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.
Hamiltonian simulation in the interaction picture
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Second-order Trotterization of many-body Coulomb Hamiltonians achieves a 1/4 convergence rate for general initial conditions in the Hamiltonian domain with polynomial particle-number scaling, and improves to first or second order under state-dependent conditions such as high-angular-momentum excited
Detectability lemma enables Gibbs sampling without Lindbladian simulation, yielding O(M) cost reduction for M-term local Lindbladians and quadratic speedup in spectral gap for frustration-free and commuting cases.
citing papers explorer
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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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Trotterization with Many-body Coulomb Interactions: Convergence for General Initial Conditions and State-Dependent Improvements
Second-order Trotterization of many-body Coulomb Hamiltonians achieves a 1/4 convergence rate for general initial conditions in the Hamiltonian domain with polynomial particle-number scaling, and improves to first or second order under state-dependent conditions such as high-angular-momentum excited
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Quantum Gibbs sampling through the detectability lemma
Detectability lemma enables Gibbs sampling without Lindbladian simulation, yielding O(M) cost reduction for M-term local Lindbladians and quadratic speedup in spectral gap for frustration-free and commuting cases.