Quantum walks of interacting fermions on a cycle graph

Melnikov, A. A.; Fedichkin, Leonid

doi:10.1038/srep34226

Cited by 38 publications

(27 citation statements)

References 55 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Unlike in classical (i.e. digital or non-quantum) walks, the state of a quantum walk is a coherent superposition of several positions (quantum superposition of quantum walks) 53 , but much like their classical (i.e. digital) equivalents, there are two categories of quantum walks: discrete-time quantum walks and continuous-time quantum walks 20 .…”

Section: Methodsmentioning

confidence: 99%

Quantum-inspired cascaded discrete-time quantum walks with induced chaotic dynamics and cryptographic applications

El‐Latif

Abd-El-Atty

Amin

et al. 2020

Sci Rep

120

View full text Add to dashboard Cite

Designing efficient and secure cryptosystems has been a preoccupation for many scientists and engineers for a long time wherein they use chaotic systems to design new cryptosystems. While one dimensional (1-D) chaotic maps possess powerful properties compared to higher dimension ones, they are vulnerable to various attacks due to their small key space, chaotic discontinuous ranges, and degradation in chaotic dynamical behaviours. Moreover, when simulated on a computer, every such chaotic system produces a periodic cycle. Meanwhile, quantum random walks exhibit the potential for deployment in efficient cryptosystem design, which makes it an excellent solution for this problem. In this context, we present a new method for constructing substitution boxes (S-boxes) based on cascaded quantum-inspired quantum walks and chaos inducement. the performance of the proposed S-box scheme is investigated via established S-box evaluation criterion and outcomes suggest that the constructed S-box has significant qualities for viable applications information security. Further, we present an efficient scheme for pseudo-random numbers generation (PRNG) whose sustainability over long periods remedies the periodicity problem associated with traditional cryptographic applications. Furthermore, by combining the two mechanisms, an atypical image encryption scheme is introduced. Simulation results and analysis validate that the proposed image encryption algorithm will offer gains in many cryptographic applications. Chaotic systems have attracted a great deal of attention across different scientific and engineering disciplines, especially in designing new cryptosystems and cryptanalysis. A chaotic system is an evolution map of a deterministic dynamical system that reconstructs the state of a system S 0 to a new state S 1 depending on the initial state of S 0 , a control parameter C, and time T 1. Chaotic maps exhibit the desired properties of ergodicity, unpredictability, and sensitivity to their control parameter(s) and initial value(s) that satisfy the requirements for cryptosystem confusion-diffusion properties 2-4. In fact, an inappropriate initial control parameter of a chaotic system can lead to non-chaotic behaviours, which implies the reduction in nonlinearity levels as well as circumvention of insecurity pitfalls 5,6. Currently, chaotic dynamical systems play a vital role in designing modern cryptographic applications, such as constructing S-boxes, generating pseudo-random numbers, designing image encryption algorithms and so on 7-16 , which are based on the unproven assumptions pertaining to computational complexity and that their constructions are based on mathematical models. However, with the development of quantum technologies, some of these traditional security mechanisms, and cryptographic applications may be effortlessly violated and abused 17-19. Among the computational models developed in quantum computation, quantum walks (QWs), which is a universal model of quantum computation that has been traditionally employed to de...

show abstract

Section: Methodsmentioning

confidence: 99%

Quantum-inspired cascaded discrete-time quantum walks with induced chaotic dynamics and cryptographic applications

El‐Latif

Abd-El-Atty

Amin

et al. 2020

Sci Rep

120

View full text Add to dashboard Cite

show abstract

“…The applications of quantum dots are plenty, from studying quantum phenomena observed in real systems [45][46][47] to micro-masers and light emitting diodes [48] to realizing quantum bits [49] to building quantum-dot-based single-photon sources [50,51]. Progress in quantum dots array sizes has been steady.…”

Section: Resultsmentioning

confidence: 99%

QFlow lite dataset: A machine-learning approach to the charge states in quantum dot experiments

Zwolak

Kalantre

et al. 2018

PLoS ONE

View full text Add to dashboard Cite

BackgroundOver the past decade, machine learning techniques have revolutionized how research and science are done, from designing new materials and predicting their properties to data mining and analysis to assisting drug discovery to advancing cybersecurity. Recently, we added to this list by showing how a machine learning algorithm (a so-called learner) combined with an optimization routine can assist experimental efforts in the realm of tuning semiconductor quantum dot (QD) devices. Among other applications, semiconductor quantum dots are a candidate system for building quantum computers. In order to employ QDs, one needs to tune the devices into a desirable configuration suitable for quantum computing. While current experiments adjust the control parameters heuristically, such an approach does not scale with the increasing size of the quantum dot arrays required for even near-term quantum computing demonstrations. Establishing a reliable protocol for tuning QD devices that does not rely on the gross-scale heuristics developed by experimentalists is thus of great importance.Materials and methodsTo implement the machine learning-based approach, we constructed a dataset of simulated QD device characteristics, such as the conductance and the charge sensor response versus the applied electrostatic gate voltages. The gate voltages are the experimental ‘knobs’ for tuning the device into useful regimes. Here, we describe the methodology for generating the dataset, as well as its validation in training convolutional neural networks.Results and discussionFrom 200 training sets sampled randomly from the full dataset, we show that the learner’s accuracy in recognizing the state of a device is ≈ 96.5% when using either current-based or charge-sensor-based training. The spread in accuracy over our 200 training sets is 0.5% and 1.8% for current- and charge-sensor-based data, respectively. In addition, we also introduce a tool that enables other researchers to use this approach for further research: QFlow lite—a Python-based mini-software suite that uses the dataset to train neural networks to recognize the state of a device and differentiate between states in experimental data. This work gives the definitive reference for the new dataset that will help enable researchers to use it in their experiments or to develop new machine learning approaches and concepts.

show abstract

“…As shown in Ref. 18, the new tools for quantum computing can be developed using two indistinguishable quantum particles in a cycle graph. It was shown that one can define qudits (d-dimensional quantum systems) by splitting a graph into two subgraphs.…”

Section: Introductionmentioning

confidence: 99%

“…It was shown that one can define qudits (d-dimensional quantum systems) by splitting a graph into two subgraphs. [18][19][20] If these two particles interact, then the corresponding qudits become entangled. Moreover, using different sizes of a cycle graph one can obtain a diverse structure of two-particle fermionic entanglement of high dimensions.…”

Section: Introductionmentioning

confidence: 99%

Hitting time for quantum walks of identical particles

Melnikov

Alodjants

Fedichkin

2019

International Conference on Micro- And Nano-Electronics 2018

Self Cite

View full text Add to dashboard Cite

Quantum particles are known to be faster than classical when they propagate stochastically on certain graphs. A time needed for a particle to reach a target node on a distance, the hitting time, can be exponentially less for quantum walks than for classical random walks. It is however not known how fast would interacting quantum particles propagate on different graphs. Here we present our results on hitting times for quantum walks of identical particles on cycle graphs, and relate the results to our previous findings on the usefulness of identical interacting particles in quantum information theory. We observe that interacting fermions traverse cycle graphs faster than non-interacting fermions. We show that the rate of propagation is related to fermionic entanglement: interacting fermions keep traversing the cycle graph as long as their entanglement grows. Our results demonstrate the role of entanglement in quantum particles propagation. These results are of importance for understanding quantum transport properties of identical particles.

show abstract

Quantum walks of interacting fermions on a cycle graph

Cited by 38 publications

References 55 publications

Quantum-inspired cascaded discrete-time quantum walks with induced chaotic dynamics and cryptographic applications

Quantum-inspired cascaded discrete-time quantum walks with induced chaotic dynamics and cryptographic applications

QFlow lite dataset: A machine-learning approach to the charge states in quantum dot experiments

Hitting time for quantum walks of identical particles

Contact Info

Product

Resources

About