Related papers: Towards Hamiltonian Simulation with Decision Diagr…
We significantly enhance the simulation accuracy of initial Trotter circuits for Hamiltonian simulation of quantum systems by integrating first-order Riemannian optimization with tensor network methods. Unlike previous approaches, our…
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.…
We present a framework for learning Hamiltonian systems using data. This work is based on a lifting hypothesis, which posits that nonlinear Hamiltonian systems can be written as nonlinear systems with cubic Hamiltonians. By leveraging this,…
Determining the physically accessible unitary dynamics of a quantum system under finite Hamiltonian resources is a central problem in quantum control and Hamiltonian engineering. Dynamical Lie algebras (DLAs) provide the fundamental link…
The evolution of a quantum system under time-dependent driving exhibits phenomena that are absent in its stationary counterpart. However, the high dimensionality and non-commutative nature of quantum dynamics make this a challenging…
Density functional theory is a successful branch of numerical simulations of quantum systems. While the foundations are rigorously defined, the universal functional must be approximated resulting in a `semi'-ab initio approach. The search…
Building on the established methods for superconducting circuit quantization, we present a new theoretical framework for approximate numerical simulation of Josephson quantum circuits. Simulations based on this framework provide access to a…
Decision diagrams for classification have some notable advantages over decision trees, as their internal connections can be determined at training time and their width is not bound to grow exponentially with their depth. Accordingly,…
Multi-physics simulations play a crucial role in understanding complex systems. However, their computational demands are often prohibitive due to high dimensionality and complex interactions, such that actual calculations often rely on…
We present a quantum algorithm to achieve higher-order transformations of Hamiltonian dynamics. Namely, the algorithm takes as input a finite number of queries to a black-box seed Hamiltonian dynamics to simulate a desired Hamiltonian. Our…
We present a quantum algorithm for the dynamical simulation of time-dependent Hamiltonians. Our method involves expanding the interaction-picture Hamiltonian as a sum of generalized permutations, which leads to an integral-free Dyson series…
In this paper we investigate the effectiveness of direct statistical simulation (DSS) for two low-order models of dynamo action. The first model, which is a simple model of solar and stellar dynamo action, is third-order and has cubic…
Decision Boundary Maps (DBMs) are an effective tool for visualising machine learning classification boundaries. Yet, DBM quality strongly depends on the dimensionality reduction (DR) technique and high dimensional space used for the data…
We provide a new paradigm for quantum simulation that is based on path integration that allows quantum speedups to be observed for problems that are more naturally expressed using the path integral formalism rather than the conventional…
Markov decisions processes (MDPs) are becoming increasing popular as models of decision theoretic planning. While traditional dynamic programming methods perform well for problems with small state spaces, structured methods are needed for…
Quantum computing can efficiently simulate Hamiltonian dynamics of many-body quantum physics, a task that is generally intractable with classical computers. The hardness lies at the ubiquitous anti-commutative relations of quantum…
Quantum computing is finding promising applications in optimization, machine learning and physics, leading to the development of various models for representing quantum information. Because these representations are often studied in…
Recently much attention has been paid to quantum circuit design to prepare for the future "quantum computation era." Like the conventional logic synthesis, it should be important to verify and analyze the functionalities of generated…
We study the efficiency of algorithms simulating a system evolving with Hamiltonian $H=\sum_{j=1}^m H_j$. We consider high order splitting methods that play a key role in quantum Hamiltonian simulation. We obtain upper bounds on the number…
Simulating Hamiltonian dynamics is one of the most fundamental and significant tasks for characterising quantum materials. Recently, a series of quantum algorithms employing block-encoding of Hamiltonians have succeeded in providing…