Related papers: High-Order Hermite Optimization: Fast and Exact Gr…
This paper proposes a new hybrid high-order discretization for the biharmonic problem and the corresponding eigenvalue problem. The discrete ansatz space includes degrees of freedom in $n-2$ dimensional submanifolds (e.g., nodal values in…
Farhi et al. recently proposed a class of quantum algorithms, the Quantum Approximate Optimization Algorithm (QAOA), for approximately solving combinatorial optimization problems. A level-p QAOA circuit consists of p steps; in each step a…
High-fidelity control of quantum systems is essential for scalable quantum technologies. We introduce a shooting-based method which yields smooth control pulses designed to implement gates on discrete quantum systems, and demonstrate its…
Simulating the time evolution of a physical system at quantum mechanical levels of detail -- known as Hamiltonian Simulation (HS) -- is an important and interesting problem across physics and chemistry. For this task, algorithms that run on…
This paper is concerned with the theory, construction and application of variable-stepsize implicit Peer two-step methods that are super-convergent for variable stepsizes, i.e., preserve their classical order achieved for uniform stepsizes…
In this paper, we study the Multi-Objective Bi-Level Optimization (MOBLO) problem, where the upper-level subproblem is a multi-objective optimization problem and the lower-level subproblem is for scalar optimization. Existing gradient-based…
Variational quantum algorithms are believed to be promising for solving computationally hard problems and are often comprised of repeated layers of quantum gates. An example thereof is the quantum approximate optimization algorithm (QAOA),…
A new methodology is proposed to solve classical Boolean problems as Hamiltonians, using the quantum approximate optimization algorithm (QAOA). Our methodology successfully finds all optimized approximated solutions for Boolean problems,…
We demonstrate the efficiency of a recent exact-gradient optimal control methodology by applying it to a challenging many-body problem, crossing the superfluid to Mott-insulator phase transition in the Bose-Hubbard model. The system size…
Auto-correlated noise appears in many solid state qubit systems and hence needs to be taken into account when developing gate operations for quantum information processing. However, explicitly simulating this kind of noise is often less…
Designing a high-quality control is crucial for reliable quantum computation. Among the existing approaches, closed-loop leaning control is an effective choice. Its efficiency depends on the learning algorithm employed, thus deserving…
Developing scalable, fault-tolerant atomic quantum processors requires precise control over large arrays of optical beams. This remains a major challenge due to inherent imperfections in classical control hardware, such as inter-channel…
Current quantum programs are mostly synthesized and compiled on the gate-level, where quantum circuits are composed of quantum gates. The gate-level workflow, however, introduces significant redundancy when quantum gates are eventually…
Constrained combinatorial optimization with strict linear constraints underpins applications in drug discovery, power grids, logistics, and finance, yet remains computationally demanding for classical algorithms, especially at large scales.…
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.…
The increasing demand for democratizing machine learning algorithms calls for hyperparameter optimization (HPO) solutions at low cost. Many machine learning algorithms have hyperparameters which can cause a large variation in the training…
This work proposes a higher-order iterative framework for solving matrix equations, inspired by the structure and functionality of neural networks. A modification of the classical Jacobi iterative method is introduced to compute…
The quantum approximate optimization algorithm (QAOA) has been introduced as a heuristic digital quantum computing scheme to find approximate solutions of combinatorial problems with shallow circuits. We present a scheme to parallelize this…
We develop universal gradient methods for Stochastic Convex Optimization (SCO). Our algorithms automatically adapt not only to the oracle's noise but also to the H\"older smoothness of the objective function without a priori knowledge of…
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…