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The spatial localization of quantum states plays a central role in condensed-matter phenomena, ranging from many-body localization to topological matter. Building on the dissipation-fluctuation theorem, we propose that the localization…
The quantum kicked rotor (QKR) map is embedded into a continuous unitary transformation generated by a time-independent quasi-Hamiltonian. In some vicinity of a quantum resonance of order $q$, we relate the problem to the {\it regular}…
A randomly walking quantum particle searches in Grover's $\Theta(\sqrt{N})$ iterations for a marked vertex on the complete graph of $N$ vertices by repeatedly querying an oracle that flips the amplitude at the marked vertex, scattering by a…
The quantum kicked rotor (QKR) is known to exhibit dynamical localization in the space of its angular momentum. The present paper is devoted to the systematic first--principal (without a regularizer) diagrammatic calculations of the…
Recently, we have been witnessing the scale-up of superconducting quantum computers; however, the noise of quantum bits (qubits) is still an obstacle for real-world applications to leveraging the power of quantum computing. Although there…
Searching a database is a central task in computer science and is paradigmatic of transport and optimization problems in physics. For an unstructured search, Grover's algorithm predicts a quadratic speedup, with the search time…
Variational quantum algorithms have become the de facto model for current quantum computations. A prominent example of such algorithms -- the quantum approximate optimization algorithm (QAOA) -- was originally designed for combinatorial…
We propose a gate-based quantum algorithm for the prediction step of Bayesian state estimation based on the Fokker-Planck equation on a discretized position-velocity state space. The probability density is encoded in the amplitudes of a…
The search operation for a marked state by means of Grover's quantum searching algorithm is shown to be an element of group SU(2) which acts on a 2-dimensional space spanned by the marked state and the unmarked collective state. Based on…
We present a novel quantum algorithm for solving the unstructured search problem with one marked element. Our algorithm allows generating quantum circuits that use asymptotically fewer additional quantum gates than the famous Grover's…
External environment influences on Grover's search algorithm modeled by quantum noise are investigated. The algorithm is shown to be robust under that external dissipation. Explicitly we prove that the resulting search positive maps acting…
We study the intermediate statistics of the spectrum of quasi-energies and of the eigenfunctions in the kicked rotator, in the case when the corresponding system is fully chaotic while quantally localized. As for the eigenphases, we find…
Consider a Boolean function $\chi: X \to \{0,1\}$ that partitions set $X$ between its good and bad elements, where $x$ is good if $\chi(x)=1$ and bad otherwise. Consider also a quantum algorithm $\mathcal A$ such that $A |0\rangle=…
In this paper, we present a novel formulation of traditional sampling-based motion planners as database-oracle structures that can be solved via quantum search algorithms. We consider two complementary scenarios: for simpler sparse…
In this work, we study quantum chaos by focusing on the evolution of initially close states in the dynamics of the Quantum Kicked Rotor (QKR). We propose a novel measure, the Quantum Lyapunov Exponent (QLE), to quantify the degree of chaos…
We study the performance and resource usage of the variational quantum factoring (VQF) algorithm for different instance sizes and optimization algorithms. Our simulations show better chance of finding the ground state when using VQE rather…
Despite the advent of Grover's algorithm for the unstructured search, its successful implementation on near-term quantum devices is still limited. We apply three strategies to reduce the errors associated with implementing quantum search…
Recently we find several candidates of quantum algorithms that may be implementable in near-term devices for estimating the amplitude of a given quantum state, which is a core sub- routine in various computing tasks such as the Monte Carlo…
By employing a nonlinear quantum kicked rotor model, we investigate the transport of energy in multidimensional quantum chaos. Parallel numerical simulations and analytic theory demonstrate that the interplay between nonlinearity and…
Grover's search algorithm is one of the first quantum algorithms to exhibit a provable quantum advantage. It forms the backbone of numerous quantum applications and is widely used in benchmarking efforts. Here, we report…