Related papers: A Lyapunov Framework for Quantum Algorithm Design …
Let $f:\mathbb{R}^n \to \mathbb{R}$ be a continuously differentiable convex function with its minimizer denoted by $x_*$ and optimal value $f_* = f(x_*)$. Optimization algorithms such as the gradient descent method can often be interpreted…
Von Neumann projections are the main operations by which information can be extracted from the quantum to the classical realm. They are however static processes that do not adapt to the states they measure. Advances in the field of adaptive…
In many real-world reinforcement learning (RL) problems, besides optimizing the main objective function, an agent must concurrently avoid violating a number of constraints. In particular, besides optimizing performance it is crucial to…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
Algorithms which compute locally optimal continuous designs often rely on a finite design space or on repeatedly solving a complex non-linear program. Both methods require extensive evaluations of the Jacobian Df of the underlying model.…
The continuous-time differential Lyapunov equation is widely used in linear optimal control theory, a branch of mathematics and engineering. In quantum physics, it is known to appear in Markovian descriptions of linear (quadratic…
The quantum approximate optimization algorithm (QAOA) promises to solve classically intractable computational problems in the area of combinatorial optimization. A growing amount of evidence suggests that the originally proposed form of the…
One of the main limitations of variational quantum algorithms is the classical optimization of the highly dimensional non-convex variational parameter landscape. To simplify this optimization, we can reduce the search space using problem…
The MaxCut problem is a fundamental problem in Combinatorial Optimization, with significant implications across diverse domains such as logistics, network design, and statistical physics. The algorithm represents innovative approaches that…
We initiate the algorithmic study of the Quantum Max-$d$-Cut problem, a quantum generalization of the well-known Max-$d$-Cut problem. The Quantum Max-$d$-Cut problem involves finding a quantum state that maximizes the expected energy…
Quantum algorithms have been widely studied in the context of combinatorial optimization problems. While this endeavor can often analytically and practically achieve quadratic speedups, theoretical and numeric studies remain limited,…
Variational quantum algorithms involve training parameterized quantum circuits using a classical co-processor. An important variational algorithm, designed for combinatorial optimization, is the quantum approximate optimization algorithm.…
Hybrid quantum-classical optimization algorithms represent one of the most promising application for near-term quantum computers. In these algorithms the goal is to optimize an observable quantity with respect to some classical parameters,…
We present a general framework for finding the time-optimal evolution and the optimal Hamiltonian for a quantum system with a given set of initial and final states. Our formulation is based on the variational principle and is analogous to…
Imaginary-time evolution is fundamental for analyzing quantum many-body systems, yet classical simulation requires exponentially growing resources in both system size and evolution time. While quantum approaches reduce the system-size…
Advances in quantum algorithms suggest a tentative scaling advantage on certain combinatorial optimization problems. Recent work, however, has also reinforced the idea that barren plateaus render variational algorithms ineffective on large…
As combinatorial optimization is one of the main quantum computing applications, many methods based on parameterized quantum circuits are being developed. In general, a set of parameters are being tweaked to optimize a cost function out of…
This paper presents new sufficient conditions for convergence and asymptotic or exponential stability of a stochastic discrete-time system, under which the constructed Lyapunov function always decreases in expectation along the system's…
Efficient simulation of quantum dynamics with time-dependent Hamiltonians is important not only for time-varying systems but also for time-independent Hamiltonians in the interaction picture. Such simulations are more challenging than their…
For complex nonlinear systems, it is challenging to design algorithms that are fast, scalable, and give an accurate approximation of the stability region. This paper proposes a sampling-based approach to address these challenges. By…