Hamiltonian Decoded Quantum Interferometry for General Pauli Hamiltonians

• URL: http://arxiv.org/abs/2601.18773v1
• Date: Mon, 26 Jan 2026 18:44:59 GMT
• Title: Hamiltonian Decoded Quantum Interferometry for General Pauli Hamiltonians
• Authors: Kaifeng Bu, Weichen Gu, Xiang Li,
• Abstract summary: We study the Hamiltonian Decoded Quantum Interferometry (HDQI) for the general Hamiltonians $H=sum_ic_iP_i$ on an $n$-qubit system.<n>We show that, given access to an appropriate decoding oracle, there exist efficient quantum algorithms for preparing the state $_mathcal P(H) = fracmathcal P(H)textTr[$cal P(H)]$, where $mathcal P(H)textTr[$
• Score: 6.4675604105664
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this work, we study the Hamiltonian Decoded Quantum Interferometry (HDQI) for the general Hamiltonians $H=\sum_ic_iP_i$ on an $n$-qubit system, where the coefficients $c_i\in \mathbb{R}$ and $P_i$ are Pauli operators. We show that, given access to an appropriate decoding oracle, there exist efficient quantum algorithms for preparing the state $ρ_{\mathcal P}(H) = \frac{\mathcal P^2(H)}{\text{Tr}[\mathcal P^2(H)]}$, where $\mathcal P(H)$ denotes the matrix function induced by a univariate polynomial $\mathcal P(x)$. Such states can be used to approximate the Gibbs states of $H$ for suitable choices of polynomials. We further demonstrate that the proposed algorithms are robust to imperfections in the decoding procedure. Our results substantially extend the scope of HDQI beyond stabilizer-like Hamiltonians, providing a method for Gibbs-state preparation and Hamiltonian optimization in a broad class of physically and computationally relevant quantum systems.

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