Related papers: Hamiltonian Property Testing
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…
The principle of tomographic locality states that the operational state of a multipartite system can be fully characterized by the statistics obtained from measurements that are local to the individual subsystems. This property holds in…
We study the general problem of testing whether an unknown distribution belongs to a specified family of distributions. More specifically, given a distribution family $\mathcal{P}$ and sample access to an unknown discrete distribution…
Property testing has been a major area of research in computer science in the last three decades. By property testing we refer to an ensemble of problems, results and algorithms which enable to deduce global information about some data by…
We investigate the computational complexity of the Local Hamiltonian (LH) problem and the approximation of the Quantum Partition Function (QPF), two central problems in quantum many-body physics and quantum complexity theory. Both problems…
A fundamental problem in statistics and learning theory is to test properties of distributions. We show that quantum computers can solve such problems with significant speed-ups. In particular, we give fast quantum algorithms for testing…
A $k$-modal probability distribution over the discrete domain $\{1,...,n\}$ is one whose histogram has at most $k$ "peaks" and "valleys." Such distributions are natural generalizations of monotone ($k=0$) and unimodal ($k=1$) probability…
We study the problem of learning the Hamiltonian of a many-body quantum system from experimental data. We show that the rate of learning depends on the amount of control available during the experiment. We consider three control models: one…
The characterization of the Hamiltonian parameters defining a quantum walk is of paramount importance when performing a variety of tasks, from quantum communication to computation. When dealing with physical implementations of quantum…
To effectively realize a $\cal PT$-symmetric system, one can dilate a $\cal PT$-symmetric Hamiltonian to some global Hermitian one and simulate its evolution in the dilated Hermitian system. However, with only a global Hermitian…
We investigate whether commutativity is necessary to represent relativistic locality for localization observables of relativistic quantum systems in Minkowski spacetime. A well known no-go theorem by Halvorson and Clifton shows that…
A relevant problem in quantum computing concerns how fast a source state can be driven into a target state according to Schr\"odinger's quantum mechanical evolution specified by a suitable driving Hamiltonian. In this paper, we study in…
Time-local master equations are more generally applicable than is often recognised, but at first sight it would seem that they can only safely be used in time intervals where the time evolution is invertible. Using the Jaynes-Cummings…
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…
Entanglement allows for the nonlocality of quantum theory, which is the resource behind device-independent quantum information protocols. However, not all entangled quantum states display nonlocality, and a central question is to determine…
We develop a computational method to learn a molecular Hamiltonian matrix from matrix-valued time series of the electron density. As we demonstrate for three small molecules, the resulting Hamiltonians can be used for electron density…
In recent years quantum simulation has made great strides culminating in experiments that operate in a regime that existing supercomputers cannot easily simulate. Although this raises the possibility that special purpose analog quantum…
In this paper, we present a gradient algorithm for identifying unknown parameters in an open quantum system from the measurements of time traces of local observables. The open system dynamics is described by a general Markovian master…
Quantum correlations, like entanglement, represent the characteristic trait of quantum mechanics, and pose essential issues and challenges to the interpretation of this pillar of modern physics. Although quantum correlations are largely…
Despite the successes of machine learning methods in physical sciences, prediction of the Hamiltonian, and thus electronic properties, is still unsatisfactory. Here, based on graph neural network architecture, we present an extendable…