Quantum Walks Research Articles

A Dynamic Image Encryption Scheme Based on Quantum Walk and Chaos-Induced DNA

The development of quantum information technology and increasing attention of people to the secure transmission of image information in the Internet have put forward higher requirements for traditional image encryption algorithms that not only take advantage of the exponential acceleration ability of quantum computing compared with classical computing but also reduce the risk of encryption algorithms being cracked. Therefore, in order to seek the combination of the advantages of quantum computing and classical image encryption algorithms, this paper proposes a new dynamic encryption image scheme of quantum walk and chaos-induced DNA. Firstly, the RGB three-channel pixels of the color image are extracted and combined into a one-dimensional array, and a random sequence is generated by quantum walk to reorder it to obtain a preliminary scrambled image; secondly, the color image is processed by the SHA-256 algorithm and divided into the generated message digest as the initial condition of the chaotic model. The random sequence was generated by the high-dimensional chaotic model which encodes each pixel independently and disorderly as DNA bases. The difference of the chaotic sequence ensures the dynamic selection of random DNA encoding and decoding rules during encryption. At the same time, the number of times of DNA encryption of the encoded pixel value is also controlled by the dynamic induction of the chaotic sequence, and ultimately, the DNA coding sequence is replaced with the decimal pixel value to obtain the encrypted image. The simulation results show that the information entropy of the encrypted image is above 7.99, and the correlation of each channel is close to 0, which can effectively resist brute force attacks, plaintext attacks, statistical analysis attacks, noise attacks, etc. In addition, in this paper, extracting the watermark embedded in the encrypted image to judge whether image information is tampered or forged further improves the security of the image information.

Speed-up and suppression effect of side chain in quantum searching on a graph

Searching efficiency, which biologists and roboticists are ever concerned about, has become important in physics and information science nowadays. In classical probability-based searching problems, as stigmergy, the increase in graph complexity will decrease the searching efficiency. Here we study the searching efficiency based on the first-passage probability and find a counterintuitive phenomenon in quantum walk on a graph with floating vertices. Connecting one vertex in the floating layer to that in the base layer will speed up the searching rapidity, but such a speed-up effect will be suppressed at once if one more vertex is connected to the already connected vertex in the floating layer. This is a counterintuitive phenomenon in comparison to its classical counterpart, where additional vertices at the side chain will retard the searching rapidity. We also propose an ancillary model that bridges the measurement of the probability and the first-passage probability, which is expected to provide new ideas for quantum simulation by means of qubit chips.

Quantum walker in presence of a moving detector

Quantum walker in presence of a moving detector

A new definition of hitting time and an embedded Markov chain in continuous-time quantum walks

A new definition of hitting time and an embedded Markov chain in continuous-time quantum walks

Bandit Algorithm Driven by a Classical Random Walk and a Quantum Walk.

Quantum walks (QWs) have a property that classical random walks (RWs) do not possess-the coexistence of linear spreading and localization-and this property is utilized to implement various kinds of applications. This paper proposes RW- and QW-based algorithms for multi-armed-bandit (MAB) problems. We show that, under some settings, the QW-based model realizes higher performance than the corresponding RW-based one by associating the two operations that make MAB problems difficult-exploration and exploitation-with these two behaviors of QWs.

Many topological regions on the Bloch sphere of the spin-1/2 double-kicked top

Floquet topological systems have been shown to exhibit features not commonly found in conventional topological systems such as topological phases characterized by arbitrarily large winding numbers. This is clearly highlighted in the quantum double kicked rotor coupled to spin-1/2 degrees of freedom [Phys. Rev. A 97, 063603 (2018)] where large winding numbers are achieved by tuning the kick strengths. Here, we extend the results to the spin-1/2 quantum double kicked top and find not only does the system exhibit topological regions with large winding numbers, but a large number of them are needed to fully characterize the topology of the Bloch sphere of the top for general kick strengths. Due to the geometry of the Bloch sphere it is partitioned into regions with different topology and the boundaries separating them are home to 0 and $\ensuremath{\pi}$ quasienergy bound states. We characterize the regions by comparing local versions of the mean field, quantum, and mean chiral displacement winding numbers. We also use a probe state to locate the boundaries by observing localization as the state evolves when it has a large initial overlap with bound states. Finally, we briefly discuss the connections between the spin-1/2 quantum double kicked top and multistep quantum walks, putting the system in the context of some current experiments in the exploration of topological phases.

Combinatorial necessary conditions for regular graphs to induce periodic quantum walks

We derive combinatorial necessary conditions for discrete-time quantum walks defined by regular mixed graphs to be periodic. One useful necessary condition is that if a k-regular mixed graph with n vertices is periodic, then 2n/k must be an integer. As an application of this work, we determine periodicity of mixed complete graphs and mixed graphs with a prime number of vertices. Furthermore, we study periodicity of mixed strongly regular graphs and several classes of mixed distance-regular graphs, and extend existing results to mixed graphs.

Application of quantum computing in discrete portfolio optimization

This study proposes a novel and more efficient quantum algorithm for portfolio optimization using quantum combinatorial optimization (QCO) techniques. A recent construction developed in 2021 has sparked the field of financial portfolio optimization through the Quantum Walk Optimization Algorithm (QWOA). In this study, we investigated the complexity and efficiency of quantum optimization algorithms with a special interest in QWOA. The objective is to minimize investment risk by having a good combination of assets in the portfolio. We also focused on reducing the number of iterations while attaining a high-quality resolution through contraction of the solution space to ease computations. The concept of QWOA was extended by constructing a newly outperforming scheme known as the “Quantum Mix Optimization Algorithm (QMOA).” QMOA algorithm codes were provided for the implementation and simulation of numerical results. In addition, the efficiency of QMOA, which is better than the existing QCO algorithms, was discussed. For instance, the least QWOA number of computations required to execute the initial state equation was p > 2, whereas this value was p ≥ 2 in the proposed QMOA.

Swift chiral quantum walks

A continuous-time quantum walk (CTQW) is sedentary if the return probability in the starting vertex is close to one at all times. Recent results imply that, when starting from a maximal degree vertex, the CTQW dynamics generated by the Laplacian and adjacency matrices are typically sedentary. In this paper, we show that the addition of appropriate complex phases to the edges of the graph, defining a chiral CTQW, can cure sedentarity and lead to swift chiral quantum walks of the adjacency type, which bring the return probability to zero in the shortest time possible. We also provide a no-go theorem for swift chiral CTQWs of the Laplacian type. Our results provide one of the first, general characterization of tasks that can and cannot be achieved with chiral CTQWs.

Reconfigurable refraction manipulation at synthetic temporal interfaces with scalar and vector gauge potentials

Photonic gauge potentials, including scalar and vector ones, play fundamental roles in emulating photonic topological effects and for enabling intriguing light transport dynamics. While previous studies mainly focus on manipulating light propagation in uniformly distributed gauge potentials, here we create a series of gauge-potential interfaces with different orientations in a nonuniform discrete-time quantum walk and demonstrate various reconfigurable temporal-refraction effects. We show that for a lattice-site interface with the potential step along the lattice direction, the scalar potentials can yield total internal reflection (TIR) or Klein tunneling, while vector potentials manifest direction-invariant refractions. We also reveal the existence of penetration depth for the temporal TIR by demonstrating frustrated TIR with a double lattice-site interface structure. By contrast, for an interface emerging in the time-evolution direction, the scalar potentials have no effect on the packet propagation, while the vector potentials can enable birefringence, through which we further create a "temporal superlens" to achieve time-reversal operations. Finally, we experimentally demonstrate electric and magnetic Aharonov-Bohm effects using combined lattice-site and evolution-step interfaces of either scalar or vector potential. Our work initiates the creation of artificial heterointerfaces in synthetic time dimension by employing nonuniformly and reconfigurable distributed gauge potentials. This paradigm may find applications in optical pulse reshaping, fiber-optic communications, and quantum simulations.

Monitored recurrence of a one-parameter family of three-state quantum walks

Monitored recurrence of a one-parameter set of three-state quantum walks on a line is investigated. The calculations are considerably simplified by choosing a suitable basis of the coin space. We show that the Polya number (i.e. the site recurrence probability) depends on the coin parameter and the probability that the walker is initially in a particular coin state for which the walk returns to the origin with certainty. Finally, we present a brief investigation of the exact quantum state recurrence.

Quantum walks in an inhomogeneous off-diagonal Aubry-André-Harper model

Quantum walks in an inhomogeneous off-diagonal Aubry-André-Harper model

Demonstration of a photonic router via quantum walks

Motivated by the need for quantum computers to communicate between multiple, well separated qubits, we introduce the task of routing the quantum state from one input mode to a superposition of several output modes coherently. We report an experimental demonstration of a deterministic photonic routing protocol applied to an entangled state. We show in a quantum walk architecture, quantum networks perfectly route entangled states from an initial input mode to an arbitrary output mode coherently and deterministically. Our results demonstrate the key principle of a perfect router, opening a route toward data routing and transferring for quantum computing systems. The routing algorithm in our work can be applied to a wide range of physical systems, which provides a way for effective design of efficient routing protocols on practical quantum networks.

Twisted quantum walks, generalised Dirac equation and Fermion doubling

Quantum discrete-time walkers have, since their introduction, demonstrated applications in algorithmic and in modeling and simulating a wide range of transport phenomena. They have long been considered the discrete-time and discrete space analogue of the Dirac equation and have been used as a primitive to simulate quantum field theories precisely because of some of their internal symmetries. In this paper we introduce a new family of quantum walks, said twisted, which admits, as continuous limit, a generalized Dirac operator equipped with a dispersion term. Moreover, this quadratic term in the energy spectrum acts as an effective mass, leading to a regularization of the well known Fermion doubling problem.

Site recurrence for continuous-time open quantum walks on the line

In recent years, several properties and recurrence criteria of discrete-time open quantum walks (OQWs) have been presented. Recently, Pellegrini introduced continuous-time open quantum walks (CTOQWs) as continuous-time natural limits of discrete-time OQWs. In this work, we study semifinite CTOQWs and some of their basic properties concerning statistics, such as transition probabilities and site recurrence. The notion of SJK-recurrence for CTOQWs is introduced, and it is shown to be equivalent to the traditional concept of recurrence. This statistic arises from the definition of $\delta$-skeleton of CTOQWs, which is a dynamic that allows us to obtain a discrete-time OQW in terms of a CTOQW. We present a complete criterion for site recurrence in the case of CTOQW induced by a coin of finite dimension with a set of vertices $\mathbb{Z}$ such that its auxiliary Lindblad operator has a single stationary state. Finally, we present a similar criterion that completes the case in which the internal degree of freedom of each site is of dimension 2.

Multi Watermarking for Medical Images using Fractal Encoding and Concept of UNET

Abstract: The Internet of Medical Things, smart healthcare systems are becoming ubiquitous in our daily lives. Patients, doctors, and other medical personnel rely on the safe and efficient storage, transmission, and analysis of electronic health records , medical images such as scanning reports X-rays for successful treatment and management of different ailments. A Multi watermarking method is proposed for medical images based on quantum random walk and optimization algorithm. A logo image is used to verifying medical image integrity is embedding in region of interest and text data are embedded in the region of non interest to conceal private hospital and patient informations. This method improves the authenticity and integrity of medical images. A number of experiments are conducted to validate the security ,robustness and capacity of the proposed multi watermarking scheme.

Link Prediction with Continuous-Time Classical and Quantum Walks.

Protein-protein interaction (PPI) networks consist of the physical and/or functional interactions between the proteins of an organism, and they form the basis for the field of network medicine. Since the biophysical and high-throughput methods used to form PPI networks are expensive, time-consuming, and often contain inaccuracies, the resulting networks are usually incomplete. In order to infer missing interactions in these networks, we propose a novel class of link prediction methods based on continuous-time classical and quantum walks. In the case of quantum walks, we examine the usage of both the network adjacency and Laplacian matrices for specifying the walk dynamics. We define a score function based on the corresponding transition probabilities and perform tests on six real-world PPI datasets. Our results show that continuous-time classical random walks and quantum walks using the network adjacency matrix can successfully predict missing protein-protein interactions, with performance rivalling the state-of-the-art.

Anderson localization without eigenstates in photonic quantum walks.

Anderson localization is ubiquitous in wavy systems with strong static and uncorrelated disorder. The delicate destructive interference underlying Anderson localization is usually washed out in the presence of temporal fluctuations or aperiodic drives in the Hamiltonian, leading to delocalization and restoring transport. However, in one-dimensional lattices with off diagonal disorder, Anderson localization can persist for arbitrary time-dependent drivings that do not break a hidden conservation law originating from the chiral symmetry, leading to the dubbed "localization without eigenstates." Here it is shown that such an intriguing phenomenon can be observed in discrete-time photonic quantum walks with static disorder applied to the coin operator and can be extended to non-Hermitian dynamics as well.

Phase transitions in non-Hermitian superlattices

We investigate the energy spectral phase transitions arising in one-dimensional superlattices under an imaginary gauge field and possessing $M$ sites in each unit cell in the large $M$ limit. It is shown that in models displaying nearly flat bands, a smooth phase transition, from quasi-entirely-real to complex energies, can be observed as the imaginary gauge field is increased, and that the phase transition becomes sharper and sharper (exact) as $M$ is increased. In this limiting case, for superlattices with random or incommensurate disorder, the spectral phase transition corresponds to a localization-delocalization transition of the eigenfunctions within each unit cell, dubbed non-Hermitian delocalization transition and originally predicted by Hatano and Nelson [N. Hatano and D. R. Nelson, Phys. Rev. Lett. 77, 570 (1996)]. However, it is shown here that in superlattices without disorder, a spectral phase transition can be observed as well, which does not correspond to a non-Hermitian delocalization phase transition. The predicted phenomena could be observed in non-Hermitian photonic quantum walks, where synthetic superlattices with controllable $M$ and imaginary gauge fields can be realized with existing experimental apparatus.

Anomalous non-Hermitian dynamical phenomenon on the quantum circuit

The anomalous non-Hermitian dynamical phenomenon with the non-Hermitian skin effect (NHSE) attracts wide attention due to its novel physics and promising applications. Here, we propose a new type of non-unitary discrete-time quantum walk system demonstrating the NHSE and anomalous non-Hermitian dynamical phenomena, including the dynamical chiral phenomenon, the funneling phenomenon on the domain wall, and the anomalous reflection on the phase impurity. Furthermore, we design the quantum circuit experiments of these quantum walk systems and numerically simulate them with quantum noises to verify the robustness of the non-Hermitian dynamical phenomenon on the noisy intermediate-scale quantum (NISQ) devices. Our work paves the way for implementing the non-Hermitian dynamical phenomenon on the quantum circuit.