Model-independent quantum phases classifier.

Machine learning has transformed science and technology. In this article, we present a model-independent classifier that uses the k-Nearest Neighbors algorithm to classify phases of a model for which it has never been trained. This is done by studying three different spin-1 chains with some common phases: the XXZ chains with uniaxial single-ion-type anisotropy, the bond alternating XXZ chains, and the bilinear biquadratic chain. We show that the algorithm trained with two of these models can, with high probability, determine phases common to the third one. This is the first step towards a universal classifier, where an algorithm can recognize an arbitrary phase without knowing the Hamiltonian, since it knows only partial information about the quantum state.

Computational speed-up with a single qudit.

Quantum algorithms are known for providing more efficient solutions to certain computational tasks than any corresponding classical algorithm. Here we show that a single qudit is sufficient to implement an oracle based quantum algorithm, which can solve a black-box problem faster than any classical algorithm. For 2d permutation functions defined on a set of d elements, deciding whether a given permutation is even or odd, requires evaluation of the function for at least two elements. We demonstrate that a quantum circuit with a single qudit can determine the parity of the permutation with only one evaluation of the function. Our algorithm provides an example for quantum computation without entanglement since it makes use of the pure state of a qudit. We also present an experimental realization of the proposed quantum algorithm with a quadrupolar nuclear magnetic resonance using a single four-level quantum system, i.e., a ququart.

Emergence of the pointer basis through the dynamics of correlations.

We use the classical correlation between a quantum system being measured and its measurement apparatus to analyze the amount of information being retrieved in a quantum measurement process. Accounting for decoherence of the apparatus, we show that these correlations may have a sudden transition from a decay regime to a constant level. This transition characterizes a nonasymptotic emergence of the pointer basis, while the system apparatus can still be quantum correlated. We provide a formalization of the concept of emergence of a pointer basis in an apparatus subject to decoherence. This contrast of the pointer basis emergence to the quantum to classical transition is demonstrated in an experiment with polarization entangled photon pairs.