Related papers: Optimal Control for Closed and Open System Quantum…
This work explores the relationship between optimal control theory and adiabatic passage techniques in quantum systems. The study is based on a geometric analysis of the Hamiltonian dynamics constructed from the Pontryagin Maximum…
We consider the optimal control of quantum systems interacting non-linearly with an electromagnetic field. We propose new monotonically convergent algorithms to solve the optimal equations. The monotonic behavior of the algorithm is ensured…
Quantum adiabatic optimization (QAO) is performed using a time-dependent Hamiltonian $H(s)$ with spectral gap $\gamma(s)$. Assuming the existence of an oracle $\Gamma$ such that $\gamma_\min = \Theta\left(\min_s\Gamma(s)\right)$, we provide…
Nonadiabatic unitary evolution with tailored time-dependent Hamiltonians can prepare systems of cold atomic gases with various desired properties. For a system of two one-dimensional quasicondensates coupled with a time-varying tunneling…
Quantum annealing is a promising algorithm for solving combinatorial optimization problems. It searches for the ground state of the Ising model, which corresponds to the optimal solution of a given combinatorial optimization problem. The…
To overcome the limitations of classical partially connected Boltzmann machines and mainstream quantum Boltzmann machines (QBMs), this work extends the conventional circuit of the quantum approximate optimization algorithm (QAOA) to a…
Extracting useful work from quantum systems is a fundamental problem in quantum thermodynamics. In scenarios where rapid protocols are desired -- whether due to practical constraints or deliberate design choices -- a fundamental trade-off…
We show how a digitized version of Quantum Annealing can be made optimal, realizing the best possible solution allowed by quantum mechanics in the shortest time, without any prior knowledge on the location and properties of the spectral…
Quantum annealing (QA) is a promising method for solving combinatorial optimization problems whose solutions are embedded into a ground state of the Ising Hamiltonian. This method employs two types of Hamiltonians: a driver Hamiltonian and…
We present a general theoretical framework for finding the time-optimal unitary evolution of the quantum systems when the Hamiltonian is subject to arbitrary constraints. Quantum brachistochrone (QB) is such a framework based on the…
Task scheduling with constrained time intervals and limited resources remains a fundamental challenge across domains such as manufacturing, logistics, cloud computing, and healthcare. This study presents a novel variant of the Quantum…
Optimal Control Theory is a powerful mathematical tool, which has known a rapid development since the 1950s, mainly for engineering applications. More recently, it has become a widely used method to improve process performance in quantum…
We consider the energy-optimal control problem for double-integrator systems subject to state and control constraints, with fixed terminal time and free terminal speed. When the constraints become active, the optimal trajectory consists of…
The quantum approximate optimization algorithm (QAOA) is a hybrid quantum-classical variational algorithm that offers the potential to handle combinatorial optimization problems. Introducing constraints in such combinatorial optimization…
We propose a quantum optimal control framework based on the Pontryagin Maximum Principle to design energy- and time-efficient pulses for open quantum systems. By formulating the Langevin equation of a dissipative LC circuit as a linear…
Quantum annealing (QA) is a method for solving combinatorial optimization problems. We can estimate the computational time for QA using the adiabatic condition. The adiabatic condition consists of two parts: an energy gap and a transition…
Quantum variational algorithms have garnered significant interest recently, due to their feasibility of being implemented and tested on noisy intermediate scale quantum (NISQ) devices. We examine the robustness of the quantum approximate…
Quantum Random Access Optimizer (QRAO) is a quantum-relaxation based optimization algorithm proposed by Fuller et al. that utilizes Quantum Random Access Code (QRAC) to encode multiple variables of binary optimization in a single qubit.…
Quantum computing holds promise for outperforming classical computing in specialized applications such as optimization. With current Noisy Intermediate Scale Quantum (NISQ) devices, only variational quantum algorithms like the Quantum…
We consider bilinear optimal control problems, whose objective functionals do not depend on the controls. Hence, bang-bang solutions will appear. We investigate sufficient second-order conditions for bang-bang controls, which guarantee…