相关论文: O-Sensing: Operator Sensing for Interaction Geomet…
The recently proposed interior boundary conditions approach [S. Teufel and R. Tumulka: Avoiding Ultraviolet Divergence by Means of Interior Boundary Conditions, arXiv:1506.00497] is a method for defining Hamiltonians without UV divergence…
A defining quantity of a physical system is its energy which is represented by the Hamiltonian. In closed quantum mechanical or/and coherent wave-based systems the Hamiltonian is introduced as a Hermitian operator which ensures real energy…
Recent work has demonstrated that using a carefully designed sensing matrix rather than a random one, can improve the performance of compressed sensing. In particular, a well-designed sensing matrix can reduce the coherence between the…
We study several classes of non-Hermitian Hamiltonian systems, which can be expressed in terms of bilinear combinations of Euclidean Lie algebraic generators. The classes are distinguished by different versions of antilinear (PT)-symmetries…
Quantum many-body systems realise many different phases of matter characterised by their exotic emergent phenomena. While some simple versions of these properties can occur in systems of free fermions, their occurrence generally implies…
Hamiltonian Learning is a process of recovering system Hamiltonian from measurements, which is a fundamental problem in quantum information processing. In this study, we investigate the problem of learning the symmetric Hamiltonian from its…
Characterizing noisy quantum devices requires methods for learning the underlying quantum Hamiltonian which governs their dynamics. Often, such methods compare measurements to simulations of candidate Hamiltonians, a task which requires…
We explore the principles of many-body Hamiltonian complexity reduction via downfolding on an effective low-dimensional representation. We present a unique measure of fidelity between the effective (reduced-rank) description and the full…
The action of the quantum mechanical volume operator, introduced in connection with a symmetric representation of the three-body problem and recently recognized to play a fundamental role in discretized quantum gravity models, can be given…
Recovering dynamical equations from observed noisy data is the central challenge of system identification. We develop a statistical mechanics approach to analyze sparse equation discovery algorithms, which typically balance data fit and…
Understanding extreme non-locality in many-body quantum systems can help resolve questions in thermostatistics and laser physics. The existence of symmetry selection rules for Hamiltonians with non-decaying terms on infinite-size lattices…
We introduce a novel approach for estimating the spectrum of quantum many-body Hamiltonians, and more generally, of Hermitian operators, using quantum time evolution. In our approach we are evolving a maximally mixed state under the…
Offline reinforcement learning leverages large datasets to train policies without interactions with the environment. The learned policies may then be deployed in real-world settings where interactions are costly or dangerous. Current…
For one-dimensional systems with delta-contact interactions, the convergence of the exact-diagonalization method is tested with a basis of harmonic oscillator eigenfunctions with frequency $\Omega$ optimized through the minimization of the…
Recovering an unknown Hamiltonian from measurements is an increasingly important task for certification of noisy quantum devices and simulators. Recent works have succeeded in recovering the Hamiltonian of an isolated quantum system with…
In this paper, motivated by network inference and tomography applications, we study the problem of compressive sensing for sparse signal vectors over graphs. In particular, we are interested in recovering sparse vectors representing the…
Optimal transport (OT) is a widely used technique in machine learning, graphics, and vision that aligns two distributions or datasets using their relative geometry. In symmetry-rich settings, however, OT alignments based solely on pairwise…
Efficiently learning an unknown Hamiltonian given access to its dynamics is a problem of interest for quantum metrology, many-body physics and machine learning. A fundamental question is whether learning can be performed at the Heisenberg…
We study the family $H_{\gamma \lambda \mu}(K)$, $K\in \mathbb{T}^2,$ of discrete Schr\"odinger operators, associated to the Hamiltonian of a system of two identical bosons on the two-dimen\-sional lattice $\mathbb{Z}^2,$ interacting…
Identifying and characterizing multi-body interactions in quantum processes remains a significant challenge. This is partly because 2-body interactions can produce an arbitrary time evolution, a fundamental fact often called the…