We theoretically analyze the dynamical evolution of photonic quantum walks on M\"obius strips and other exotic structures in three-dimensional integrated photonics. Our flexible design allows discrete observations of continuous-time quantum walks of photons in a variety of waveguide arrays. Furthermore, our design allows one to inject photons during the evolution, allowing the possibility of interacting with the photons as they are ``walking.'' We find that nontrivial array topologies introduce time-dependent symmetries of the two-photon correlations. These properties allow a large degree of control for quantum state engineering of multimode entangled states in these devices.
We theoretically analyze the dynamical evolution of photonic quantum walks on M"obius strips and other exotic structures in three-dimensional integrated photonics. Our flexible design allows discrete observations of continuous-time quantum walks of photons in a variety of waveguide arrays. Furthermore, our design allows one to inject photons during the evolution, allowing the possibility of interacting with the photons as they are ``walking.'' We find that nontrivial array topologies introduce time-dependent symmetries of the two-photon correlations. These properties allow a large degree of control for quantum state engineering of multimode entangled states in these devices.
Unlike discrete photonic circuits, which manipulate photons step-by-step using a series of optical elements, arrays of coupled waveguides enable photons to interfere continuously across the entire structure. When composed of a nonlinear material, such arrays can also directly generate quantum states of light within the circuit. To clarify the similarities and distinctions between these two approaches of quantum walks, we conduct here a systematic comparison between linear waveguide arrays, injected with photons produced externally, and nonlinear arrays, where photon pairs are continuously generated via parametric down-conversion. We experimentally validate these predictions using III-V semiconductor nonlinear waveguide lattices with varied geometries, enabling us to tune the depth of the quantum walks over an order of magnitude and reveal the gradual emergence of non-classicality in the output state. Finally, we demonstrate an inverse-design approach to engineer \textit{aperiodic} waveguide arrays, whose optimized coupling profiles generate maximally entangled states such as the biphoton W-state. These results highlight the potential of continuously-coupled photonic systems to harness high-dimensional entanglement within compact architectures.
Integrated optics provides an ideal testbed for the emulation of quantum systems via continuous-time quantum walks. Here, we study the evolution of two-photon states in an elliptic array of waveguides. We characterize the photonic chip via coherent light tomography and use the results to predict distinct differences between temporally indistinguishable and distinguishable two-photon inputs, which we then compare with experimental observations. This work highlights the feasibility of emulation of coherent quantum phenomena in three-dimensional waveguide structures.
Quantum walks, in virtue of the coherent superposition and quantum interference, have exponential superiority over their classical counterpart in applications of quantum searching and quantum simulation. The quantum-enhanced power is highly related to the state space of quantum walks, which can be expanded by enlarging the photon number and/or the dimensions of the evolution network, but the former is considerably challenging due to probabilistic generation of single photons and multiplicative loss. We demonstrate a two-dimensional continuous-time quantum walk by using the external geometry of photonic waveguide arrays, rather than the inner degree of freedoms of photons. Using femtosecond laser direct writing, we construct a large-scale three-dimensional structure that forms a two-dimensional lattice with up to 49 × 49 nodes on a photonic chip. We demonstrate spatial two-dimensional quantum walks using heralded single photons and single photon-level imaging. We analyze the quantum transport properties via observing the ballistic evolution pattern and the variance profile, which agree well with simulation results. We further reveal the transient nature that is the unique feature for quantum walks of beyond one dimension. An architecture that allows a quantum walk to freely evolve in all directions and at a large scale, combining with defect and disorder control, may bring up powerful and versatile quantum walk machines for classically intractable problems.
Abstract Over the last 20 years quantum walks (QWs) have gained increasing interest in the field of quantum information science and processing. In contrast to classical walkers, quantum objects exhibit intrinsic properties like non-locality and non-classical many-particle correlations, which renders QWs a versatile tool for quantum simulation and computation as well as for a deeper understanding of genuine quantum mechanics. Since they are highly controllable and hardly interact with their environment, photons seem to be ideally suited quantum walkers. In order to study and exploit photonic QWs, lattice structures that allow low loss coherent evolution of quantum states are demanded. Such requirements are perfectly met by integrated optical waveguide devices that additionally allow a substantial miniaturization of experimental settings. Moreover, by utilizing the femtosecond direct laser writing technique three-dimensional waveguide structures are capable of analyzing QWs also on higher dimensional geometries. In this context, advances and findings of photonic QWs are discussed in this review. Various concepts and experimental results are presented covering, such as different quantum transport regimes, the Boson sampling problem, and the discrete fractional quantum Fourier transform.
In recent years, quantum walks have been proposed as promising resources for the simulation of physical quantum systems. In fact it is widely adopted to simulate quantum dynamics. Up to now single particle quantum walks have been experimentally demonstrated by different approaches, while only few experiments involving many-particle quantum walks have been realized. Here we simulate the 2-particle dynamics on a discrete time quantum walk, built on an array of integrated waveguide beam splitters. The polarization independence of the quantum walk circuit allowed us to exploit the polarization entanglement to encode the symmetry of the two-photon wavefunction, thus the bunching-antibunching behavior of non interacting bosons and fermions has been simulated. We have also characterized the possible distinguishability and decoherence effects arising in such a structure. This study is necessary in view of the realization of a quantum simulator based on an integrated optical array built on a large number of beam splitters.
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.