Abstract: We consider a pure two-state quantum system illuminated by two lasers. A photo-detector captures the fluorescence of the system. We build an invariant observer which yields a (local) estimation of the wave function (or density matrix) and the two key parameters (laser de-tuning and the atomlaser coupling strength) of the hamiltonian. The design exploits the symmetries of the system and can be interpreted geometrically. The convergence proof is based on averaging arguments. Simulation with noise illustrates the robustness of the obtained estimation algorithm.Abstract: We consider a pure two-state quantum system illuminated by two lasers. A photo-detector captures the fluorescence of the system. We build an invariant observer which yields a (local) estimation of the wave function (or density matrix) and the two key parameters (laser de-tuning and the atomlaser coupling strength) of the hamiltonian. The design exploits the symmetries of the system and can be interpreted geometrically. The convergence proof is based on averaging arguments. Simulation with noise illustrates the robustness of the obtained estimation algorithm.

Jan 1, 20080 citations

Emergent Prethermal Symmetries for Scalable Hamiltonian Learning

Myeongjin Shin, Junseo Lee, Iman Marvian +1 more

Learning an interacting many-body Hamiltonian at the Heisenberg limit generally requires control that preserves local information for evolution times of order $1/\varepsilon$ to attain $\varepsilon$ precision. To achieve this, existing protocols often rely on trusted many-qubit operations or increasingly rapid control pulses, creating a precision barrier when gates involve unknown multi-qubit interaction or have finite duration. We show that neither resource is necessary for geometrically local Hamiltonians. Our protocol applies only static single-qubit fields, whose strength is independent of system size and grows polylogarithmically with $1/\varepsilon$ . These fields generate emergent prethermal symmetries that suppress thermalization for the entire learning experiment while retaining informative symmetry-preserving dynamics. On a $d$ -dimensional lattice of $n$ qubits, this enables learning every coefficient to accuracy $\varepsilon$ , with failure probability at most $δ$ , using total evolution time $\mathcal{O}(\log^d(1/\varepsilon)\log^2(n/δ)/\varepsilon).$ Thus, our learning protocol attains the information-theoretically optimal $1/\varepsilon$ dependence up to polylogarithmic factors using product-state preparation, single-qubit measurements, and non-adaptive experiments. More broadly, our results establish emergent prethermal symmetries as a resource for quantum learning, opening a route to Heisenberg-limited characterization of many-body systems where fast or trusted many-qubit control is unavailable.Learning an interacting many-body Hamiltonian at the Heisenberg limit generally requires control that preserves local information for evolution times of order $1/\varepsilon$ to attain $\varepsilon$ precision. To achieve this, existing protocols often rely on trusted many-qubit operations or increasingly rapid control pulses, creating a precision barrier when gates involve unknown multi-qubit interaction or have finite duration. We show that neither resource is necessary for geometrically local Hamiltonians. Our protocol applies only static single-qubit fields, whose strength is independent of system size and grows polylogarithmically with $1/\varepsilon$. These fields generate emergent prethermal symmetries that suppress thermalization for the entire learning experiment while retaining informative symmetry-preserving dynamics. On a $d$-dimensional lattice of $n$ qubits, this enables learning every coefficient to accuracy $\varepsilon$, with failure probability at most $δ$, using total evolution time $\mathcal{O}(\log^d(1/\varepsilon)\log^2(n/δ)/\varepsilon).$ Thus, our learning protocol attains the information-theoretically optimal $1/\varepsilon$ dependence up to polylogarithmic factors using product-state preparation, single-qubit measurements, and non-adaptive experiments. More broadly, our results establish emergent prethermal symmetries as a resource for quantum learning, opening a route to Heisenberg-limited characterization of many-body systems where fast or trusted many-qubit control is unavailable.

quant-pharXiv:2609.27181Sep 24, 20260 citations

IDENTIFICATION OF QUANTUM SYSTEMS

Robert L. Kosut, HERSCHEL A. RABITZ

IFAC Proceedings VolumesJan 1, 20029 citations

Learning an interacting many-body Hamiltonian at the Heisenberg limit generally requires control that preserves local information for evolution times of order

1/\varepsilon

to attain

\varepsilon

precision. To achieve this, existing protocols often rely on trusted many-qubit operations or increasingly rapid control pulses, creating a precision barrier when gates involve unknown multi-qubit interaction or have finite duration. We show that neither resource is necessary for geometrically local Hamiltonians. Our protocol applies only static single-qubit fields, whose strength is independent of system size and grows polylogarithmically with

1/\varepsilon

. These fields generate emergent prethermal symmetries that suppress thermalization for the entire learning experiment while retaining informative symmetry-preserving dynamics. On a

d

-dimensional lattice of

n

qubits, this enables learning every coefficient to accuracy

\varepsilon

, with failure probability at most

δ

, using total evolution time

\mathcal{O}(\log^d(1/\varepsilon)\log^2(n/δ)/\varepsilon).

Thus, our learning protocol attains the information-theoretically optimal

1/\varepsilon

dependence up to polylogarithmic factors using product-state preparation, single-qubit measurements, and non-adaptive experiments. More broadly, our results establish emergent prethermal symmetries as a resource for quantum learning, opening a route to Heisenberg-limited characterization of many-body systems where fast or trusted many-qubit control is unavailable.