Related papers: Quantum state estimation and large deviations
A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems and to express different statistical operations such as measurement,…
We present a quantum algorithm for estimating the matrix determinant based on quantum spectral sampling. The algorithm estimates the logarithm of the determinant of an $n \times n$ positive sparse matrix to an accuracy $\epsilon$ in time…
Estimating quantum amplitude, or the overlap between two quantum states, is a fundamental task in quantum computing and underpins numerous quantum algorithms. In this work, we introduce a novel algorithmic framework for quantum amplitude…
A simple and efficient method for characterization of multidimensional Gaussian states is suggested and experimentally demonstrated. Our scheme shows analogies with tomography of finite dimensional quantum states, with the covariance matrix…
One drawback of conventional quantum state tomography is that it does not readily provide access to single density matrix elements, since it requires a global reconstruction. Here we experimentally demonstrate a scheme that can be used to…
We introduce new measures of decoherence appropriate for evaluation of quantum computing designs. Environment-induced deviation of a quantum system's evolution from controlled dynamics is quantified by a single numerical measure. This…
Quantum state tomography aims to estimate the state of a quantum mechanical system which is described by a trace one, Hermitian positive semidefinite complex matrix, given a set of measurements of the state. Existing works focus on…
Quantum computation has been growing rapidly in both theory and experiments. In particular, quantum computing devices with a large number of qubits have been developed by IBM, Google, IonQ, and others. The current quantum computing devices…
We provide a brief overview of approaches for calculating the density of states of quantum systems and random matrix Hamiltonians using the tools of free probability theory. For a given Hamiltonian of a quantum system or a generic random…
Simulating the dynamics and the non-equilibrium steady state of an open quantum system are hard computational tasks on conventional computers. For the simulation of the time evolution, several efficient quantum algorithms have recently been…
We present an approach that allows quantifying decoherence processes in an open quantum system subject to external time-dependent control. Interactions with the environment are modeled by a standard bosonic heat bath. We develop two…
We show that probabilities of results of all possible measurements performing on a quantum system depend on the system's state only through its density matrix. Therefore all experimentally available information about the state contains in…
When an informationally complete measurement is not available, the reconstruction of the density operator that describes the state of a quantum system can be accomplish, in a reliable way, by adopting the maximum entropy principle (MaxEnt…
We present a quantum information-inspired framework for analyzing complex systems through multivariate time series. In this approach the system's state is encoded into a density matrix, providing a compact representation of higher-order…
We present a technique for enhancing the estimation of quantum state properties by incorporating approximate prior knowledge about the quantum state of interest. This method involves performing randomized measurements on a quantum processor…
In quantum theory, the inescapable interaction between a system and its surroundings would lead to a loss of coherence and leakage of information into the environment. An effective approach to retain the quantum characteristics of the…
Recently we find several candidates of quantum algorithms that may be implementable in near-term devices for estimating the amplitude of a given quantum state, which is a core sub- routine in various computing tasks such as the Monte Carlo…
We introduce a measure Q of bipartite quantum correlations for arbitrary two-qubit states, expressed as a state-independent function of the density matrix elements. The amount of quantum correlations can be quantified experimentally by…
The density matrix of a two-level system (spin, atom) is usually determined by measuring the three non-commuting components of the Pauli vector. This density matrix can also be obtained via the measurement data of two commuting variables,…
We establish methods for quantum state tomography based on compressed sensing. These methods are specialized for quantum states that are fairly pure, and they offer a significant performance improvement on large quantum systems. In…