balance between Toffoli gates and logical qubits.
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