Bivariate quantum signal processing simulates non-Hermitian Hamiltonians H_eff = H_R + i H_I with query-optimal complexity O((α_R + β_I)T + log(1/ε)/log log(1/ε)) in the separate-oracle model.
Theorem H.1(Operator Fejér–Riesz;Rosenblum [47], Dritschel–Rovnyak [48]).LetF(θ)∈C r×r be a matrix- valued trigonometric polynomial of degreedwithF(θ)⪰0for allθ
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Simulation of Non-Hermitian Hamiltonians with Bivariate Quantum Signal Processing
Bivariate quantum signal processing simulates non-Hermitian Hamiltonians H_eff = H_R + i H_I with query-optimal complexity O((α_R + β_I)T + log(1/ε)/log log(1/ε)) in the separate-oracle model.