Tight anti-Hermitian query complexity d_I = Θ(β_I T + log(1/ε)/log log(1/ε)) is established for non-Hermitian M-QSP, with impossibility of √(β_I T) fast-forwarding, new angle-finding algorithms, and extensions to time-dependent cases.
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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.
LHAM converts nonlinear PDEs into linear recursive systems via homotopy analysis and simulates them through Lindbladian quantum dynamics, achieving logarithmic Hilbert space scaling versus polynomial scaling in prior methods.
citing papers explorer
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Optimal Bounds, Barriers, and Extensions for Non-Hermitian Bivariate Quantum Signal Processing
Tight anti-Hermitian query complexity d_I = Θ(β_I T + log(1/ε)/log log(1/ε)) is established for non-Hermitian M-QSP, with impossibility of √(β_I T) fast-forwarding, new angle-finding algorithms, and extensions to time-dependent cases.
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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.
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Lindbladian Homotopy Analysis Method to Solve Nonlinear Partial Differential Equations
LHAM converts nonlinear PDEs into linear recursive systems via homotopy analysis and simulates them through Lindbladian quantum dynamics, achieving logarithmic Hilbert space scaling versus polynomial scaling in prior methods.