We analyze the process of a discrete-time quantum walk over 4 steps and 5 positions with linear optics elements. The quantum walk is characterized by a ballistic spread of wavepackets along 4 steps. By employing different initial coin states, we observe non-Gaussian distribution of the walkers' finial position, which characterizes a quadratic enhancement of the spread of photon wavepackets compared to a classical random walk. By introducing controllable decoherence, we observe the quantum-to-classical transmission in a quantum walk architecture.
We experimentally implement a quantum walk on a circle in position space. Using a different arrangement of linear optical elements, our experiment realizes clockwise-cycling and counterclockwise-cycling walks. Periodic evolutions in quantum walks on three- and four-node circles with uniform coin flipping for each step and a localized initial walker state are observed, and the full revival of the walker+coin state occurs. Coherent information encoded in the coin state shows the periodic collapse and revival due to the interaction between the coin and walker. The technology to realize clockwise-cycling and counterclockwise-cycling walks can be expanded to simulate a quantum walk on a circle with arbitrary nodes.
Abstract We demonstrate a platform for implementing quantum walks that overcomes many of the barriers associated with photonic implementations. We use coupled fiber-optic cavities to implement time-bin encoded walks in an integrated system. We show that this platform can achieve very low losses combined with high-fidelity operations, enabling an unprecedented large number of steps in a passive system, as required for scenarios with multiple walkers. Furthermore the platform is reconfigurable, enabling variation of the coin, and readily extends to multidimensional lattices. We demonstrate variation of the coin bias experimentally for three different values.
We present an optical module to simulate one step of a quantum walk algorithm. The quantum state of a system with a
2N-dimensional Hilbert space is encoded in the spatial distribution of the amplitude of the electromagnetic field in a plane. In such spatial encoding, the probability amplitude of each state of a basis is associated with the complex electromagnetic amplitude in a given slice of the laser wave front. We discuss the design and operation of an optical module that is used to implement one step of a quantum walk algorithm. Using this module, composed by standard optical elements, the evolution of the quantum state corresponds to the application of a Hadamard gate on a single qubit (representing the two-dimensional quantum coin) followed by a displacement of the
N-dimensional quantum walker conditioned on the state of the coin. We show the actual implementation of the method and discuss its characteristics and limitations.
Discrete-time quantum walks are powerful platforms for simulating quantum transport and information processing. Here we introduce a walker on a one-dimensional lattice whose motion is controlled by three entangled coins, each initialized with the Hadamard gate, aiming to maximize information flow. The walker moves only when all three coins yield the same outcome (HHH or TTT), thus coupling the 8-dimensional coin Hilbert space to the position degree of freedom. By analyzing fully separable, fully entangled (GHZ-type) and intermediate initial states, and using the von Neumann entropy of reduced subsystems, we compute the mutual information
I(C;P;t) between coin and position. The results show that initial three-partite entanglement accelerates the growth of mutual information by up to 18\% after ten steps (when compared to the lower of the two separable states), although it exhibits short-term non-monotonic dynamics due to quantum interference. For the first time, we introduce a tunable parameter
α (amplitude of non-displacement states) and show that the GHZ state reaches a maximum of mutual information at
α≈0.71 - a key finding for optimal control of information flow. Finally, an integrated photonic implementation using polarization, spatial modes and time bins is proposed, where
α can be tuned with nonlinear or electro-optic elements. A scalable numerical framework (Python code) for simulations up to
t=5 steps is provided. Our findings establish three-partite entanglement as a dynamical resource for maximizing information flow and spatial spreading, with direct applications in quantum state transfer, entanglement-assisted sensing and programmable photonic quantum processors.
Quantum walks can be used either as tools for quantum algorithm development or as entanglement generators, potentially useful to test quantum hardware. We present a novel algorithm based on a discrete Hadamard quantum walk on a line with one coin and two walkers whose purpose is to generate entanglement between walkers. We provide several classical computer simulations of our quantum algorithm in which we show that, although the asymptotical amount of entanglement generated between walkers does not reach the highest degree of entanglement possible at each step for either coin measurement outcome, the entanglement ratio (entanglement generated/highest value of entanglement possible, for each step) tends to converge, and the actual convergence value depends on the coin initial state and on the coin measurement outcome. Furthermore, our numerical simulations show that, for the quantum walks used in our algorithm, the value towards which entanglement ratio converges also depends on the position probability distribution symmetry of a quantum walk computed with one single walker and the same coin initial state employed in the corresponding quantum walk with two walkers.