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  "path": "/abs/2605.12450v1",
  "publishedAt": "2026-05-13T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Joshua M. Courtney"
  ],
  "textContent": "**Authors:** Joshua M. Courtney\n\nWe achieve query-optimal quantum simulations of non-Hermitian Hamiltonians $H_{\\mathrm{eff}} = H_R + iH_I$, where $H_R$ is Hermitian and $H_I \\succeq 0$, using a bivariate extension of quantum signal processing (QSP) with non-commuting signal operators. The algorithm encodes the interaction-picture Dyson series as a polynomial on the bitorus, implemented through a structured multivariable QSP (M-QSP) circuit. A constant-ratio condition guarantees scalar angle-finding for M-QSP circuits with arbitrary non-commuting signal operators. A degree-preserving sum-of-squares spectral factorization permits scalar complementary polynomials in two variables. Angles are deterministically calculated in a classical precomputation step, running in $\\mathcal{O}(d_R \\cdot d_I)$ classical operations. Operator norms $α_R\\,,β_I$ contribute additively with query complexity $\\mathcal{O}((α_R + β_I)T + \\log(1/\\varepsilon)/\\log\\log(1/\\varepsilon))$ matching an information-theoretic lower bound in the separate-oracle model, where $H_R$ and $H_I$ are accessed through independent block encodings. The postselection success probability is $e^{-2β_I T}\\|e^{-iH_{\\mathrm{eff}}T}|ψ_0\\rangle\\|^2\\cdot (1 - \\mathcal{O}(\\varepsilon))$, decomposing into a state-dependent factor $\\|e^{-iH_{\\mathrm{eff}}T}|ψ_0\\rangle\\|^2$ from the intrinsic barrier and an $e^{-2β_I T}$ overhead from polynomial block-encoding.",
  "title": "Simulation of Non-Hermitian Hamiltonians with Bivariate Quantum Signal Processing"
}