QUROPE Quantum Information Processing and Communication in Europe

Matrix product states (MPS) represent a powerful ansatz for the computation of ground state properties of local Hamiltonians. In this work, the authors define MPS in the continuum limit, without any reference to an underlying lattice parameter. This allows extending the density matrix renormalization group and variational matrix product state formalism to quantum field theories and continuum models in 1 spatial dimension.

We consider quantum computations comprising only commuting gates, known as IQP computations, and provide compelling evidence that the task of sampling their output probability distributions is unlikely to be achievable by any efficient classical means. More specifically we introduce the class post-IQP of languages decided with bounded error by uniform families of IQP circuits with post-selection, and prove first that post-IQP equals the classical class PP.

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The formulation of massless relativistic fermions in lattice gauge theories is hampered by the fundamental problem of species doubling, namely, the rise of spurious fermions modifying the underlying physics. A suitable tailoring of the fermion masses prevents such abundance of species, and leads to the so-called Wilson fermions. Here we show that ultracold atoms provide us with the first controllable realization of these paradigmatic fermions, thus generating a quantum simulator of fermionic lattice gauge theories. We describe a novel scheme that exploits laser-assisted tunneling in a cubic optical superlattice to design the Wilson fermion masses. The high versatility of this proposal allows us to explore a variety of interesting phases in three-dimensional topological insulators, and to test the remarkable predictions of axion electrodynamics.

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Traditionally, quantum entanglement has played a central role in foundational discussions of quantum mechanics. The measurement of correlations between entangled particles can exhibit results at odds with classical behavior. These discrepancies increase exponentially with the number of entangled particles. When entanglement is extended from just two quantum bits (qubits) to three, the incompatibilities between classical and quantum correlation properties can change from a violation of inequalities involving statistical averages to sign differences in deterministic observations.

Entanglement is one of the key resources required for quantum computation, so experimentally creating and measuring entangled states is of crucial importance in the various physical implementations of a quantum computer. In superconducting qubits, two-qubit entangled states have been demonstrated and used to show violations of Bell's Inequality and to implement simple quantum algorithms.

The authors propose a novel approach to prepare mesoscopic mechanical systems in superposition, or entangled states at room temperatures. A promising setup for the implementation of these ideas consists of levitated nanospheres coupled to high-finesse cavities.

The authors propose a novel approach to prepare mesoscopic mechanical systems in superposition, or entangled states at room temperatures. A promising setup for the implementation of these ideas consists of levitated nanospheres coupled to high-finesse cavities.