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Quantum computing has the potential to solve complex problems faster and more efficiently than classical computing. It can achieve speedups by leveraging quantum phenomena like superposition, entanglement, and tunneling. Quantum walks (QWs)…

One of the main requirements to achieve reliable quantum communications are on-demand sources of highly entangled photon pairs, and semiconductor quantum dots have emerged as prominent candidates to satisfy the necessary conditions of…

We present a quantum-dynamical framework for identifying structurally important residues in proteins based on continuous time quantum walks (CTQWs) on weighted residue interaction networks constructed from experimentally resolved…

Continuous-time quantum walks (CTQWs) provide a valuable model for quantum transport, universal quantum computation and quantum spatial search, among others. Recently, the empowering role of new degrees of freedom in the Hamiltonian…

The random walk formalism is used across a wide range of applications, from modelling share prices to predicting population genetics. Likewise quantum walks have shown much potential as a frame- work for developing new quantum algorithms.…

The generation and control of quantum correlations in high-dimensional systems is a major challenge in the present landscape of quantum technologies. Achieving such non-classical high-dimensional resources will potentially unlock enhanced…

We present a theoretical framework for the analysis of amplitude transfer in Quantum Variational Algorithms (QVAs) for combinatorial optimisation with mixing unitaries defined by vertex-transitive graphs, based on their continuous-time…

This paper introduces in detail a non-variational quantum algorithm designed to solve a wide range of combinatorial optimisation problems, including constrained problems and problems with non-binary variables. The algorithm returns optimal…

Quantum walk (QW), which is considered as the quantum counterpart of the classical random walk (CRW), is actually the quantum extension of CRW from the single-coin interpretation. The sequential unitary evolution engenders correlation…

In this study, we investigate the emergence of the quantum boomerang effect in discrete-time quantum walks (DTQWs) subjected to random phase disorder. Our analysis shows that this effect can arise solely from the intrinsic momentum dynamics…

We report the security analysis of time-coding quantum key distribution protocols. The protocols make use of coherent single-photon pulses. The key is encoded in the photon time-detection. The use of coherent superposition of states allows…

Quantum-circuit implementations of continuous-time quantum walks (CTQWs) can provide an efficient route to model graph-based algorithms. However, constructing circuits that faithfully reproduce CTQW dynamics across arbitrary graphs remains…

We study a quantum walk in one-dimension using two different "coin" operators. By mixing two operators, both of which give a biased walk with negative expectation value for the walker position, it is possible to reverse the bias through…

We introduce a new framework to analyze quantum algorithms with the renormalization group (RG). To this end, we present a detailed analysis of the real-space RG for discrete-time quantum walks on fractal networks and show how deep insights…

Restart is a common strategy observed in nature that accelerates first-passage processes and has been extensively studied using classical random walks. In the quantum regime, restart in continuous-time quantum walks (CTQWs) has been shown…

We investigate a novel quantum random walk (QRW) model, possibly useful in quantum algorithm implementation, that achieves a quadratically faster diffusion rate compared to its classical counterpart. We evaluate its asymptotic behavior…

We investigate the counterparts of random walk in universal quantum computing and their implementation using standard quantum circuits. Quantum walk have been recently well investigated for traversing graphs with certain oracles. We focus…

In this paper we isolate the combinatorial property responsible (at least in part) for the computational speedups recently observed in some quantum walk algorithms. We find that continuous-time quantum walks can exploit the covering space…

Signaled by non-analyticities in the time evolution of physical observables, dynamic quantum phase transitions (DQPTs) emerge in quench dynamics of topological systems and possess an interesting geometric origin captured by dynamic…

Computational advantages gained by quantum algorithms rely largely on the coherence of quantum devices and are generally compromised by decoherence. As an exception, we present a quantum algorithm for graph isomorphism testing whose…