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arXiv:2007.06554

Two-Dimensional Quantum Walk of Correlated Photons

Zhi‐Qiang Jiao, Jun Gao, Wenhao Zhou, Xiaowei Wang, Ruo-Jing Ren, Xiao-Yun Xu, Lu‐Feng Qiao, Xian‐Min Jin

Published Jul 13, 2020• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2007.06554

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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.
Quantum walks provide a speed-up in computational power for various quantum algorithms and serve as inspiration for the construction of complex graph representations. Many pioneering works have been dedicated to expanding the experimental state space and the complexity of graphs. However, these experiments are mostly limited to small experimental scale, which do not reach a many-body level and fail to reflect the multi-particle quantum interference effects among non-adjacent modes. Here, we present a quantum walk with three photons on a two-dimensional triangular lattice, which is mapped to a 19 × 19 × 19 high-dimensional state space and constructs a complex graph with 6859 nodes and 45,486 edges. By utilizing the statistical signatures of the output combinations and incorporating machine learning techniques, we successfully validate the nonclassical properties of the experiment. Our implementation provides a paradigm for exponentially expanding the state space and graph complexity of quantum walks, paving the way for surmounting the classical regime in large-scale quantum simulations.
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.
With photonics, the quantum computational advantage has been demonstrated on the task of boson sampling. Next, developing quantum-enhanced approaches for practical problems becomes one of the top priorities for photonic systems. Quantum walks are powerful kernels for developing new and useful quantum algorithms. Here we realize large-scale quantum walks using a fully programmable photonic quantum computing system. The system integrates a silicon quantum photonic chip, enabling the simulation of quantum walk dynamics on graphs with up to 400 vertices and possessing full programmability over quantum walk parameters, including the particle property, initial state, graph structure, and evolution time. In the 400-dimensional Hilbert space, the average fidelity of random entangled quantum states after the whole on-chip circuit evolution reaches as high as 94.29$\pm1.281.281.28\%$. With the system, we demonstrated exponentially faster hitting and quadratically faster mixing performance of quantum walks over classical random walks, achieving more than two orders of magnitude of enhancement in the experimental hitting efficiency and almost half of the reduction in the experimental evolution time for mixing. We utilize the system to implement a series of quantum applications, including measuring the centrality of scale-free networks, searching targets on Erdös-Rényi networks, distinguishing non-isomorphic graph pairs, and simulating the topological phase of higher-order topological insulators. Our work shows one feasible path for quantum photonics to address applications of practical interests in the near future.
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.
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.