Related papers: Quantum Approach to Fast Protein-Folding Time
Quantum annealing (QA) is a method for solving combinatorial optimization problems. We can estimate the computational time for QA using the adiabatic condition. The adiabatic condition consists of two parts: an energy gap and a transition…
Recently, several groups have investigated quantum analogues of random walk algorithms, both on a line and on a circle. It has been found that the quantum versions have markedly different features to the classical versions. Namely, the…
Modeling and simulating the protein folding process overall remains a grand challenge in computational biology. We systematically investigate end-to-end quantum algorithms for simulating various protein dynamics with effects, such as…
Quantum algorithms have demonstrated provable speedups over classical counterparts, yet establishing a comprehensive theoretical framework to understand the quantum advantage remains a core challenge. In this work, we decode the quantum…
I introduce a new type of continuous-time quantum walk on graphs called the quantum snake walk, the basis states of which are fixed-length paths (snakes) in the underlying graph. First I analyze the quantum snake walk on the line, and I…
We investigate the statistics of the first detected passage time of a quantum walk. The postulates of quantum theory, in particular the collapse of the wave function upon measurement, reveal an intimate connection between the wave function…
A central goal of protein-folding theory is to predict the stochastic dynamics of transition paths --- the rare trajectories that transit between the folded and unfolded ensembles --- using only thermodynamic information, such as a…
We present an efficient general method for realizing a quantum walk operator corresponding to an arbitrary sparse classical random walk. Our approach is based on Grover and Rudolph's method for preparing coherent versions of efficiently…
In this paper we present a model exhibiting a new type of continuous-time quantum walk (as a quantum mechanical transport process) on networks, which is described by a non-Hermitian Hamiltonian possessing a real spectrum. We call it…
Quantum walks are well-known for their ballistic dispersion, traveling $\Theta(t)$ away in $t$ steps, which is quadratically faster than a classical random walk's diffusive spreading. In physical implementations of the walk, however, the…
A quantum walk places a traverser into a superposition of both graph location and traversal "spin." The walk is defined by an initial condition, an evolution determined by a unitary coin/shift-operator, and a measurement based on the…
We introduce the concept of a quantum walk with two particles and study it for the case of a discrete time walk on a line. A quantum walk with more than one particle may contain entanglement, thus offering a resource unavailable in the…
We investigate the splitting probability of a monitored continuous-time quantum walk with two targets and show that, in stark contrast to a classical random walk, it exhibits a nonanalytic, phase-transition-like behavior controlled by the…
This letter treats the quantum random walk on the line determined by a 2 times 2 unitary matrix U. A combinatorial expression for the mth moment of the quantum random walk is presented by using 4 matrices, P, Q, R and S given by U. The…
In this work we focus on the notion of quantum hitting time for discrete-time Szegedy quantum walks, compared to its classical counterpart. Under suitable hypotheses, quantum hitting time is known to be of the order of the square root of…
Discrete-time quantum walks, quantum generalizations of classical random walks, provide a framework for quantum information processing, quantum algorithms and quantum simulation of condensed matter systems. The key property of quantum…
In this work, we generalize the recently-introduced graph composition framework to the non-boolean setting. A quantum algorithm in this framework is represented by a hypergraph, where each hyperedge is adjacent to multiple vertices. The…
We study the motion of two non-interacting quantum particles performing a random walk on a line and analyze the probability that the two particles are detected at a particular position after a certain number of steps (meeting problem). The…
We analyze continuous-time quantum and classical random walk on spidernet lattices. In the framework of Stieltjes transform, we obtain density of states, which is an efficiency measure for the performance of classical and quantum mechanical…
Protein folding, which dictates the protein structure from its amino acid sequence, is half a century old problem of biology. The function of the protein correlates with its structure, emphasizing the need of understanding protein folding…