Related papers: Quantum-probabilistic Hamiltonian learning for gen…
We show in detail how the Jordan-Wigner transformation can be used to simulate any fermionic many-body Hamiltonian on a quantum computer. We develop an algorithm based on appropriate qubit gates that takes a general fermionic Hamiltonian,…
We derive the effective Hamiltonian $H - \mu N$ for open quantum systems with varying particle number from first principles within the framework of non-relativistic quantum statistical mechanics. We prove that under physically motivated…
Hybrid machine learning based on Hamiltonian formulations has recently been successfully demonstrated for simple mechanical systems, both energy conserving and not energy conserving. We introduce a pseudo-Hamiltonian formulation that is a…
Variational representations of quantum states abound and have successfully been used to guess ground-state properties of quantum many-body systems. Some are based on partial physical insight (Jastrow, Gutzwiller projected, and fractional…
We have developed a theoretical formalism to introduce temperature as a parameter into the framework of non-relativistic quantum mechanics using the laws of classical thermodynamics and the canonical ensemble scheme of statistical…
We present a systematic study of statistical mechanics for non-Hermitian quantum systems. Our work reveals that the stability of a non-Hermitian system necessitates the existence of a single path-dependent conserved quantity, which, in…
We introduce Extreme Quantum Cognition Machines, a class of quantum learning architectures for deliberative decision making that is tolerant to noisy and contradictory training data. Inspired by the quantum cognition paradigm, Extreme…
In this work, we develop a mathematical framework to model a quantum system whose Hamiltonian may depend on the state of changing environment, that evolves according to a Markovian process. When the environment changes its state, the…
A hybrid quantum-classical method for learning Boltzmann machines (BM) for a generative and discriminative task is presented. Boltzmann machines are undirected graphs with a network of visible and hidden nodes where the former is used as…
Anomaly detection is a crucial task in machine learning that involves identifying unusual patterns or events in data. It has numerous applications in various domains such as finance, healthcare, and cybersecurity. With the advent of quantum…
Despite the complexity of quantum systems in the real world, models with just a few effective many-body states often suffice to describe their quantum dynamics, provided decoherence is accounted for. We show that a machine learning…
Anomaly detection is a vital technique for exploring signatures of new physics Beyond the Standard Model (BSM) at the Large Hadron Collider (LHC). The vast number of collisions generated by the LHC demands sophisticated deep learning…
Concepts like `typicality' and the `eigenstate thermalization hypothesis' aim at explaining the apparent equilibration of quantum systems, possibly after a very long time. However, these concepts are not concerned with the specific way in…
We present a new machine learning technique which calculates a real-valued, time independent, finite dimensional Hamiltonian matrix from only experimental data. A novel cost function is given along with a proof that the cost function has…
We show that it is possible to uniquely reconstruct a generic many-body local Hamiltonian from a single pair of initial and final states related by time evolution with the Hamiltonian. We then propose a practical version of the protocol…
Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that heretofore were not believed to be obtainable by such methods. The novel feature of adaptive…
We describe some general results that constrain the dynamical fluctuations that can occur in non-equilibrium steady states, with a focus on molecular dynamics. That is, we consider Hamiltonian systems, coupled to external heat baths, and…
Advancements in the implementation of quantum hardware have enabled the acquisition of data that are intractable for emulation with classical computers. The integration of classical machine learning (ML) algorithms with these data holds…
As the size of quantum devices continues to grow, the development of scalable methods to characterise and diagnose noise is becoming an increasingly important problem. Recent methods have shown how to efficiently estimate Hamiltonians in…
Quantum machine learning (QML) shows promise for analyzing quantum data. A notable example is the use of quantum convolutional neural networks (QCNNs), implemented as specific types of quantum circuits, to recognize phases of matter. In…