Mapping a quantum walk by tuning the coupling coefficient

Abstract

We present a method to map the evolution of photonic random walks that is compatible with nonclassical input light. Our approach leverages a newly developed flexible waveguide platform to tune the jumping rate between spatial modes, allowing the observation of a range of evolution times in a chip of fixed length. In a proof-of-principle demonstration we reconstruct the evolution of photons through a uniform array of coupled waveguides by monitoring the end-face alone. This approach enables direct observation of mode occupancy at arbitrary resolution, extending the utility of photonic random walks for quantum simulations and related applications.Quantum walks have been studied extensively in the context of quantum computing and simulation [1][2][3][4]. Systems built around a quantum walk have been proposed as physical simulators for a wide variety of quantum [5] and classical [6] phenomena. When random walks are leveraged for physical simulation the dynamics and evolution of the random walker as it traverses the graph are often of primary interest.In the experimental domain, quantum walks have been demonstrated across a range of physical systems, employing trapped particles [7-9] and photons [10][11][12][13][14][15]. The field of photonic quantum walks is particularly developed, owing to the ease of access to long coherence times and the ability to perform high fidelity manipulation of single particles using relatively low cost devices. Within this class, devices comprising waveguide arrays have proved popular due to their favourable scaling properties [16].When simulating a physical system, the evolution of the quantum walker is commonly inferred by monitoring fluorescence in the host device [11,[17][18][19]. Unfortunately, this signal is able to capture only the intensity of the propagating optical modes, and so is unsuitable for following the evolution of more complicated inputs, for example multi-photon entangled states. Systems which leverage these inputs are only able to obtain a snapshot of the random walk at a fixed propagation length corresponding to the output plane [20]. Even where the evolution of the walker is not of primary interest, access to this information may be desired as a diagnostic or calibration tool.We have designed and implemented an optical circuit in which the evolution of a photonic quantum walk can be observed in a chip of constant length. In our system, a sequence of observations at the end face combined with appropriate tuning of the device parameters exposes the evolution of the input state in a manner that is compatible with single photon intensities, and extensible to multiphoton states. We demonstrate this technique by implementing the well-studied [12] one dimensional, continuous-time random walk on a uniform graph.A continuous-time, discrete-space quantum walk on a one-dimensional graph comprising a set of vertices connected with edges (as depicted in Fig 1, middle row) can be realized physically by injecting photons into an array of identical, continuously coupled waveguides....

Compact Itinerant Microwave Photonics with Superconducting High-Kinetic Inductance Microstrips

“…Nevertheless, the result in Fig. 2(e) resembles numeric results for quantum walks [31], with consequent applications also for quantum photonics [32].…”

Compact itinerant microwave photonics with superconducting high-kinetic inductance microstrips

“…Similar theoretical considerations as for the double-line can be employed for the 7PMT. Besides the band structure and symmetry of the eigenmodes, our simulations (see appendix E) show that propagation through the waveguides resembles quantum walks observed in optical systems [47] with a diffraction pattern, related to the frequency-dependent transmission in figure 6(a).…”