Heisenberg-limited Hamiltonian learning continuous variable systems via engineered dissipation
- URL: http://arxiv.org/abs/2506.00606v1
- Date: Sat, 31 May 2025 15:33:26 GMT
- Title: Heisenberg-limited Hamiltonian learning continuous variable systems via engineered dissipation
- Authors: Tim Möbus, Andreas Bluhm, Tuvia Gefen, Yu Tong, Albert H. Werner, Cambyse Rouzé,
- Abstract summary: Identifying the Hamiltonian governing the evolution of a quantum system is a fundamental task in quantum learning theory.<n>In this work we focus on learning the Hamiltonian of a bosonic quantum system, a common type of continuous-variable quantum system.<n>We introduce an analytic framework to study the effects of strong dissipation in such systems, enabling a rigorous analysis of cat qubit stabilization.
- Score: 3.023103926472339
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Discrete and continuous variables oftentimes require different treatments in many learning tasks. Identifying the Hamiltonian governing the evolution of a quantum system is a fundamental task in quantum learning theory. While previous works mostly focused on quantum spin systems, where quantum states can be seen as superpositions of discrete bit-strings, relatively little is known about Hamiltonian learning for continuous-variable quantum systems. In this work we focus on learning the Hamiltonian of a bosonic quantum system, a common type of continuous-variable quantum system. This learning task involves an infinite-dimensional Hilbert space and unbounded operators, making mathematically rigorous treatments challenging. We introduce an analytic framework to study the effects of strong dissipation in such systems, enabling a rigorous analysis of cat qubit stabilization via engineered dissipation. This framework also supports the development of Heisenberg-limited algorithms for learning general bosonic Hamiltonians with higher-order terms of the creation and annihilation operators. Notably, our scheme requires a total Hamiltonian evolution time that scales only logarithmically with the number of modes and inversely with the precision of the reconstructed coefficients. On a theoretical level, we derive a new quantitative adiabatic approximation estimate for general Lindbladian evolutions with unbounded generators. Finally, we discuss possible experimental implementations.
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