The task of learning the Hamiltonian interactions governing a quantum system, given samples of its thermal (or 'Gibbs') states, is a foundational question at the intersection of quantum learning theory and many-body physics. In this paper, we draw connections to the quantum Gibbs sampling literature to introduce a natural learning algorithm we call the stationarity test: which simply "guesses" the Hamiltonian, and measures the rate-of-change of local observables, under the associated detailed-balanced quantum Markov chain [CKG23]. We leverage the stationarity test to address the following applications: 1. To give the first learning algorithm for the underlying interaction graph, i.e. structure learning, of lattice Hamiltonians at all temperatures, given copies of their Gibbs states. 2. To give the first learning algorithm for the coefficients of a lattice Hamiltonian, given only copies of its thermal metastable states, modeled as the "local minima" of the free energy. 3. In addition, we present a refinement to the recent area law for thermal metastable states [BCV25], which holds in the thermodynamic limit. Our learning algorithms are rigorous, time-efficient, and nearly sample-optimal in system size and accuracy. At a technical level, our arguments are based on new approximate locality and convexity properties for the quantum Fisher information of these Gibbs sampling algorithms.The task of learning the Hamiltonian interactions governing a quantum system, given samples of its thermal (or 'Gibbs') states, is a foundational question at the intersection of quantum learning theory and many-body physics. In this paper, we draw connections to the quantum Gibbs sampling literature to introduce a natural learning algorithm we call the stationarity test: which simply "guesses" the Hamiltonian, and measures the rate-of-change of local observables, under the associated detailed-balanced quantum Markov chain [CKG23]. We leverage the stationarity test to address the following applications: 1. To give the first learning algorithm for the underlying interaction graph, i.e. structure learning, of lattice Hamiltonians at all temperatures, given copies of their Gibbs states. 2. To give the first learning algorithm for the coefficients of a lattice Hamiltonian, given only copies of its thermal metastable states, modeled as the "local minima" of the free energy. 3. In addition, we present a refinement to the recent area law for thermal metastable states [BCV25], which holds in the thermodynamic limit. Our learning algorithms are rigorous, time-efficient, and nearly sample-optimal in system size and accuracy. At a technical level, our arguments are based on new approximate locality and convexity properties for the quantum Fisher information of these Gibbs sampling algorithms.

quant-pharXiv:2610.01074Oct 2, 20260 citations

Efficient Learning of Long-Range and Equivariant Quantum Systems

Štěpán Šmíd, Roberto Bondesan

In this work, we consider a fundamental task in quantum many-body physics – finding and learning ground states of quantum Hamiltonians and their properties. Recent works have studied the task of predicting the ground state expectation value of sums of geometrically local observables by learning from data. For short-range gapped Hamiltonians, a sample complexity that is logarithmic in the number of qubits and quasipolynomial in the error was obtained. Here we extend these results beyond the local requirements on both Hamiltonians and observables, motivated by the relevance of long-range interactions in molecular and atomic systems. For interactions decaying as a power law with exponent greater than twice the dimension of the system, we recover the same efficient logarithmic scaling with respect to the number of qubits, but the dependence on the error worsens to exponential. Further, we show that learning algorithms equivariant under the automorphism group of the interaction hypergraph achieve a sample complexity reduction, leading in particular to a constant number of samples for learning sums of local observables in systems with periodic boundary conditions. We demonstrate the efficient scaling in practice by learning from DMRG simulations of 1 D long-range and disordered systems with up to 128 qubits. Finally, we provide an analysis of the concentration of expectation values of global observables stemming from the central limit theorem, resulting in increased prediction accuracy.In this work, we consider a fundamental task in quantum many-body physics – finding and learning ground states of quantum Hamiltonians and their properties. Recent works have studied the task of predicting the ground state expectation value of sums of geometrically local observables by learning from data. For short-range gapped Hamiltonians, a sample complexity that is logarithmic in the number of qubits and quasipolynomial in the error was obtained. Here we extend these results beyond the local requirements on both Hamiltonians and observables, motivated by the relevance of long-range interactions in molecular and atomic systems. For interactions decaying as a power law with exponent greater than twice the dimension of the system, we recover the same efficient logarithmic scaling with respect to the number of qubits, but the dependence on the error worsens to exponential. Further, we show that learning algorithms equivariant under the automorphism group of the interaction hypergraph achieve a sample complexity reduction, leading in particular to a constant number of samples for learning sums of local observables in systems with periodic boundary conditions. We demonstrate the efficient scaling in practice by learning from DMRG simulations of 1 D long-range and disordered systems with up to 128 qubits. Finally, we provide an analysis of the concentration of expectation values of global observables stemming from the central limit theorem, resulting in increased prediction accuracy.

arXiv:2312.17019QuantumJan 15, 20252 citations

Learning Quantum Systems

Giorgos P. Tsironis

Understanding complex systemsJan 1, 20250 citations

Dissipative Quantum Multiplicative Weights with Sampling Feedback: A Classically Hard Primitive Realized via Engineered Open-System Dynamics

Agung Trisetyarso, Lenny Putri Yulianti, Kridanto Surendro

We introduce \emph{Dissipative Quantum Multiplicative Weights with Sampling Feedback} (DQMW-Sample), an online-learning primitive in which engineered open quantum-system dynamics prepare a Gibbs state whose computational-basis measurement supplies the loss feedback. The central conceptual contribution is to lift the computational hardness of constant-temperature Gibbs sampling into a physically realizable online-learning primitive. By engineering a Davies-type dissipator whose per-round feedback cannot be efficiently simulated classically, we obtain a learning-theoretic separation in which DQMW-Sample achieves asymptotically sublinear regret while every efficient classical learner suffers constant average regret on a suitably constructed instance. We further prove that the spectral gap of the engineered dissipator contracts hardware noise, yielding sublinear noise-induced regret under a balanced dissipation schedule, and we strengthen the single-round hardness to the full adaptive interaction: an efficient classical simulator of the entire $T$ -round feedback process would collapse the polynomial hierarchy. We state the required realizability assumption in explicit form and report an initial hardware characterization on the IBM Heron~r2 processor. These results position DQMW-Sample as a concrete route toward computational advantage in online learning that is grounded in complexity theory and compatible with near-term superconducting hardware.We introduce \emph{Dissipative Quantum Multiplicative Weights with Sampling Feedback} (DQMW-Sample), an online-learning primitive in which engineered open quantum-system dynamics prepare a Gibbs state whose computational-basis measurement supplies the loss feedback. The central conceptual contribution is to lift the computational hardness of constant-temperature Gibbs sampling into a physically realizable online-learning primitive. By engineering a Davies-type dissipator whose per-round feedback cannot be efficiently simulated classically, we obtain a learning-theoretic separation in which DQMW-Sample achieves asymptotically sublinear regret while every efficient classical learner suffers constant average regret on a suitably constructed instance. We further prove that the spectral gap of the engineered dissipator contracts hardware noise, yielding sublinear noise-induced regret under a balanced dissipation schedule, and we strengthen the single-round hardness to the full adaptive interaction: an efficient classical simulator of the entire $T$-round feedback process would collapse the polynomial hierarchy. We state the required realizability assumption in explicit form and report an initial hardware characterization on the IBM Heron~r2 processor. These results position DQMW-Sample as a concrete route toward computational advantage in online learning that is grounded in complexity theory and compatible with near-term superconducting hardware.

quant-pharXiv:2606.26162Jun 25, 20260 citations

Learning quantum systems

Valentin Gebhart, Raffaele Santagati, Antonio A. Gentile +7 more

arXiv:2207.00298Nature Reviews PhysicsFeb 9, 2023165 citations

T

-round feedback process would collapse the polynomial hierarchy. We state the required realizability assumption in explicit form and report an initial hardware characterization on the IBM Heron~r2 processor. These results position DQMW-Sample as a concrete route toward computational advantage in online learning that is grounded in complexity theory and compatible with near-term superconducting hardware.