Bora Baran | Searcharxiv

arXiv2026

Interaction-resolved decomposition of multi-qubit unitaries via computational-basis phases

In multi-qubit quantum control, target unitary operations are commonly specified through full-unitary target descriptions and assessed through global comparison measures. In this work, we introduce an interaction-resolved decomposition of n-qubit unitaries that provides explicit access to their many-body interaction structure through computational-basis phases collected in a diagonalizing frame. Such a frame is conveniently given by local rotations for many operationally relevant operations, including gates generated by single Pauli strings or commuting sets of Pauli strings, such as stabilizer operations, controlled-phase gates, Toffoli-type operations, and Ising interactions. We derive parity-weighted sums of these computational-basis phases that exactly and uniquely resolve k-body interaction terms supported on arbitrary qubit subsets, which we term support-selective phase invariants. These invariants provide an interaction-resolved coordinate system that organizes unitary operations according to their multipartite interaction structure, giving direct access to local, pairwise, tripartite, and general k-partite interaction content underlying entangling operations. This enables the formulation of selective quantum optimal control targets for synthesizing desired combinations of many-body interactions. We supplement this with numerical demonstrations for a representative hardware model, a realistic nitrogen-vacancy spin register, where we synthesized isolated tripartite interactions up to local equivalence within a single control pulse, guided by these invariants, for both diagonal (ZZZ) and non-diagonal (XZZ) terms.

quant-ph↗

arXiv2025

Heisenberg-Limited Quantum Hamiltonian Learning via Randomly Spread Product-States

We show how the Heisenberg-limited quadratic Fisher-information regime of short-time quantum evolution can be made practically accessible for quantum Hamiltonian learning, using only local quantum operations. Our protocol uses experiments initialized in locally Haar-random product states, accompanied by random one-shot Pauli-product measurements, leading to the activation of the full Hamiltonian spectrum in the measurement statistics. This extends the naturally given quadratic Fisher scaling of short-time dynamics into a practically accessible temporal window without requiring entanglement, globally coherent measurements, or dynamical control. Furthermore, we show that the act of ensemble averaging over these initial states makes unbiased estimation data, meaning all Hamiltonian parameters can be simultaneously estimated from the same data-set, removing the need for parameter isolation. We supplement the theoretical results by showing empirically that, even away from the asymptotic limit, one can surpass the SQL using randomly spread product-state ensembles. We do so numerically by learning a selection of different disordered multi-qubit Hamiltonians in a black-box learning scenario.

quant-ph↗