Related papers: A BQP-complete problem related to the Ising model …
We give a generating function for the number of graphs with given numerical properties and prescribed weighted number of connected components. As an application, we give a generating function for the number of bipartite graphs of given…
We present a method to approximate partition functions of quantum systems using mixed-state quantum computation. For positive semi-definite Hamiltonians, our method has expected running-time that is almost linear in $(M/(\epsilon_{\rm…
Finding the Eulerian circuit in graphs is a classic problem, but inadequately explored for parallel computation. With such cycles finding use in neuroscience and Internet of Things for large graphs, designing a distributed algorithm for…
We derive an exact path integral formulation for the partition function for the Ising model using a mapping between spins and poles of a Laurent expansion for a field on the complex plane. The advantage in using this formulation for the…
We tackle the problem of graph partitioning for image segmentation using correlation clustering (CC), which we treat as an integer linear program (ILP). We reformulate optimization in the ILP so as to admit efficient optimization via…
Quantum annealers offer an efficient way to compute high quality solutions of NP-hard problems when expressed in a QUBO (quadratic unconstrained binary optimization) or an Ising form. This is done by mapping a problem onto the physical…
We propose a hypergraph expansion which facilitates the direct treatment of quantum spin models with many-site interactions via perturbative linked cluster expansions. The main idea is to generate all relevant subclusters and sort them into…
Spin network states are a powerful tool for constructing the $SU(2)$ gauge theories on a graph. In loop quantum gravity (LQG), they have yielded many promising predictions, although progress has been limited by the computational challenge…
Here we consider using quantum annealing to solve Set Cover with Pairs (SCP), an NP-hard combinatorial optimization problem that play an important role in networking, computational biology, and biochemistry. We show an explicit construction…
The branching ratio is calculated for three different models of 2d gravity, using dynamical planar phi-cubed graphs. These models are pure gravity, the D=-2 Gaussian model coupled to gravity and the single spin Ising model coupled to…
Graph partitioning is a key fundamental problem in the area of big graph computation. Previous works do not consider the practical requirements when optimizing the big data analysis in real applications. In this paper, motivated by…
The maximum graph bisection problem is a well known graph partition problem. The problem has been proven to be NP-hard. In the maximum graph bisection problem it is required that the set of vertices is divided into two partition with equal…
Quantum circuit partitioning (QCP) is a hybrid quantum-classical approach that aims to simulate large quantum systems on smaller quantum computers. A quantum computation is divided into smaller subsystems and results of measurements on…
Quantum algorithms are usually described as monolithic circuits, becoming large at modest input size. Near-term quantum architectures can only manage a small number of qubits. We develop an automated method to distribute quantum circuits…
Of late, we are witnessing spectacular developments in Quantum Information Processing with the availability of Noisy Intermediate-Scale Quantum devices of different architectures and various software development kits to work on quantum…
Given a simple connected graph $G = (V, E)$, we seek to partition the vertex set $V$ into $k$ non-empty parts such that the subgraph induced by each part is connected, and the partition is maximally balanced in the way that the maximum…
Using an exact holographic duality formula between the inhomogeneous 2d Ising model and 3d quantum gravity, we provide a formula for "real" zeroes of the 2d Ising partition function on finite trivalent graphs in terms of the geometry of a…
Distinguishing logarithmic depth quantum circuits on mixed states is shown to be complete for QIP, the class of problems having quantum interactive proof systems. Circuits in this model can represent arbitrary quantum processes, and thus…
We study a graph partitioning problem motivated by the simulation of the physical movement of multi-body systems on an atomistic level, where the forces are calculated from a quantum mechanical description of the electrons. Several advanced…
We provide formulas for invariants defined on a tensor product of defining representations of unitary groups, under the action of the product group. This situation has a physical interpretation, as it is related to the quantum mechanical…