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About this paper
Muzhou Ma, Steven T. Flammia, John Preskill, Yu Tong
A compressed-sensing protocol learns an unknown sparse sum of weight-k Pauli interactions without assuming geometric locality, bounded interaction degree, or known support. By reshaping the dynamics into commuting Hamiltonians, estimating eigenvalue differences with non-adaptive frequency measurements, and recovering coefficients from sampled Walsh–Hadamard measurements, the method uses nearly \(\widetilde O(3^kM)\) experiments and total evolution time \(\widetilde O(9^kM^{1/p+1/2}/\epsilon)\) for \(\ell^p\) error \(\epsilon\), including a Heisenberg-like \(1/\epsilon\) dependence.
Key insights
- Sparsity can replace geometric locality as the structural assumption enabling efficient Hamiltonian learning, even when interactions connect arbitrarily distant qubits.
- The protocol separates the quantum and classical difficulties: dynamical reshaping makes the measurements linear, and compressed sensing handles unknown support in a polynomial-sized candidate space.
- Approximate sparsity and higher-body contamination can be treated as structured measurement noise, so exact \(M\)-sparsity and strict \(k\)-locality are not essential for the framework.
Summary by alphaXiv.
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