Related papers: Quantum search on graphene lattices
We consider a graphene sheet folded in an arbitrary geometry, compact or with nanotube-like open boundaries. In the continuous limit, the Hamiltonian takes the form of the Dirac operator, which provides a good description of the low energy…
We wish to suggest an algorithm for biological search including DNA search. Our argument supposes that biological search be performed by quantum search.If we assume this, we can naturally answer the following long lasting puzzles such that…
Driven by the growing demand in the energy, medical, and industrial sectors, we investigate a hydrogen isotope separation technique that offers both a high separation factor and economic feasibility. Our findings reveal that filtering…
We analyze three different quantum search algorithms, the traditional Grover's algorithm, its continuous-time analogue by Hamiltonian evolution, and finally the quantum search by local adiabatic evolution. We show that they are closely…
Sorting is a fundamental computational process, which facilitates subsequent searching of a database. It can be thought of as factorisation of the search process. The location of a desired item in a sorted database can be found by classical…
We examine the use of adiabatic quantum algorithms to solve structured, or nested, search problems. We construct suitable time dependent Hamiltonians and derive the computation times for a general class of nested searches involving n…
Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. In effect, they follow the same logical paradigm as (multi-particle)…
Analogs of fundamental physical phenomena can be used in two ways. One way consists in reproducing specific aspects of classical or quantum gravity, of quantum fields in curved space or of other high-energy scenarios, on lower-energy…
We consider a square lattice configuration of circular gate-defined quantum dots in an unbiased graphene sheet and calculate the electronic, particularly spectral properties of finite albeit actual sample sized systems by means of a…
Quantum Search Algorithm made a big impact by being able to solve the search problem for a set with $N$ elements using only $O(\sqrt{N})$ steps. Unfortunately, it is impossible to reduce the order of the complexity of this problem, however,…
We present a novel methodological framework for quantum spatial search, generalising the Childs & Goldstone ($\mathcal{CG}$) algorithm via alternating applications of marked-vertex phase shifts and continuous-time quantum walks. We…
We present two new continuous time quantum search algorithms similar to the adiabatic search algorithm, but now without an adiabatic evolution. We find that both algorithms work for a wide range of values of the parameters of the…
Kronecker graphs, obtained by repeatedly performing the Kronecker product of the adjacency matrix of an "initiator" graph with itself, have risen in popularity in network science due to their ability to generate complex networks with…
We examine the effect of network heterogeneity on the performance of quantum search algorithms. To this end, we study quantum search on a tree for the oracle Hamiltonian formulation employed by continuous-time quantum walks. We use…
We propose a strategy to achieve the Grover search algorithm by adiabatic passage in a very efficient way. An adiabatic process can be characterized by the instantaneous eigenvalues of the pertaining Hamiltonian, some of which form a gap.…
The maximal clique problem, to find the maximally sized clique in a given graph, is classically an NP-complete computational problem, which has potential applications ranging from electrical engineering, computational chemistry,…
We consider a system of Dirac fermions in graphene submitted to a constant perpendicular magnetic field and scattered by a barrier potential. We show that our system can be used to establish a link with quantum optics through the…
Motivated by phenomenological questions in quantum gravity, we consider the propagation of a scalar field on a random lattice. We describe a procedure to calculate the dispersion relation for the field by taking a limit of a periodic…
The study of quantum computation has been motivated by the hope of finding efficient quantum algorithms for solving classically hard problems. In this context, quantum algorithms by local adiabatic evolution have been shown to solve an…
We introduce a novel quantum algorithm for determining graph connectedness using a constant number of measurements. The algorithm can be extended to find connected components with a linear number of measurements. It relies on non-unitary…