Related papers: A computable branching random walk for the many-bo…
Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a…
Quantum random walks are shown to have non-intuitive dynamics which makes them an attractive area of study for devising quantum algorithms for long-standing open problems as well as those arising in the field of quantum computing. In the…
By decomposing the random walk path, we construct a multitype branching process with immigration in random environment for corresponding random walk with bounded jumps in random environment. Then we give two applications of the branching…
Quantum devices are preparing increasingly more complex entangled quantum states. How can one effectively study these states in light of their increasing dimensions? Phase spaces such as Wigner functions provide a suitable framework. We…
Two specialized algorithms for the numerical integration of the equations of motion of a Brownian walker obeying detailed balance are introduced. The algorithms become symplectic in the appropriate limits, and reproduce the equilibrium…
Numerical stochastic integration is a powerful tool for the investigation of quantum dynamics in interacting many body systems. As with all numerical integration of differential equations, the initial conditions of the system being…
With the increasing crossover between quantum information and machine learning, quantum simulation of neural networks has drawn unprecedentedly strong attention, especially for the simulation of associative memory in Hopfield neural…
There are well developed theoretical tools to analyse how quantum dynamics can solve computational problems by varying Hamiltonian parameters slowly, near the adiabatic limit. On the other hand, there are relatively few tools to understand…
The coherent superposition of position states in a quantum walk (QW) can be precisely engineered towards the desired distributions to meet the need of quantum information applications. The coherent distribution can make full use of quantum…
The horizontal dynamics of a bouncing ball interacting with an irregular surface is investigated and is found to demonstrate behavior analogous to a random walk. Its stochastic character is substantiated by the calculation of a permutation…
We modify the path integral representation of exciton transport in open quantum systems such that an exact description of the quantum fluctuations around the classical evolution of the system is possible. As a consequence, the time…
Quantum random walks are constructed on operator spaces with the aid of matrix-space lifting, a type of ampliation intermediate between those provided by spatial and ultraweak tensor products. Using a form of Wiener-Ito decomposition, a…
The staggered quantum walk is a type of discrete-time quantum walk model without a coin which can be generated on a graph using particular partitions of the graph nodes. We design Hamiltonians for potential realization of the staggered…
The equation of motion for the reduced Wigner function of a system coupled to an external quantum system is presented for the specific case when the external quantum system can be modeled as a set of harmonic oscillators. The result is…
The behaviour of random quantum walks is known to be diffusive. Here we study discrete time quantum walks in weak stochastic gauge fields. In the case of position and spin dependent gauge field, we observe a transition from ballistic to…
Variational quantum algorithms have been proposed to solve static and dynamic problems of closed many-body quantum systems. Here we investigate variational quantum simulation of three general types of tasks---generalised time evolution with…
With photonics, the quantum computational advantage has been demonstrated on the task of boson sampling. Next, developing quantum-enhanced approaches for practical problems becomes one of the top priorities for photonic systems. Quantum…
We present an approach to the numerical simulation of open quantum many-body systems based on the semiclassical framework of the discrete truncated Wigner approximation. We establish a quantum jump formalism to integrate the quantum master…
We introduce a quantum algorithm for simulating the time-dependent Dirac equation in 3+1 dimensions using discrete-time quantum walks. Thus far, promising quantum algorithms have been proposed to simulate quantum dynamics in…
Coherent dynamics of interacting quantum particles plays a central role in the study of strongly correlated quantum matter and the pursuit of quantum information processors. Here, we present the state-space of interacting Rydberg atoms as a…