Universal quantum computation can be realised using both continuous-time and discrete-time quantum walks. We present a version based on single particle discrete-time quantum walk to realize multi-qubit computation tasks. The scalability of the scheme
is demonstrated by using a set of walk operations on a closed lattice form to implement the universal set of quantum gates on multi-qubit system. We also present a set of experimentally realizable walk operations that can implement Grovers algorithm, quantum Fourier transformation and quantum phase estimation algorithms. An elementary implementation of error detection and correction is also presented. Analysis of space and time complexity of the scheme highlights the advantages of quantum walk based model for quantum computation on systems where implementation of quantum walk evolution operations is an inherent feature of the system.
Cognitive ad-hoc networks allow users to access an unlicensed/shared spectrum without the need for any coordination via a central controller and are being envisioned for futuristic ultra-dense wireless networks. The ad-hoc nature of networks require
each user to learn and regularly update various network parameters such as channel quality and the number of users, and use learned information to improve the spectrum utilization and minimize collisions. For such a learning and coordination task, we propose a distributed algorithm based on a multi-player multi-armed bandit approach and novel signaling scheme. The proposed algorithm does not need prior knowledge of network parameters (users, channels) and its ability to detect as well as adapt to the changes in the network parameters thereby making it suitable for static as well as dynamic networks. The theoretical analysis and extensive simulation results validate the superiority of the proposed algorithm over existing state-of-the-art algorithms.
Quantum walks are a promising framework for developing quantum algorithms and quantum simulations. Quantum walks represent an important test case for the application of quantum computers. Here we present different forms of discrete-time quantum walks
and show their equivalence for physical realizations. Using an appropriate digital mapping of the position space on which a walker evolves onto the multi-qubit states in a quantum processor, we present different configurations of quantum circuits for the implementation of discrete-time quantum walks in one-dimensional position space. With example circuits for a five qubit machine we address scalability to higher dimensions and larger quantum processors.
Quantum walk has been regarded as a primitive to universal quantum computation. By using the operations required to describe the single particle discrete-time quantum walk on a position space we demonstrate the realization of the universal set of qua
ntum gates on two- and three-qubit systems. The idea is to utilize the effective Hilbert space of the single qubit and the position space on which it evolves in order to realize multi-qubit states and universal set of quantum gates on them. Realization of many non-trivial gates and engineering arbitrary states is simpler in the proposed quantum walk model when compared to the circuit based model of computation. We will also discuss the scalability of the model and some propositions for using lesser number of qubits in realizing larger qubit systems.
In discrete-time quantum walk (DTQW) the walkers coin space entangles with the position space after the very first step of the evolution. This phenomenon may be exploited to obtain the value of the coin parameter $theta$ by performing measurements on
the sole position space of the walker. In this paper, we evaluate the ultimate quantum limits to precision for this class of estimation protocols, and use this result to assess measurement schemes having limited access to the position space of the walker in one dimension. We find that the quantum Fisher information (QFI) of the walkers position space $H_w(theta)$ increases with $theta$ and with time which, in turn, may be seen as a metrological resource. We also find a difference in the QFI of {em bounded} and {em unbounded} DTQWs, and provide an interpretation of the different behaviors in terms of interference in the position space. Finally, we compare $H_w(theta)$ to the full QFI $H_f(theta)$, i.e., the QFI of the walkers position plus coin state, and find that their ratio is dependent on $theta$, but saturates to a constant value, meaning that the walker may probe its coin parameter quite faithfully.
We present a scheme to describe the dynamics of accelerating discrete-time quantum walk for one- and two-particle in position space. We show the effect of acceleration in enhancing the entanglement between the particle and position space in one-parti
cle quantum walk and in generation of entanglement between the two unentangled particle in two-particle quantum walk. By introducing the disorder in the form of phase operator we study the transition from localization to delocalization as a function of acceleration. These inter-winding connection between acceleration, entanglement generation and localization along with well established connection of quantum walks with Dirac equation can be used to probe further in the direction of understanding the connection between acceleration, mass and entanglement in relativistic quantum mechanics and quantum field theory. Expansion of operational tools for quantum simulations and for modelling quantum dynamics of accelerated particle using quantum walks is an other direction where these results can play an important role.
We seek for the optimal strategy to infer the width $a$ of an infinite potential wells by performing measurements on the particle(s) contained in the well. In particular, we address quantum estimation theory as the proper framework to formulate the p
roblem and find the optimal quantum measurement, as well as to evaluate the ultimate bounds to precision. Our results show that in a static framework the best strategy is to measure position on a delocalized particle, corresponding to a width-independent quantum signal-to-noise ratio (QSNR), which increases with delocalisation. Upon considering time-evolution inside the well, we find that QSNR increases as $t^2$. On the other hand, it decreases with $a$ and thus time-evolution is a metrological resource only when the width is not too large compared to the available time evolution. Finally, we consider entangled probes placed into the well and observe super-additivity of the QSNR: it is the sum of the single-particle QSNRs, plus a positive definite term, which depends on their preparation and may increase with the number of entangled particles. Overall, entanglement represents a resource for the precise characterization of potential wells.
One-dimensional discrete-time quantum walk has played an important role in development of quantum algorithms and protocols for different quantum simulations. The speedup observed in quantum walk algorithms is attributed to quantum interference and co
herence of the wave packet in position space. Similarly, localization in quantum walk due to disorder is also attributed to quantum interference effect. Therefore, it is intriguing to have a closer look and understand the way quantum interference manifests in different forms of quantum walk dynamics. Quantum coherence in the system is responsible for quantum interference in the system. Here we will use coherence measure to quantify the interference in the discrete-time quantum walk. We show coherence in the position and coin space, together and independently, and present the contribution of coherence to the quantum interference in the system. This study helps us to differentiate the localization seen in one dimensional discrete-time quantum walks due to different forms of disorders and topological effects.
