Andreas Schreiber

Photons Walking the Line: A Quantum Walk with Adjustable Coin Operations

We present the first robust implementation of a coined quantum walk over five steps using only passive optical elements. By employing a fiber network loop we keep the amount of required resources constant as the walkers position Hilbert space is increased. We observed a non-Gaussian distribution of the walkers final position, thus characterizing a faster spread of the photon wave packet in comparison to the classical random walk. The walk is realized for many different coin settings and initial states, opening the way for the implementation of a quantum-walk-based search algorithm.

Decoherence and disorder in quantum walks: From ballistic spread to localization

We investigate the impact of decoherence and static disorder on the dynamics of quantum particles moving in a periodic lattice. Our experiment relies on the photonic implementation of a one-dimensional quantum walk. The pure quantum evolution is characterized by a ballistic spread of a photons wave packet along 28 steps. By applying controlled time-dependent operations we simulate three different environmental influences on the system, resulting in a fast ballistic spread, a diffusive classical walk, and the first Anderson localization in a discrete quantum walk architecture.

A 2D quantum walk simulation of two-particle dynamics

Here, There, Everywhere Random walks are a powerful mathematical method that can be used to simulate certain processes in biology, chemistry, or even the stock market. They present a statistical method for mapping the possible routes that processes can take. Quantum walks are expected to be able to probe multiple paths simultaneously. Quantum walks have been demonstrated for one-dimensional, or straight-line, walks. Now, Schreiber et al. (p. 55, published online 8 March) demonstrate an optical system that can simulate quantum walks over a two-dimensional system, thereby providing the capability of describing much more complex processes. An optical approach extends quantum walk methodology from one to two dimensions. Multidimensional quantum walks can exhibit highly nontrivial topological structure, providing a powerful tool for simulating quantum information and transport systems. We present a flexible implementation of a two-dimensional (2D) optical quantum walk on a lattice, demonstrating a scalable quantum walk on a nontrivial graph structure. We realized a coherent quantum walk over 12 steps and 169 positions by using an optical fiber network. With our broad spectrum of quantum coins, we were able to simulate the creation of entanglement in bipartite systems with conditioned interactions. Introducing dynamic control allowed for the investigation of effects such as strong nonlinearities or two-particle scattering. Our results illustrate the potential of quantum walks as a route for simulating and understanding complex quantum systems.

Photon Propagation in a Discrete Fiber Network: An Interplay of Coherence and Losses

We study light propagation in a photonic system that shows stepwise evolution in a discretized environment. It resembles a discrete-time version of photonic waveguide arrays or quantum walks. By introducing controlled photon losses to our experimental setup, we observe unexpected effects like subexponential energy decay and formation of complex fractal patterns. This demonstrates that the interplay of linear losses, discreteness and energy gradients leads to genuinely new coherent phenomena in classical and quantum optical experiments. Moreover, the influence of decoherence is investigated.

Multi-walker discrete time quantum walks on arbitrary graphs, their properties and their photonic implementation

Quantum walks have emerged as an interesting alternative to the usual circuit model for quantum computing. While still universal for quantum computing, the quantum walk model has very different physical requirements, which lends itself more naturally to some physical implementations, such as linear optics. Numerous authors have considered walks with one or two walkers, on one-dimensional graphs, and several experimental demonstrations have been performed. In this paper, we discuss generalizing the model of discrete time quantum walks to the case of an arbitrary number of walkers acting on arbitrary graph structures. We present a formalism that allows for the analysis of such situations, and several example scenarios for how our techniques can be applied. We consider the most important features of quantum walks—measurement, distinguishability, characterization and the distinction between classical and quantum interference. We also discuss the potential for physical implementation in the context of linear optics, which is of relevance to present-day experiments.

Spatio-spectral characteristics of parametric down-conversion in waveguide arrays

High dimensional quantum states are of fundamental interest for quantum information processing. They give access to large Hilbert spaces and, in turn, enable the encoding of quantum information on multiple modes. One method to create such quantum states is parametric down-conversion (PDC) in waveguide arrays (WGAs) which allows for the creation of highly entangled photon pairs in controlled, easily accessible spatial modes, with unique spectral properties.In this paper we examine both theoretically and experimentally the PDC process in a lithium niobate WGA. We measure the spatial and spectral properties of the emitted photon pairs, revealing correlations between spectral and spatial degrees of freedom of the created photons. Our measurements show that, in contrast to prior theoretical approaches, spectrally dependent coupling effects have to be taken into account in the theory of PDC in WGAs. To interpret the results, we developed a theoretical model specifically taking into account spectrally dependent coupling effects, which further enables us to explore the capabilities and limitations for engineering the spatial correlations of the generated quantum states.

Simulations of two-particle interactions with 2D quantum walks in time

We present the experimental implementation of a quantum walk on a two-dimensional lattice and show how to employ the optical system to simulate the quantum propagation of two interacting particles. Our quantum walk in time transfers the spatial spread of a quantum walk into the time domain, which guarantees a high stability and scalability of the setup. We present with our device quantum walks over 12 steps on a 2D lattice. By changing the properties of the driving quantum coin, we investigate different kinds of two-particle interactions and reveal their impact on the occurring quantum propagation.

Simulations of two particle dynamics employing dynamic coin control in 2D quantum walks

Summary form only given. There has been constantly rising interest in quantum walks in recent years, as they are a well-snited framework to study quantum algorithms, for example [1, 2] or to use them as a simulator for other quantum systems, which are not as readily accessible [3]. A key element for a versatile simulator is the ability to dynamically control the quantum-coin, which is the main entity responsible for the evolution of the quantum walk.Here we demonstrate the simulation of interacting bosonic particles by using a photonic realization of a 2D discrete-time quantum walk, as introduced in [3]. We investigate different interaction types making use of the direct dynamic access to the internal coin state of the walker in our setup and realize either a bunching or anti-bunching behavior of the particles, as shown in figure 1. The utilization of the polarization state as coin state allows for easy manipulation by simply introducing controlled phase shifts through an electro optic modulator to selectively modify the coin state. This enables us to tune interaction strengths and patterns to engineer simulations of different kinds of particles or environments and thus enhancing the abilities of photonic experiments to include controlled interactions.

Nonlinear Quantum Walks at the Edge of Quadratic Waveguide Arrays

We realize experimentally quantum walks of photon-pairs generated in a quadratic nonlinear waveguide array, and demonstrate that the pump distance from the edge strongly affects the spatial correlations through the interference from virtual biphoton sources.

Quantum simulations with a two-dimensional quantum walk

We present an experimental implementation of a quantum walk in two dimensions, employing an optical fiber network. We simulated entangling operations and nonlinear multi-particle interactions revealing phenomena such as bound states.