Global Minimization of Electronic Hamiltonian 1-Norm via Linear Programming in the Block Invariant Symmetry Shift (BLISS) Method

TL;DR

This paper introduces a linear programming approach to optimize the BLISS method for reducing the 1-norm of Hamiltonian encodings in quantum computing, leading to more efficient simulations of complex chemical systems.

Contribution

It reformulates the BLISS optimization as a linear programming problem, guaranteeing global optimality and reducing computational costs compared to previous nonlinear methods.

Findings

Significant reduction in Hamiltonian 1-norms for complex catalysts.

Enhanced spectral range reduction of the modified Hamiltonian.

Improved efficiency in Hamiltonian simulation techniques.

Abstract

The cost of encoding a system Hamiltonian in a digital quantum computer as a linear combination of unitaries (LCU) grows with the 1-norm of the LCU expansion. The Block Invariant Symmetry Shift (BLISS) technique reduces this 1-norm by modifying the Hamiltonian action on only the undesired electron-number subspaces. Previously, BLISS required a computationally expensive nonlinear optimization that was not guaranteed to find the global minimum. Here, we introduce various reformulations of this optimization as a linear programming problem, which guarantees optimality and significantly reduces the computational cost. We apply BLISS to industrially-relevant homogeneous catalysts in active spaces of up to 76 orbitals, finding substantial reductions in both the spectral range of the modified Hamiltonian and the 1-norms of Pauli and fermionic LCUs. Our linear programming techniques for obtaining the BLISS operator enable more efficient Hamiltonian simulation and, by reducing the Hamiltonian's spectral range, offer opportunities for improved LCU groupings to further reduce the 1-norm.