  Quantum phase estimation based on qubitization is the state-of-the-art
fault-tolerant quantum algorithm for computing ground-state energies in
chemical applications. In this context, the 1-norm of the Hamiltonian plays a
fundamental role in determining the total number of required iterations and
also the overall computational cost. In this work, we introduce the
symmetry-compressed double factorization (SCDF) approach, which combines a
compressed double factorization of the Hamiltonian with the symmetry shift
technique, significantly reducing the 1-norm value. The effectiveness of this
approach is demonstrated numerically by considering various benchmark systems,
including the FeMoco molecule, cytochrome P450, and hydrogen chains of
different sizes. To compare the efficiency of SCDF to other methods in absolute
terms, we estimate Toffoli gate requirements, which dominate the execution time
on fault-tolerant quantum computers. For the systems considered here, SCDF
leads to a sizeable reduction of the Toffoli gate count in comparison to other
variants of double factorization or even tensor hypercontraction, which is
usually regarded as the most efficient approach for qubitization.
