相关论文: Bounds on the number of time steps for simulating …
The adjacency matrix of a graph G is the Hamiltonian for a continuous-time quantum walk on the vertices of G. Although the entries of the adjacency matrix are integers, its eigenvalues are generally irrational and, because of this, the…
It is shown micromagnetic and atomistic spin dynamics simulations can use multiple GPUs in order to reduce computation time, but also to allow for a larger simulation size than is possible on a single GPU. Whilst interactions which depend…
A graph construction that produces a k-regular graph on n vertices for any choice of k >= 3 and n = m(k+1) for integer m >= 2 is described. The number of Hamiltonian cycles in such graphs can be explicitly determined as a function of n and…
We derive an exact closed-form analytical expression for the distribution of the cover time for a random walk over an arbitrary graph. In special case, we derive simplified exact expressions for the distributions of cover time for a…
To date, all proposed quantum algorithms for simulating quantum field theory (QFT) simulate (continuous-time) Hamiltonian lattice QFT as a stepping stone. Two overlooked issues are how large we can take the timestep in these simulations…
We report on a recent breakthrough in rule-based graph programming, which allows us to reach the time complexity of imperative linear-time algorithms. In general, achieving the complexity of graph algorithms in conventional languages using…
We report on recent advances in rule-based graph programming, which allow us to match the time complexity of some fundamental imperative graph algorithms. In general, achieving the time complexity of graph algorithms implemented in…
Learning system dynamics directly from observations is a promising direction in machine learning due to its potential to significantly enhance our ability to understand physical systems. However, the dynamics of many real-world systems are…
We present implementations of a fourth-order symplectic integrator on graphic processing units for three $N$-body models with long-range interactions of general interest: the Hamiltonian Mean Field, Ring and two-dimensional self-gravitating…
In quantum computing, the connectivity of qubits placed on two-dimensional chips limits the scalability and functionality of solid-state quantum computers. This paper presents two approaches to constructing complex quantum networks from…
We derive an upper bound for the time needed to implement a generic unitary transformation in a $d$ dimensional quantum system using $d$ control fields. We show that given the ability to control the diagonal elements of the Hamiltonian,…
We present quantum complexity lower and upper bounds for independent set problems in graphs. In particular, we give quantum algorithms for computing a maximal and a maximum independent set in a graph. We present applications of these…
The ability to simulate one Hamiltonian with another is an important primitive in quantum information processing. In this paper, a simulation method for arbitrary $\sigma_z \otimes \sigma_z$ interaction based on Hadamard matrices…
Face-to-face interactions reveal recurring patterns, suggesting the possibility of shared underlying mechanisms. More specifically, inter-contact durations, contact durations and number of contacts per edge share similar heavy-tail…
We consider unitary dynamical evolutions on n qubits caused by time dependent pair-interaction Hamiltonians and show that the running time of a parallelized two-qubit gate network simulating the evolution is given by the time integral over…
Quantum walks provide a natural framework to approach graph problems with quantum computers, exhibiting speedups over their classical counterparts for tasks such as the search for marked nodes or the prediction of missing links.…
In this paper we present the first deterministic polynomial time algorithm for determining the existence of a Hamiltonian cycle and finding a Hamiltonian cycle in general graphs. Our algorithm can also solve the Hamiltonian path problem in…
Controlling the interaction graph between spins or qubits in a quantum simulator allows user-controlled tailoring of native interactions to achieve a target Hamiltonian. The flexibility of engineering long-ranged phonon-mediated spin-spin…
We study two random processes on an $n$-vertex graph inspired by the internal diffusion limited aggregation (IDLA) model. In both processes $n$ particles start from an arbitrary but fixed origin. Each particle performs a simple random walk…
We present exponential and super factorial lower bounds on the number of Hamiltonian cycles passing through any edge of the basis graphs of a graphic, generalized Catalan and uniform matroids. All lower bounds were obtained by a common…