Related papers: Guided quantum walk
For a continuous-time quantum walk on a line the variance of the position observable grows quadratically in time, whereas, for its classical counterpart on the same graph, it exhibits a linear, diffusive, behaviour. A quantum walk, thus,…
It is demonstrated that in gate-based quantum computing architectures quantum walk is a natural mathematical description of quantum gates. It originates from field-matter interaction driving the system, but is not attached to specific qubit…
Continuous-time quantum walks and adiabatic quantum evolution are two general techniques for quantum computing, both of which are described by Hamiltonians that govern their evolutions by Schr\"odinger's equation. In the former, the…
The Quantum Approximate Optimization Algorithm (QAOA) follows a single, fixed evolution path, overlooking the potential computational advantage of coherently superposing multiple trajectories. Here we overcome this limitation with a hybrid…
Adiabatic processes can keep the quantum system in its instantaneous eigenstate, which is robust to noises and dissipation. However, it is limited by sufficiently slow evolution. Here, we experimentally demonstrate the transitionless…
We introduce quantum walks with a time-dependent coin, and show how they include, as a particular case, the generalized quantum walk recently studied by Wojcik et al. {[}Phys. Rev. Lett. \textbf{93}, 180601(2004){]} which exhibits…
A quantum computing algorithm for rhythm generation is presented, which aims to expand and explore quantum computing applications in the arts, particularly in music. The algorithm maps quantum random walk trajectories onto a rhythmspace --…
Quantum walks are the quantum-mechanical analog of random walks, in which a quantum `walker' evolves between initial and final states by traversing the edges of a graph, either in discrete steps from node to node or via continuous evolution…
We describe a quantum trajectories technique for the unraveling of the quantum adiabatic master equation in Lindblad form. By evolving a complex state vector of dimension $N$ instead of a complex density matrix of dimension $N^2$,…
Distributing arbitrary graph states across quantum networks is a central challenge for modular quantum computing and measurement-based quantum communication. We introduce the phase quantum walk (PQW), a discrete-time quantum walk in which…
The enormous successes have been made by quantum algorithms during the last decade. In this paper, we combine the quantum random walk (QRW) with the problem of data clustering, and develop two clustering algorithms based on the one…
Topological phases, edge states, and flat bands in synthetic quantum systems are a key resource for topological quantum computing and noise-resilient information processing. We introduce a scheme based on step-dependent quantum walks on…
The study of optimal control of quantum annealing by modulating the pace of evolution and by introducing a counterdiabatic potential has gained significant attention in recent times. In this work, we present a numerical approach based on…
A particular example is produced to prove that quantum walks can be used to simulate full-fledged discrete gauge theories. A new family of $2D$ walks is introduced and its continuous limit is shown to coincide with the dynamics of a Dirac…
Mathematical analysis on the existence of eigenvalues is essential because it is equivalent to the occurrence of localization, which is an exceptionally crucial property of quantum walks. We construct the method for the eigenvalue problem…
Quantum annealing approximately solves combinatorial optimization problems by leveraging the principles of adiabatic quantum systems. In this approach, the system's Hamiltonian evolves from an initial general state to a problem-specific…
Quantum adiabatic optimization (QAO) is performed using a time-dependent Hamiltonian $H(s)$ with spectral gap $\gamma(s)$. Assuming the existence of an oracle $\Gamma$ such that $\gamma_\min = \Theta\left(\min_s\Gamma(s)\right)$, we provide…
Quantum walks function as essential means to implement quantum simulators, allowing one to study complex and often directly inaccessible quantum processes in controllable systems. In this contribution, the notion of a driven Gaussian…
Continuous-time quantum walks (CTQWs) on static graphs provide efficient methods for search and sampling as well as a model for universal quantum computation. We consider an extension of CTQWs to the case of dynamic graphs, in which an…
Quantum algorithms have emerged as a promising tool to solve combinatorial optimization problems. The quantum walk optimization algorithm (QWOA) is one such variational approach that has recently gained attention. In the broader context of…