Related papers: Towards Hamiltonian Simulation with Decision Diagr…

We propose a new approach to constructing a phase diagram using the effective Hamiltonian derived only from a single real-space image produced by scanning tunneling microscopy (STM). Currently, there have been two main methods to construct…

We present efficient quantum algorithms for simulating time-dependent Hamiltonian evolution of general input states using an oracular model of a quantum computer. Our algorithms use either constant or adaptively chosen time steps and are…

Simulation of quantum chemistry is expected to be a principal application of quantum computing. In quantum simulation, a complicated Hamiltonian describing the dynamics of a quantum system is decomposed into its constituent terms, where the…

We address the problem of simulating pair-interaction Hamiltonians in n node quantum networks where the subsystems have arbitrary, possibly different, dimensions. We show that any pair-interaction can be used to simulate any other by…

Analogue Hamiltonian simulation is a promising near-term application of quantum computing and has recently been put on a theoretical footing. In Hamiltonian simulation, a physical Hamiltonian is engineered to have identical physics to…

This work is concerned with tree tensor network operators (TTNOs) for representing quantum Hamiltonians. We first establish a mathematical framework connecting tree topologies with state diagrams. Based on these, we devise an algorithm for…

While machine learning models are typically trained to solve prediction problems, we might often want to use them for optimization problems. For example, given a dataset of proteins and their corresponding fluorescence levels, we might want…

Operations research practitioners frequently want to model complicated functions that are are difficult to encode in their underlying optimisation framework. A common approach is to solve an approximate model, and to use a simulation to…

We introduce an algorithm to compute Hamiltonian dynamics on digital quantum computers that requires only a finite circuit depth to reach an arbitrary precision, i.e. achieves zero discretization error with finite depth. This finite number…

The physics of quantum mechanics is the inspiration for, and underlies, quantum computation. As such, one expects physical intuition to be highly influential in the understanding and design of many quantum algorithms, particularly…

We explore the use of Physics Informed Neural Networks to analyse nonlinear Hamiltonian Dynamical Systems with a first integral of motion. In this work, we propose an architecture which combines existing Hamiltonian Neural Network…

Learning to simulate complex physical systems from data has emerged as a promising way to overcome the limitations of traditional numerical solvers, which often require prohibitive computational costs for high-fidelity solutions. Recent…

One of the fundamental problems in machine learning is the estimation of a probability distribution from data. Many techniques have been proposed to study the structure of data, most often building around the assumption that observations…

We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially…

Over the last century, a large number of physical and mathematical developments paired with rapidly advancing technology have allowed the field of quantum chemistry to advance dramatically. However, the lack of computationally efficient…

High-performance graphical processing units (GPU) are used for the repeated parallelised propagation of non-linear partial differential equations on large spatio-temporal grids. The main challenge results as a combination of the requirement…

The limits of direct unitary transformation of many-fermion Hamiltonians are explored. Practical application of such transformations requires that effective many-body interactions be discarded over the course of a calculation. The…

Mapping functions on bits to Hamiltonians acting on qubits has many applications in quantum computing. In particular, Hamiltonians representing Boolean functions are required for applications of quantum annealing or the quantum approximate…

The advanced data structure of the zero-suppressed binary decision diagram (ZDD) enables us to efficiently enumerate nonequivalent substitutional structures. Not only can the ZDD store a vast number of structures in a compressed manner, but…

Differential dependencies (DDs) capture the relationships between data columns of relations. They are more general than functional dependencies (FDs) and and the difference is that DDs are defined on the distances between values of two…