Related papers: Nonlinear Quantum Search Using the Gross-Pitaevski…
Numerous conceptually important quantum algorithms rely on a black-box device known as an oracle, which is typically difficult to construct without knowing the answer to the problem that the algorithm is intended to solve. A notable example…
We propose a continuous time quantum search algorithm using a generalization of the Jaynes-Cummings model. In this model the states of the atom are the elements among which the algorithm realizes the search, exciting resonances between the…
We consider strongly coupled competitive elliptic systems of Gross-Pitaevskii type that arise in the study of two-component Bose-Einstein condensates, in general smooth bounded domains of $\mathbb{R}^N$, $N\geq 1$. As the coupling parameter…
We formulate Grover's unstructured search algorithm as a chiral quantum walk, where transitioning in one direction has a phase conjugate to transitioning in the opposite direction. For small phases, this breaking of time-reversal symmetry…
Grover's quantum search algorithm can be formulated as a quantum particle randomly walking on the (highly symmetric) complete graph, with one vertex marked by a nonzero potential. From an initial equal superposition, the state evolves in a…
Developing hardware-efficient implementations of quantum algorithms is crucial in the NISQ era to achieve practical quantum advantage. Here, we construct a generic quantum solver for NP problems based on Grover's search algorithm,…
We establish a lower bound concerning the computational complexity of Grover's algorithms on fractal networks. This bound provides general predictions for the quantum advantage gained for searching unstructured lists. It yields a…
A many-body Hamiltonian can be block-diagonalized by expressing it in terms of symmetry-adapted basis states. Finding the group orbit representatives of these basis states and their corresponding symmetries is currently a…
The research community has been actively working on the realization of quantum computer. But the large scale commercial quantum computers are not a reality yet quantum computing field has become richer by day with the advent of algorithms…
We prove that any exact quantum algorithm searching an ordered list of N elements requires more than \frac{1}{\pi}(\ln(N)-1) queries to the list. This improves upon the previously best known lower bound of {1/12}\log_2(N) - O(1). Our proof…
This paper shows that, if we could examine the entire history of a hidden variable, then we could efficiently solve problems that are believed to be intractable even for quantum computers. In particular, under any hidden-variable theory…
We study the unsorted database search problem with items $N$ from the viewpoint of unitary discrimination. Instead of considering the famous $O(\sqrt{N})$ Grover's the bounded-error algorithm for the original problem, we seek for the…
The landmark Grover algorithm for amplitude amplification serves as an essential subroutine in various type of quantum algorithms, with guaranteed quantum speedup in query complexity. However, there have been no proposal to realize the…
We derive in this study a Hamiltonian to solve with certainty the analog quantum search problem analogue to the Grover algorithm. The general form of the initial state is considered. Since the evaluation of the measuring time for finding…
Given a parameterized quantum circuit such that a certain setting of these real-valued parameters corresponds to Grover's celebrated search algorithm, can a variational algorithm recover these settings and hence learn Grover's algorithm? We…
The success probability of a search of $M$ targets from a database of size $N$, using Grover's search algorithm depends critically on the number of iterations of the composite operation of the oracle followed by Grover's diffusion…
It is questionable that Grover algorithm may be more valuable than a classical one, when a partial information is given in a unstructured database. In this letter, to consider quantum search when a partial information is given, we replace…
Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending…
It is shown that the energy levels of the one-dimensional nonlinear Schrodinger, or Gross-Pitaevskii, equation with the homogeneous trap potential $x^{2p}$, $p\geq 1$, obey an approximate scaling law and as a consequence the energy…
The rapid progress of computer science has been accompanied by a corresponding evolution of computation, from classical computation to quantum computation. As quantum computing is on its way to becoming an established discipline of…