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Nonadiabatic holonomic quantum computation (NHQC) has been developed to shorten the construction times of geometric quantum gates. However, previous NHQC gates require the driving Hamiltonian to satisfy a set of rather restrictive…
Loop Quantum Gravity faces challenges in constructing a well-defined Hamiltonian constraint and understanding the quantum notion of time. In this paper these issues are studied by quantizing the $U(1)^3$ model, a simplified system…
The aim of this paper is to adapt the general multitime maximum principle to a Riemannian setting. More precisely, we intend to study geometric optimal control problems constrained by the metric compatibility evolution PDE system; the…
Quantum walks are the quantum-mechanical analog of random walks, in which a quantum `walker' evolves between initial and final states by traversing the edges of a graph, either in discrete steps from node to node or via continuous evolution…
What is the shortest path between two data points lying in a high-dimensional space? While the answer is trivial in Euclidean geometry, it becomes significantly more complex when the data lies on a curved manifold -- requiring a Riemannian…
We propose a new variational quantum algorithm, which we refer to as TIMES-ADAPT, that prepares time-evolved states in a low-energy or symmetric subspace of a time-independent Hamiltonian on a quantum computer. Using a specially trained…
We analyze a scheme for quantum computation where quantum gates can be continuously changed from standard dynamic gates to purely geometric ones. These gates are enacted by controlling a set of parameters that are subject to unwanted…
Quantum computation based on geometric phase is generally believed to be more robust against certain errors or noises than the conventional dynamical strategy. However, the gate error caused by the decoherence effect is inevitable, and thus…
Recent advancements in the discipline of quantum algorithms have displayed the importance of the geometry of quantum operators. Given this thrust, this paper develops a rigorous geometric framework to analyze how the Riemannian structure of…
The Rodeo Algorithm is a quantum computing method for computing the energy spectrum of a Hamiltonian and preparing its energy eigenstates. We discuss how to improve the performance of the rodeo algorithm for each of these two applications.…
We study the Hamiltonian-independent contribution to the complexity of quantum optimal control problems. The optimization of controls that steer quantum systems to desired objectives can itself be considered a classical dynamical system…
Entangled resources enable quantum sensing that achieves Heisenberg scaling, a quadratic improvement on the standard quantum limit, but preparing large scale entangled states is challenging in the presence of decoherence. We present a…
Quantum gates (unitary gates) on physical systems are usually implemented by controlling the Hamiltonian dynamics. When full descriptions of the Hamiltonians parameters is available, the set of implementable quantum gates is easily…
A challenge for molecular quantum dynamics (QD) calculations is the curse of dimensionality with respect to the nuclear degrees of freedom. A common approach that works especially well for fast reactive processes is to reduce the…
In this work, we consider a model of two qubits driven by coherent and incoherent time-dependent controls. The dynamics of the system is governed by a Gorini-Kossakowski-Sudarshan-Lindblad master equation, where coherent control enters into…
We present a unitary control pulse design method for a scalable quantum computer architecture based on electron spins in lateral quantum dots. We employ simultaneous control of spin interactions and derive the functional forms of spin…
We propose a nonadiabatic non-Abelian geometric quantum operation scheme to realize universal quantum computation with mesoscopic Rydberg atoms. A single control atom entangles a mesoscopic ensemble of target atoms through long-range…
The geometry of generative models serves as the basis for interpolation, model inspection, and more. Unfortunately, most generative models lack a principal notion of geometry without restrictive assumptions on either the model or the data…
When the gate set has continuous parameters, synthesizing a unitary operator as a quantum circuit is always possible using exact methods, but finding minimal circuits efficiently remains a challenging problem. The landscape is very…
Reliable quantum information technologies depend on precise actuation and techniques to mitigate the effects of undesired disturbances such as environmental noise and imperfect calibration. In this work, we present a general framework based…