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We investigate the quantum dynamics of a spin chain that implements a quantum analog of Conways game of life. We solve the time-dependent Schrodinger equation starting with initial separable states and analyse the evolution of quantum correlations across the lattice. We report examples of evolutions leading to all-entangled chains and/or to time oscillating entangling structures and characterize them by means of entanglement and network measures. The quantum patterns result to be quite different from the classical ones, even in the dynamics of local observables. A peculiar instance is a structure behaving as the quantum analog of a blinker, but that has no classical counterpart.
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We introduce a quantum version of the Game of Life and we use it to study the emergence of complexity in a quantum world. We show that the quantum evolution displays signatures of complex behaviour similar to the classical one, however a regime exists, where the quantum Game of Life creates more complexity, in terms of diversity, with respect to the corresponding classical reversible one.
We propose an extended version of quantum dynamics for a certain system S, whose evolution is ruled by a Hamiltonian $H$, its initial conditions, and a suitable set $rho$ of {em rules}, acting repeatedly on S. The resulting dynamics is not necessarily periodic or quasi-periodic, as one could imagine for conservative systems with a finite number of degrees of freedom. In fact, it may have quite different behaviors depending on the explicit forms of $H$, $rho$ as well as on the initial conditions. After a general discussion on this $(H,rho)$-{em induced dynamics}, we apply our general ideas to extend the classical game of life, and we analyze several aspects of this extension.
Quantum entanglement, as the strictly non-classical phenomena, is the kernel of quantum computing and quantum simulation, and has been widely applied ranging from fundamental tests of quantum physics to quantum information processing. The decoherence of quantum states restricts the capability of building quantum simulators and quantum computers in a scalable fashion. Meanwhile, the topological phase is found inherently capable of protecting physical fields from unavoidable fabrication-induced disorder, which inspires the potential application of topological protection on quantum states. Here, we present the first experimental demonstration of topologically protected quantum polarization entangled states on a photonic chip. The process tomography shows that quantum entanglement can be well preserved by the boundary states even when the chip material substantially introduces relative polarization rotation in phase space. Our work links topology, material and quantum physics, opening the door to wide applications of topological enhancement in genuine quantum regime.
The symmetries associated with discrete-time quantum walks (DTQWs) and the flexibilities in controlling their dynamical parameters allow to create a large number of topological phases. An interface in position space, which separates two regions with different topological numbers, can, for example, be effectively modelled using different coin parameters for the walk on either side of the interface. Depending on the neighbouring numbers, this can lead to localized states in one-dimensional configurations and here we carry out a detailed study into the strength of such localized states. We show that it can be related to the amount of entanglement created by the walks, with minima appearing for strong localizations. This feature also persists in the presence of small amounts of $sigma_x$ (bit flip) noise.
We introduce and explore a one-dimensional hybrid quantum circuit model consisting of both unitary gates and projective measurements. While the unitary gates are drawn from a random distribution and act uniformly in the circuit, the measurements are made at random positions and times throughout the system. By varying the measurement rate we can tune between the volume law entangled phase for the random unitary circuit model (no measurements) and a quantum Zeno phase where strong measurements suppress the entanglement growth to saturate in an area-law. Extensive numerical simulations of the quantum trajectories of the many-particle wavefunctions (exploiting Clifford circuitry to access systems up to 512 qubits) provide evidence for a stable weak measurement phase that exhibits volume-law entanglement entropy, with a coefficient decreasing with increasing measurement rate. We also present evidence for a novel continuous quantum dynamical phase transition between the weak measurement phase and the quantum Zeno phase, driven by a competition between the entangling tendencies of unitary evolution and the disentangling tendencies of projective measurements. Detailed steady-state and dynamic critical properties of this novel quantum entanglement transition are accessed.
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