Related papers: Exact solutions for the time-evolution of quantum …
We establish efficient algorithms for weakly-interacting quantum spin systems at arbitrary temperature. In particular, we obtain a fully polynomial-time approximation scheme for the partition function and an efficient approximate sampling…
The evolution of spin network states in loop quantum gravity can be described by introducing a time variable, defined by the surfaces of constant value of an auxiliary scalar field. We regulate the Hamiltonian, generating such an evolution,…
Universal quantum computation can be realised using both continuous-time and discrete-time quantum walks. We present a version based on single particle discrete-time quantum walk to realize multi-qubit computation tasks. The scalability of…
Quantum walks are the quantum-mechanical analog of random walks, in which a quantum `walker' evolves between initial and final states by traversing the edges of a graph, either in discrete steps from node to node or via continuous evolution…
The problem of finding a marked node in a graph can be solved by the spatial search algorithm based on continuous-time quantum walks (CTQW). However, this algorithm is known to run in optimal time only for a handful of graphs. In this work,…
The study of quantum evolution on graphs for diversified topologies is beneficial to modeling various realistic systems. A systematic method, the dimerized decomposition, is proposed to analyze the dynamics on an arbitrary network. By…
Quantum walks obey unitary dynamics: they form closed quantum systems. The system becomes open if the walk suffers from imperfections represented as missing links on the underlying basic graph structure, described by dynamical percolation.…
Efficient simulations of quantum evolutions of spin-1/2 systems are relevant for ensemble quantum computation as well as in typical NMR experiments. We propose an efficient method to calculate the dynamics of an observable provided that the…
Simulating time evolution of generic quantum many-body systems using classical numerical approaches has an exponentially growing cost either with evolution time or with the system size. In this work, we present a polynomially scaling hybrid…
Quantum walk is a potent technique for building quantum algorithms. This paper examines the quantum walk search algorithm on complete multipartite graphs with multiple marked vertices, which has not been explored before. Two specific cases…
We study the real-time simulation of open quantum systems, where the system is modeled by a spin chain, with each spin associated with its own harmonic bath. Our method couples the inchworm method for the spin-boson model and the modular…
In this paper we present closed-form expressions for the wave function that governs the evolution of the discrete-time quantum walk on a line when the coin operator is arbitrary. The formulas were derived assuming that the walker can either…
A path integral method, combined with atomistic spin dynamics simulations, has been developed to calculate thermal quantum expectation values using a classical approach. In this study, we show how to treat Hamiltonians with non-linear…
Based on the Dirac representation of Maxwell equations we present an explicit, discrete space-time, quantum walk-inspired algorithm suitable for simulating the electromagnetic wave propagation and scattering from inhomogeneities within…
Understanding which physical processes are symmetric with respect to time inversion is a ubiquitous problem in physics. In quantum physics, effective gauge fields allow emulation of matter under strong magnetic fields, realizing the…
Using the spectral distribution associated with the adjacency matrix of graphs, we introduce a new method of calculation of amplitudes of continuous-time quantum walk on some rather important graphs, such as line, cycle graph $C_n$,…
Quantum walks have been employed widely to develop new tools for quantum information processing recently. A natural quantum walk dynamics of interacting particles can be used to implement efficiently the universal quantum computation. In…
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…
We consider the temporal evolution of strong correlated degrees of freedom in $2+1$~$D$ spin systems using the Wilson operator eigenvalues as variables. It is shown that the quantum-group diffusion equation at deformation parameter $q$…
In quantum field theory the path integral is usually formulated in the wave picture, i.e., as a sum over field evolutions. This path integral is difficult to define rigorously because of analytic problems whose resolution may ultimately…