相关论文: On the adiabatic condition and the quantum hitting…
We solve an open problem by constructing quantum walks that not only detect but also find marked vertices in a graph. In the case when the marked set $M$ consists of a single vertex, the number of steps of the quantum walk is quadratically…
Spatial search by discrete-time quantum walk can find a marked node on any ergodic, reversible Markov chain $P$ quadratically faster than its classical counterpart, i.e.\ in a time that is in the square root of the hitting time of $P$.…
Continuous-time quantum walks provide a natural framework to tackle the fundamental problem of finding a node among a set of marked nodes in a graph, known as spatial search. Whether spatial search by continuous-time quantum walk provides a…
Computing using a continuous-time evolution, based on the natural interaction Hamiltonian of the quantum computer hardware, is a promising route to building useful quantum computers in the near-term. Adiabatic quantum computing, quantum…
The quantum-walk-based spatial search problem aims to find a marked vertex using a quantum walk on a graph with marked vertices. We describe a framework for determining the computational complexity of spatial search by continuous-time…
Quantum walks play an important role in the area of quantum algorithms. Many interesting problems can be reduced to searching marked states in a quantum Markov chain. In this context, the notion of quantum hitting time is very important,…
The design of new quantum algorithms has proven to be an extremely difficult task. This paper considers a different approach to the problem, by studying the problem of 'quantum state generation'. This approach provides intriguing links…
The quantum walk is a powerful tool to develop quantum algorithms, which usually are based on searching for a vertex in a graph with multiple marked vertices, Ambainis's quantum algorithm for solving the element distinctness problem being…
Random walks (or Markov chains) are models extensively used in theoretical computer science. Several tools, including analysis of quantities such as hitting and mixing times, are helpful for devising randomized algorithms. A notable example…
In this paper we define new Monte Carlo type classical and quantum hitting times, and we prove several relationships among these and the already existing Las Vegas type definitions. In particular, we show that for some marked state the two…
In this paper we continue our work on adiabatic time of time-inhomogeneous Markov chains first introduced in Kovchegov (2010) and Bradford and Kovchegov (2011). Our study is an analog to the well-known Quantum Adiabatic (QA) theorem which…
The lackadaisical quantum walk is a quantum analogue of the lazy random walk obtained by adding a self-loop to each vertex in the graph. We analytically prove that lackadaisical quantum walks can find a unique marked vertex on any regular…
The problem of sampling from the stationary distribution of a Markov chain finds widespread applications in a variety of fields. The time required for a Markov chain to converge to its stationary distribution is known as the classical…
We present a 2-local quantum algorithm for graph isomorphism GI based on an adiabatic protocol. By exploiting continuous-time quantum-walks, we are able to avoid a mere diffusion over all possible configurations and to significantly reduce…
We study quantum Markov chains on graphs, described by completely positive maps, following the model due to S. Gudder (J. Math. Phys. 49, 072105, 2008) and which includes the dynamics given by open quantum random walks as defined by S.…
We propose a new method for designing quantum search algorithms for finding a "marked" element in the state space of a classical Markov chain. The algorithm is based on a quantum walk \'a la Szegedy (2004) that is defined in terms of the…
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.…
A quantum walk algorithm can detect the presence of a marked vertex on a graph quadratically faster than the corresponding random walk algorithm (Szegedy, FOCS 2004). However, quantum algorithms that actually find a marked element…
In the classical theory of Markov chains, one may study the mean time to reach some chosen state, and it is well-known that in the irreducible, finite case, such quantity can be calculated in terms of the fundamental matrix of the walk, as…
We derive an adiabatic theorem for Markov chains using well known facts about mixing and relaxation times. We discuss the results in the context of the recent developments in adiabatic quantum computation.