The presence of global conserved quantities in interacting systems generically leads to diffusive transport at late times. Here, we show that systems conserving the dipole moment of an associated global charge, or even higher-moment generalizations thereof, escape this scenario, displaying subdiffusive decay instead. Modeling the time evolution as cellular automata for specific cases of dipole- and quadrupole conservation, we numerically find distinct anomalous exponents of the late time relaxation. We explain these findings by analytically constructing a general hydrodynamic model that results in a series of exponents depending on the number of conserved moments, yielding an accurate description of the scaling form of charge correlation functions. We analyze the spatial profile of the correlations and discuss potential experimentally relevant signatures of higher-moment conservation.Dispersive shock waves in thermal optical media are nonlinear phenomena whose intrinsic irreversibility is described by time asymmetric quantum mechanics. Recent studies demonstrated that the nonlocal wave breaking evolves in an exponentially decaying dynamics ruled by the reversed harmonic oscillator, namely, the simplest irreversible quantum system in the rigged Hilbert spaces. The generalization of this theory to more complex scenarios is still an open question. In this work, we use a thermal third-order medium with an unprecedented giant Kerr coefficient, the m-cresol/nylon mixed solution, to access an extremely nonlinear, highly nonlocal regime and realize anisotropic shock waves with internal gaps. We compare our experimental observations to results obtained under similar conditions but in hemoglobin solutions from human red blood cells, and found that the gap formation strongly depends on the nonlinearity strength. We prove that a superposition of Gamow vectors in an ad hoc rigged Hilbert space, that is, a tensorial product between the reversed and the standard harmonic oscillators spaces, describes the beam propagation beyond the shock point.  https://www.selleckchem.com/ALK.html  The anisotropy turns out from the interaction of trapping and antitrapping potentials. Our work furnishes the description of novel intriguing shock phenomena mediated by extreme nonlinearities.The development of useful photon-photon interactions can trigger numerous breakthroughs in quantum information science, however, this has remained a considerable challenge spanning several decades. Here, we demonstrate the first room-temperature implementation of large phase shifts (≈π) on a single-photon level probe pulse (1.5  μs) triggered by a simultaneously propagating few-photon-level signal field. This process is mediated by Rb^87 vapor in a double-Λ atomic configuration. We use homodyne tomography to obtain the quadrature statistics of the phase-shifted quantum fields and perform maximum-likelihood estimation to reconstruct their quantum state in the Fock state basis. For the probe field, we have observed input-output fidelities higher than 90% for phase-shifted output states, and high overlap (over 90%) with a theoretically perfect coherent state. Our noise-free, four-wave-mixing-mediated photon-photon interface is a key milestone toward developing quantum logic and nondemolition photon detection using schemes such as coherent photon conversion.Using quantum walks (QWs) to rank the centrality of nodes in networks, represented by graphs, is advantageous compared to certain widely used classical algorithms. However, it is challenging to implement a directed graph via QW, since it corresponds to a non-Hermitian Hamiltonian and thus cannot be accomplished by conventional QW. Here we report the realizations of centrality rankings of a three-, a four-, and a nine-vertex directed graph with parity-time (PT) symmetric quantum walks by using high-dimensional photonic quantum states, multiple concatenated interferometers, and dimension dependent loss to achieve these. We demonstrate the advantage of the QW approach experimentally by breaking the vertex rank degeneracy in a four-vertex graph. Furthermore, we extend our experiment from single-photon to two-photon Fock states as inputs and realize the centrality ranking of a nine-vertex graph. Our work shows that a PT symmetric multiphoton quantum walk paves the way for realizing advanced algorithms.Classical mechanics obeys the intuitive logic that a physical event happens at a definite spatial point. Entanglement, however, breaks this logic by enabling interactions without a specific location. In this work we study these delocalized interactions. These are quantum interactions that create less locational information than would be possible classically, as captured by the disturbance induced on some spatial superposition state. We introduce quantum games to capture the effect and demonstrate a direct operational use for quantum concurrence in that it bounds the nonclassical performance gain. We also find a connection with quantum teleportation, and demonstrate the games using an IBM quantum processor.High-quality two-qubit gate operations are crucial for scalable quantum information processing. Often, the gate fidelity is compromised when the system becomes more integrated. Therefore, a low-error-rate, easy-to-scale two-qubit gate scheme is highly desirable. Here, we experimentally demonstrate a new two-qubit gate scheme that exploits fixed-frequency qubits and a tunable coupler in a superconducting quantum circuit. The scheme requires less control lines, reduces cross talk effect, and simplifies calibration procedures, yet produces a controlled-Z gate in 30 ns with a high fidelity of 99.5%, derived from the interleaved randomized benchmarking method. Error analysis shows that gate errors are mostly coherence limited. Our demonstration paves the way for large-scale implementation of high-fidelity quantum operations.Fractional kinetic equations employ noninteger calculus to model anomalous relaxation and diffusion in many systems. While this approach is well explored, it so far failed to describe an important class of transport in disordered systems. Motivated by work on contaminant spreading in geological formations, we propose and investigate a fractional advection-diffusion equation describing the biased spreading packet. While usual transport is described by diffusion and drift, we find a third term describing symmetry breaking which is omnipresent for transport in disordered systems. Our work is based on continuous time random walks with a finite mean waiting time and a diverging variance, a case that on the one hand is very common and on the other was missing in the kaleidoscope literature of fractional equations. The fractional space derivatives stem from long trapping times, while previously they were interpreted as a consequence of spatial Lévy flights.