Quantum Walks Research Articles

Parrondo's effect in continuous-time quantum walks

Parrondo's effect in continuous-time quantum walks

Cooperative bound states in quantum walks of interacting particles

Although multiparticle quantum walks have been claimed to be universal for quantum computing, fundamental issues still need further understanding, such as the formation of bound states and their role in particle dynamics. By considering the framework of two-particle quantum walks, we study particles with short- or long-range interactions between them and observe the emergence of local and non-local bound states associated with these interactions. We show that such bound states can perform competitive and cooperative influence with existing states, sometimes resulting in unusual dynamics. In addition to revealing the optimal scenarios for particles to perform coherent dynamics, we also show that cooperative scenarios between bound states are responsible for robustly correlated quantum walks. Thus, coherent dynamics of particles can be maintained even for strong interaction strengths, avoiding the nonmonotonic behavior exhibited by systems with only on-site interaction.

Efficient learning of mixed-state tomography for photonic quantum walk.

Noise-enhanced applications in open quantum walk (QW) has recently seen a surge due to their ability to improve performance. However, verifying the success of open QW is challenging, as mixed-state tomography is a resource-intensive process, and implementing all required measurements is almost impossible due to various physical constraints. To address this challenge, we present a neural-network-based method for reconstructing mixed states with a high fidelity (∼97.5%) while costing only 50% of the number of measurements typically required for open discrete-time QW in one dimension. Our method uses a neural density operator that models the system and environment, followed by a generalized natural gradient descent procedure that significantly speeds up the training process. Moreover, we introduce a compact interferometric measurement device, improving the scalability of our photonic QW setup that enables experimental learning of mixed states. Our results demonstrate that highly expressive neural networks can serve as powerful alternatives to traditional state tomography.

Mobility edges and localization characteristics in one-dimensional quasiperiodic quantum walk

Abstract We construct a one-dimensional quasiperiodic quantum walk to investigate the localization–delocalization transition. The inverse participation ratio and Lyapunov exponent are employed as two indexes to determine the mobility edge, a critical energy to distinguish the energy regions of extended and localized states. The analytical solution of mobility edge is obtained by the Lyapunov exponents in global theory, and the consistency of the two indexes is confirmed. We further study the dynamic characteristics of the quantum walk and show that the probabilities are localized to some specific lattice sites with time evolution. This phenomenon is explained by the effective potential of the Hamiltonian which corresponds to the phase in the coin operator of the quantum walk.

Experimental Proposal on Non-Hermitian Skin Effect by Two-dimensional Quantum Walk with a Single Trapped Ion

Non-Hermitian Hamiltonians are widely used in describing open systems with gain and loss, among which a key phenomenon is the non-Hermitian skin effect. Here we report an experimental scheme to realize a two-dimensional (2D) discrete-time quantum walk with non-Hermitian skin effect in a single trapped ion. It is shown that the coin and 2D walker states can be labeled in the spin of the ion and the coherent-state lattice of the ion motion, respectively. We numerically observe a directional bulk flow, whose orientations are controlled by dissipative parameters, showing the emergence of the non-Hermitian skin effect. We then discuss an experimental implementation of our scheme in a laser-controlled trapped Ca+ ion. Our experimental proposal may be applicable to research of dissipative quantum walk systems and may be able to generalize to other platforms, such as superconducting circuits and atoms in cavity.

Remote State Preparation of qubits Using Quantum Walks in the Presence of Controller

Remote State Preparation of qubits Using Quantum Walks in the Presence of Controller

High-fidelity state transfer via quantum walks from delocalized states

High-fidelity state transfer via quantum walks from delocalized states

Quantum hash function based on continuous quantum walks

A method of constructing a quantum hash function (QHF) based on continuous-time quantum walk is proposed, in which the time of quantum walk is controlled by the binary string message, namely, a binary string message as the input of the constructed QHF and the probability value of finally walking to the nodes on the cycle is used as the output of the QHF. Numerical simulation and performance analysis show that our QHF has obvious advantages in the efficiency of the QHF compared with the existing QHF based on the discrete-time quantum walk, that is, the efficiency of our scheme is nearly 4 times faster in computing the hash value of the same size file compared with the most efficient scheme. Besides, the QHF has also better collision resistance compared with the existing QHF based on the discrete-time quantum walk.

Strongly interacting photonic quantum walk using single atom beamsplitters

Photonics provide an efficient way to implement quantum walks, the quantum analog of classical random walks, which demonstrate rich physics with potential applications. However, most photonic quantum walks do not involve photon interactions, which limits their potential to explore strongly correlated many-body physics of light. We propose a strongly interacting discrete-time photonic quantum walk using a network of single atom beamsplitters. We calculate output statistics of the quantum walk for the case of two photons, which reveals the strongly correlated transport of photons. Particularly, the walk can exhibit either bosonlike or fermionlike statistics which is tunable by postselecting the two-photon detection time interval. Also, the walk can sort different types of two-photon bound states into distinct pairs of output ports under certain conditions. These unique phenomena show that our quantum walk is an intriguing platform to explore strongly correlated quantum many-body states of light. Finally, we propose an experimental realization based on time-multiplexed synthetic dimensions. Published by the American Physical Society 2024

Continuous-time open quantum walks in one dimension: matrix-valued orthogonal polynomials and Lindblad generators

Continuous-time open quantum walks in one dimension: matrix-valued orthogonal polynomials and Lindblad generators

Experimental realization of quantum walks near synthetic horizons on photonic lattices

Entanglement plays crucial roles in quantum optics, providing a prerequisite for these recent unprecedented leaps. Nevertheless, the study of quantum entanglement under the influence of relativity, an important ingredient of quantum optics, still needs to be explored. In parallel, integrated photonic chips, particularly those with the aid of transformation optics, have simulated various relativity phenomena including gravitational lensing and Unruh radiation. However, thus far, studying relativistic quantum optics on this type of platform has not yet occurred. Here, we propose and experimentally realize quantum walks of entangled photons near an emulated Rindler horizon. Remarkably, we find that quantum interference near the synthetic horizon leads to a counterintuitive phenomenon of optical escape. Our study paves the way to a tabletop platform for studying quantum phenomena in various relativistic space-time metrics, and may bring an implication for the test of quantum theory in relativity. Published by the American Physical Society 2024

Color image encryption algorithm based on Mackey–Glass time-delay chaotic system and quantum random walk

To ensure the confidentiality and integrity of image data and prevent unauthorized data tampering and privacy leaks. This study proposes a new color image encryption scheme based on the Mackey–Glass time-delay chaotic system and quantum random walk. This approach fully leverages the unpredictability of quantum random walks to generate random values. It combines the differences in Hamming distance between the three RGB channels of color images to create a highly complex and random key. The overall image and the three independent RGB channels are arranged in ascending order using Logistic-tent chaotic mapping and the Mackey–Glass time-delay chaotic system to obfuscate the image data. The deformed fractional-order Lorenz chaotic system is introduced, integrated with DNA encoding and decoding technology, and XOR operations are performed to achieve encryption at the spatial and pixel levels, thereby increasing the complexity of decryption. Through extensive experimental research, this solution has demonstrated excellent results in tests such as adjacent pixel correlation, information entropy, and key sensitivity. It has an excellent ability to protect the privacy of images and provides a reliable guarantee for the security of image data.

Cycle discrete-time quantum walks on a noisy quantum computer

The rapid development of quantum computing has led to increasing interest in quantum algorithms for a variety of different applications. Quantum walks have also experienced a surge in interest due to their potential use in quantum algorithms. Using the qiskit software package, we test how accurately the current generation of quantum computers provided by IBM can simulate a cycle discrete-time quantum walk. Implementing an 8-node, 8-step walk and a simpler 4-node, 4-step discrete-time quantum walk on an IBM quantum device known as ibmq_quito, the results for each step of the respective walks are presented. A custom noise model is developed in order to estimate that noise levels in the ibmq_santiago quantum device would need to be reduced by at least 94% in order to execute a 16-node, 16-step cycle discrete-time quantum walk to a reasonable level of fidelity.Graphic abstract

Identifying network topologies via quantum walk distributions

Control and characterization of networks are paramount steps in the development of many quantum technologies. Even for moderate-sized networks, this amounts to exploring an extremely vast parameter space in search for the couplings defining the network topology. Here, we explore the use of a genetic algorithm to retrieve the topology of a network from the measured probability distribution obtained from the evolution of a continuous-time quantum walk on the network. We show that we can successfully retrieve the topology of different networks with efficiencies above 70% in all the examined scenarios and that the algorithm is capable of efficiently retrieving the required information even in the presence of noise.

Quantum transport on multilayer generalized scale-free networks

Abstract We study single-particle quantum transport on multilayer generalized scale-free networks using the continuous-time quantum walk model. Our focus is directed at the average return probability and its long-time average value as measures for the transport efficiency. In the continuous-time model these quantities are completely determined by all the eigenvalues and eigenvectors of the connectivity matrix. For all multilayer networks a nontrivial interplay between good spreading and localization effects is observed. The spreading is enhanced by increasing the number of layers L or the power-law exponent γ of the degree distribution. For our choice of the parameters, namely L (1 ≤ L ≤ 50) or γ (1 ≤ γ ≤ 4), the quantum efficiency is increased by at least one order of magnitude. The topological transition between networks without loops, which corresponds to a single scale-free network layer (L = 1), and networks with loops (L = 2) is the most impactful. Another important change occurs when L gets higher than the average diameter d of the layers, namely a new scaling behavior for random walks and lower fluctuations around the long-time average value for quantum walks. The quantum transport is more sensitive to changes of the minimum allowed degree, K min, than to the maximum allowed degree, K max. The same quantum efficiency is found by varying at least one of the parameters: L, γ, K min, or K max, although the network’s topology is different. The quantum efficiency of all multilayer scale-free networks shows a universal behavior for any size of the layers, more precise, is inversely proportional to the number of layers.

Experimental implementation of quantum-walk-based portfolio optimization

The application of quantum algorithms has attracted much attention as it holds the promise of solving practical problems that are intractable to classical algorithms. One such application is the recent development of a quantum-walk-based optimization algorithm approach to portfolio optimization under the modern portfolio theory framework. In this paper, we demonstrate an experimental realization of the alternating phase-shift and continuous-time quantum walk unitaries that underpin this quantum algorithm using optical networks and single photons. The experimental analysis confirms that the probability of states corresponding to high-quality solutions is efficiently amplified by increasing the number of phase-shift and quantum walk iterations. This work provides strong evidence for practical applications of quantum-walk-based algorithms such as financial portfolio optimization.

Probing fractal spatiotemporal inhomogeneity in a quantum walk

We investigate the transport and entanglement properties exhibited by quantum walks with coin operators concatenated in a space-time fractal structure. Inspired by recent developments in photonics, we choose the paradigmatic Sierpinski gasket. The 0-1 pattern of the fractal is mapped into an alternation of the generalized Hadamard-Fourier operators. This two-state coin-operator approach overcomes the intricacies caused by the utilization of high-dimensional coin operators required in prior studies of discrete-time quantum walks on fractals. In fulfilling the blank space on the analysis of the impact of inhomogeneity in quantum walk properties, specifically, fractal deterministic inhomogeneity, our results show a robust effect of entanglement enhancement as well as an interesting road to superdiffusive spreading with a tunable scaling exponent attaining robust superdiffusion, subballistic though. Explicitly, with this fractal approach it is possible to obtain an increase in quantum entanglement with reduced impact on standard quantum walk theoretical spreading. Alongside those features, we analyze further properties such as the degree of interference and visibility. The present model corresponds to an application of fractals in an experimentally viable setting, namely, the building block for the construction of photonic patterned structures. Published by the American Physical Society 2024

Perfect state transfer, equitable partition and continuous-time quantum walk based search

Perfect state transfer, equitable partition and continuous-time quantum walk based search

Continuous-time quantum walks for MAX-CUT are hot

By exploiting the link between time-independent Hamiltonians and thermalisation, heuristic predictions on the performance of continuous-time quantum walks for MAX-CUT are made. The resulting predictions depend on the number of triangles in the underlying MAX-CUT graph. We extend these results to the time-dependent setting with multi-stage quantum walks and Floquet systems. The approach followed here provides a novel way of understanding the role of unitary dynamics in tackling combinatorial optimisation problems with continuous-time quantum algorithms.

Discrete-Time Quantum Walks Community Detection in Multi-Domain Networks

Abstract The problem of detecting communities in real-world networks has been extensively studied in the past, but most of the existing approaches work on single-domain networks, i.e. they consider only one type of relationship between nodes. Single-domain networks may contain noisy edges and they may lack some important information. Thus, some authors have proposed to consider the multiple relationships that connect the nodes of a network, thus obtaining multi-domain networks. However, most community detection approaches are limited to multi-layer networks, i.e. networks generated from the superposition of several single-domain networks (called layers) that are regarded as independent of each other. In addition to being computationally expensive, multi-layer approaches might yield inaccurate results because they ignore potential dependencies between layers. This paper proposes a multi-domain discrete-time quantum walks (MDQW) model for multi-domain networks. First, the walking space of network nodes in multi-domain network is constructed. Second, the quantum permutation circuit of the coin state is designed based on the coded particle state. Then, using different coin states, the shift operator performs several quantum walks on the particles. Finally, the corresponding update rule is selected to move the node according to the measurement result of the quantum state. With continuous update iteration, the shift operator automatically optimizes the discovered community structure. We experimentally compared our MDQW method with four state-of-the-art competitors on five real datasets. We used the normalized mutual information (NMI) to compare clustering quality, and we report an increase in NMI of up to 3.51 of our MDQW method in comparison with the second-best performing competitor. The MDQW method is much faster than its competitors, allowing us to conclude that MDQW is a useful tool in the analysis of large real-life multi-domain networks. Finally, we illustrate the usefulness of our approach on two real-world case studies.