A Quantum Ensemble

Gregor Skačej, P. Ziherl

Abbas, Amira, Maria Schuld, Francesco Petruccione

Quantum machine learning seeks to exploit the underlying nature of a quantum computer to enhance machine learning techniques. A particular framework uses the quantum property of superposition to store sets of parameters, thereby creating an ensemble of quantum classifiers that may be computed in parallel. The idea stems from classical ensemble methods where one attempts to build a stronger model by averaging the results from many different models. In this work, we demonstrate that a specific implementation of the quantum ensemble of quantum classifiers, called the accuracy-weighted quantum ensemble, can be fully dequantised. On the other hand, the general quantum ensemble framework is shown to contain the well-known Deutsch-Jozsa algorithm that notably provides a quantum speedup and creates the potential for a useful quantum ensemble to harness this computational advantage.

Alexander Bernal, Gabriele Cobucci, Martin J. Renner +1 more

The dimension of a quantum state is traditionally seen as the number of superposed distinguishable states in a given basis. We propose an absolute, i.e., basis-independent, notion of dimensionality for ensembles of quantum states. It is based on whether a quantum ensemble can be simulated with states confined to arbitrary lower-dimensional subspaces and classical postprocessing. In order to determine the absolute dimension of quantum ensembles, we develop both analytical witness criteria and a semidefinite programming criterion based on the ensemble's information capacity. Furthermore, we construct explicit simulation models for arbitrary ensembles of pure quantum states subject to white noise, and in natural cases we prove their optimality. Also, efficient numerical methods are provided for simulating generic ensembles. Finally, we discuss the role of absolute dimensionality in high-dimensional quantum information processing.

Dick J. Hoekzema

Jian Bo Fu

In this paper, we introduce a new conception of pseudorandom phase ensemble to simulate a quantum ensemble. A pseudorandom sequence is inseparability and integral that are demonstrated only for a whole sequence not for a single phase unit, which is similar to that of quantum ensembles and a quantum particle. By using the ensemble conception, we demonstrate non-locality properties for classical fields similar to quantum entanglement.