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

Understand

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.