Hamiltonian Decoded Quantum Interferometry for General Pauli Hamiltonians

TL;DR

This paper introduces efficient quantum algorithms for preparing Gibbs states of general Pauli Hamiltonians using Hamiltonian Decoded Quantum Interferometry, extending its applicability beyond stabilizer Hamiltonians.

Contribution

It develops a method to prepare Gibbs states for general Pauli Hamiltonians via polynomial-induced matrix functions, broadening HDQI's scope.

Findings

Algorithms are efficient and robust to imperfections.

Applicable to a broad class of Hamiltonians beyond stabilizer types.

Enables Hamiltonian optimization and Gibbs-state preparation.

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 $\rho_{\mathcal P}(H) = \frac{\mathcal P^2(H)}{\text{Tr}[\mathcal P^2(H)]}$, 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.