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

Abstract

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.

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• Molecular Properties from Quantum Krylov Subspace Diagonalization
• Compressing Hamiltonians with ab initio downfolding for simulating strongly-correlated materials on quantum computers
• Error mitigation and circuit division for early fault-tolerant quantum phase estimation
• The Role of Quantum Computing in Advancing Scientific High-Performance Computing: A perspective from the ADAC Institute
• Trotter simulation of vibrational Hamiltonians on a quantum computer
• Simulating methylamine using symmetry adapted qubit-excitation-based variational quantum eigensolver
• Phase estimation with partially randomized time evolution