The topological insulator is a fundamentally new phase of matter, with the striking property that the conduction of electrons occurs only on its surface, not within the bulk, and that conduction is topologically protected. Topological protection, the total lack of scattering of electron waves by disorder, is perhaps the most fascinating

Universal quantum computers promise a dramatic speed-up over classical computers but a fullsize realization remains challenging. However, intermediate quantum computational models have been proposed that are not universal, but can solve problems that are strongly believed to be classically hard. Aaronson and Arkhipov have shown that interference of single photons in random optical networks can solve the hard problem of sampling the bosonic output distribution which is directly connected to computing matrix permanents. Remarkably, this computation does not require measurement-based interactions or adaptive feed-forward techniques. Here we demonstrate this model of computation using high-quality laser-written integrated quantum networks that were designed to implement random unitary matrix transformations. We experimentally characterize the integrated devices using an in-situ reconstruction method and observe three-photon interference that leads to the boson-sampling output distribution. Our results set a benchmark for quantum computers, that hold the potential of outperforming conventional ones using only a few dozen photons and linear-optical elements.

Parity-time (PT)-symmetric crystals are a class of non-Hermitian systems that allow, for example, the existence of modes with real propagation constants, for self-orthogonality of propagating modes, and for uni-directional invisibility at defects. Photonic PT-symmetric systems that also support topological states could be useful for shaping and routing light waves. However, it is currently debated whether topological interface states can exist at all in PT-symmetric systems. Here, we show theoretically and demonstrate experimentally the existence of such states: states that are localized at the interface between two topologically distinct PT-symmetric photonic lattices. We find analytical closed form solutions of topological PT-symmetric interface states, and observe them through fluorescence microscopy in a passive PT-symmetric dimerized photonic lattice. Our results are relevant towards approaches to localize light on the interface between non-Hermitian crystals.

We present the first experimental demonstration of a new type of localized state in the continuum, namely, compacton-like linear states in flat-band lattices. To this end, we employ photonic Lieb lattices, which exhibit three tight-binding bands, with one being perfectly flat. Discrete predictions are confirmed by realistic continuous numerical simulations as well as by direct experiments. Our results could be of great importance for fundamental physics as well as for various applications where light needs to be conducted in a diffractionless and localized manner over long distances.

Topological insulators are insulating in the bulk but feature conducting states on their surfaces. Standard methods for probing their topological properties largely involve probing the surface, even though topological invariants are defined via the bulk band structure. Here, we utilize non-hermiticy to experimentally demonstrate a topological transition in an optical system, using bulk behavior only, without recourse to surface properties. This concept is relevant for a wide range of systems beyond optics, where the surface physics is difficult to probe.The notion of topological protection of electronic properties was first explored by Thouless and coworkers [1], who demonstrated that the Hall conductance of a two-dimensional electron gas (with Fermi energy placed within a bulk gap) is proportional to an integer-valued topological quantity. The global nature of the topological quantity introduces a striking robustness: small changes to the system (including the addition of disorder) have almost no effect on the Hall conductance [2]. Non-trivial topology implies the presence of conducting surface states (via the "bulk-edge correspondence principle"), which play a central role in many topological phenomena. A subsequent resurgence of interest in topological phenomena began with the prediction and observation of the quantum spin Hall effect [3][4][5], followed by the prediction [6,7] and observation [8] of an analogue for microwave photons. This scheme relies on the large magnetic response occurring in the microwave regime, which is not generalizable to