Related papers: Complexity for one-dimensional discrete time quant…
Discrete-time quantum walks with position-dependent coin operators have numerous applications. For a position dependence that is sufficiently smooth, it has been provided in Ref. [1] an approximate quantum-circuit implementation of the coin…
We consider quantum walks with position dependent coin on 1D lattice $\mathbb{Z}$. The dispersive estimate $\|U^tP_c u_0\|_{l^\infty}\lesssim (1+|t|)^{-1/3} \|u_0\|_{l^1}$ is shown under $l^{1,1}$ perturbation for the generic case and…
Quantum processes can be divided into two categories: unitary and non-unitary ones. For a given quantum process, we can define a \textit{degree of the unitarity (DU)} of this process to be the fidelity between it and its closest unitary…
We define the model of quantum circuits with density matrices, where non-unitary gates are allowed. Measurements in the middle of the computation, noise and decoherence are implemented in a natural way in this model, which is shown to be…
The complexity of the quantum state of a multiparticle system and the maximum possible accuracy of its quantum description are connected by a relation similar to the coordinate-momentum uncertainty relation. The coefficient in this relation…
Multilayer network is a potent platform which paves a way to study the interactions among entities in various networks with multiple types of relationships. In this study, the dynamics of discrete-time quantum walk on a multilayer network…
Quantum walks, both discrete (coined) and continuous time, form the basis of several quantum algorithms and have been used to model processes such as transport in spin chains and quantum chemistry. The enhanced spreading and mixing…
Density-functional theory (DFT) has revolutionized computer simulations in chemistry and material science. A faithful implementation of the theory requires self-consistent calculations. However, this effort involves repeatedly diagonalizing…
In this paper, a study on discrete-time coined quantum walks on the line is presented. Clear mathematical foundations are still lacking for this quantum walk model. As a step towards this objective, the following question is being…
In Nielsen's geometric approach to quantum complexity, the introduction of a suitable geometrical space, based on the Lie group formed by fundamental operators, facilitates the identification of complexity through geodesic distance in the…
We introduce the driven discrete time quantum walk, where walkers are added during the walk instead of only at the beginning. This leads to interference in walker number and very different dynamics when compared to the original quantum…
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…
Dissipation and irreversibility are central to most physical processes, yet they lead to non-unitary dynamics that are challenging to realise on quantum processors. High-order operator splitting is an attractive approach for simulating…
We investigate circuit complexity to characterize chaos in multiparticle quantum systems. In the process, we take a stride to analyze open quantum systems by using complexity. We propose a new diagnostic of quantum chaos from complexity…
Compatibility with noisy intermediate-scale quantum (NISQ) devices is crucial for the realistic implementation of quantum cryptographic protocols. We investigate a cryptographic scheme based on discrete-time quantum walks (DTQWs) on cyclic…
In this work, we are interested in the detailed analysis of complexity aspects of both time and space that arises from the implementation of a quantum algorithm on a quantum based hardware. In particular, some steps of the implementation,…
Practical implementations of quantum computing are always done in the presence of decoherence. Geometric phase is useful in the context of quantum computing as a tool to achieve fault tolerance. Recent experimental progresses on coherent…
We formulate three current models of discrete-time quantum walks in a combinatorial way. These walks are shown to be closely related to rotation systems and 1-factorizations of graphs. For two of the models, we compute the traces and total…
Quantum walks provide a versatile framework for probing the structural and dynamical properties of complex systems ranging from biological networks to synthetic materials. However, their realization on current noisy pre-fault-tolerant…
A discrete time quantum walker is considered in one dimension, where at each step, the translation can be more than one unit length chosen randomly. In the simplest case, the probability that the distance travelled is $\ell$ is taken as…