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.
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.
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.
Quantum walks are the quantum mechanical analog to classical random walks. However, due to the wavelike nature of quantum particles, they reveal drastically different dynamics compared to their classical counterpart. These unique properties make quantum walks a new promising platform for quantum algorithms and a powerful tool to understand complex transport phenomena. This thesis presents three experiments specifically designed to send photons on a quantum walk. The experiments are based on a fiber network spreading the photonic wave packets over discrete time bins. With these Quantum Walks in Time we simulate the propagation of quantum particles in various different environments, revealing diverse dynamics such as a fast ballistic spread and an Anderson-like localization effect. Furthermore we use our concept to implement the first quantum walk on a two-dimensional lattice. The underlying topology allows for investigations of the intriguing dynamics of two strongly interacting quantum particles, which reveals unique effects such as the creation of bound states.
Quantum walks in an elaborately designed graph, is a powerful tool simulating physical and topological phenomena, constructing analog quantum algorithms and realizing universal quantum computing. Integrated photonics technology has emerged as a versatile platform to implement various quantum information tasks and a promising candidate to perform large-scale quantum walks. Both extending physical dimensions and involving more particles will increase the complexity of the evolving systems and the desired quantum resources. Pioneer works have demonstrated single particle walking on two-dimensional (2D) lattices and multiple walkers interfering on a one-dimensional structure. However, 2D multi-particle quantum walk, genuinely being not classically simulatable, has been a vacancy for nearly ten years. Here, we present a genuine 2D quantum walk with correlated photons on a triangular photonic lattice, which can be mapped to a state space up to 37X37 dimensions. This breaks through the physically restriction of single-particle evolution, which can encode information in a large space and constitute high-dimensional graphs indeed beneficial to quantum information processing. A site-by-site addressing between the chip facet and the 2D fanout interface enables an observation of over 600 non-classical interferences simultaneously, violating a classical limit up to 57 standard deviations. Our platform offers a promising prospect for multi-photon quantum walks in a large-scale 2D arrangement, paving the way for practical quantum simulation and quantum computation beyond classical regime.
Quantum walks in an elaborately designed graph are a powerful tool for simulating physical and topological phenomena, constructing novel quantum algorithms, and realizing universal quantum computing. Integrated photonics technology has emerged as a versatile platform for implementing a variety of quantum information tasks and as a promising candidate for performing large-scale quantum walks. Both extending physical dimensions and involving more particles will increase the complexity of the evolving systems. Pioneering studies have demonstrated a single particle walking on two-dimensional lattices and multiple walkers interfering on a one-dimensional structure. However, multiple particles evolving in a genuine two-dimensional space in a scalable fashion has remained a vacancy for nearly 10 years. We present a genuine two-dimensional quantum walk with correlated photons on a triangular photonic lattice, which is mapped to a 37 × 37 high-dimensional state space. The genuine two-dimensional quantum walk breaks through the physical restrictions of single-particle evolution, allowing for the encoding of information in large spaces and construction of high-dimensional graphs, which are beneficial for quantum information processing. Between the chip and the two-dimensional fanout interface, site-by-site addressing enables simultaneous detection of over 600 nonclassical interferences and observation of quantum correlations that violate a classical limit by 57 standard deviations. Our implementation provides a paradigm for multi-photon quantum walks in a two-dimensional configuration on a large scale, paving the way for practical quantum simulation and computation beyond the classical regime.
In this paper, we present a simulator for two-particle quantum walks on the line and one-particle on a two-dimensional squared lattice. It can be used to investigate the equivalence between the two cases (one- and two-particle walks) for various boundary conditions (open, circular, reflecting, absorbing and their combinations). For the case of a single walker on a two-dimensional lattice, the simulator can also implement the Möbius strip. Furthermore, other topologies for the walker are also simulated by the proposed tool, like certain types of planar graphs with degree up to 4, by considering missing links over the lattice. The main purpose of the simulator is to study the genuinely quantum effects on the global properties of the two-particle joint probability distribution on the entanglement between the walkers/axis. For that purpose, the simulator is designed to compute various quantities such as: the entanglement and classical correlations, (classical and quantum) mutual information, the average distance between the two walkers, different hitting times and quantum discord. These quantities are of vital importance in designing possible algorithmic applications of quantum walks, namely in search, 3-SAT problems, etc. The simulator can also implement the static partial measurements of particle(s) positions and dynamic breaking of the links between certain nodes, both of which can be used to investigate the effects of decoherence on the walker(s). Finally, the simulator can be used to investigate the dynamic Anderson-like particle localization by varying the coin operators of certain nodes on the line/lattice. We also present some illustrative and relevant examples of one- and two-particle quantum walks in various scenarios. The tool was implemented in C and is available on-line at http://qwsim.weebly.com/ .
Abstract Quantum walks represent paradigmatic quantum evolutions, enabling powerful applications in the context of topological physics and quantum computation. They have been implemented in diverse photonic architectures, but the realization of two-particle dynamics on a multidimensional lattice has hitherto been limited to continuous-time evolutions. To fully exploit the computational capabilities of quantum interference it is crucial to develop platforms handling multiple photons that propagate across multidimensional lattices. Here, we report a discrete-time quantum walk of two correlated photons in a two-dimensional lattice, synthetically engineered by manipulating a set of optical modes carrying quantized amounts of transverse momentum. Mode-couplings are introduced via the polarization-controlled diffractive action of thin geometric-phase optical elements. The entire platform is compact, efficient, scalable, and represents a versatile tool to simulate quantum evolutions on complex lattices. We expect that it will have a strong impact on diverse fields such as quantum state engineering, topological quantum photonics, and Boson Sampling.