Related papers: False traps on quantum-classical optimization land…
Given a training set, a loss function, and a neural network architecture, it is often taken for granted that optimal network parameters exist, and a common practice is to apply available optimization algorithms to search for them. In this…
We analyze a recent claim that almost all closed, finite dimensional quantum systems have trap-free (i.e., free from local optima) landscapes (B. Russell et.al. J. Phys. A: Math. Theor. 50, 205302 (2017)). We point out several errors in the…
We establish three tractable, jointly sufficient conditions for the control landscapes of non-linear control systems to be trap free comparable to those now well known in quantum control. In particular, our results encompass end-point…
Advancements in classical computing have significantly enhanced machine learning applications, yet inherent limitations persist in terms of energy, resource and speed. Quantum machine learning algorithms offer a promising avenue to overcome…
Variational Quantum Algorithms have emerged as a leading paradigm for near-term quantum computation. In such algorithms, a parameterized quantum circuit is controlled via a classical optimization method that seeks to minimize a…
In this paper we study the problem of learning a shallow artificial neural network that best fits a training data set. We study this problem in the over-parameterized regime where the number of observations are fewer than the number of…
One of the major application areas of interest for both near-term and fault-tolerant quantum computers is the optimization of classical objective functions. In this work, we develop intuitive constructions for a large class of these…
Quantum optimization holds promise for addressing classically intractable combinatorial problems, yet a standardized framework for benchmarking its performance, particularly in terms of solution quality, computational speed, and scalability…
Two main challenges preventing efficient training of variational quantum algorithms and quantum machine learning models are local minima and barren plateaus. Typically, barren plateaus are associated with deep circuits, while shallow…
Using a recently proposed model for combinatorial landscapes, Local Optima Networks (LON), we conduct a thorough analysis of two types of instances of the Quadratic Assignment Problem (QAP). This network model is a reduction of the…
Recent advances in quantum computers are demonstrating the ability to solve problems at a scale beyond brute force classical simulation. As such, a widespread interest in quantum algorithms has developed in many areas, with optimization…
The problems of optimizing the value of an arbitrary observable of the two-level system at both a fixed time and the shortest possible time is theoretically explored. Complete identification and classification along with comprehensive…
The prospect of achieving quantum advantage with Quantum Neural Networks (QNNs) is exciting. Understanding how QNN properties (e.g., the number of parameters $M$) affect the loss landscape is crucial to the design of scalable QNN…
One of the most important properties of classical neural networks is how surprisingly trainable they are, though their training algorithms typically rely on optimizing complicated, nonconvex loss functions. Previous results have shown that…
The control of quantum system dynamics is generally performed by seeking a suitable applied field. The physical objective as a functional of the field forms the quantum control landscape, whose topology, under certain conditions, has been…
We present a comprehensive analysis of the landscape for full quantum-quantum control associated with the expectation value of an arbitrary observable of one quantum system controlled by another quantum system. It is shown that such full…
Training quantum neural networks (QNNs) using gradient-based or gradient-free classical optimisation approaches is severely impacted by the presence of barren plateaus in the cost landscapes. In this paper, we devise a framework for…
Automated per-instance algorithm selection and configuration have shown promising performances for a number of classic optimization problems, including satisfiability, AI planning, and TSP. The techniques often rely on a set of features…
We present two quantum interior point methods for semidefinite optimization problems, building on recent advances in quantum linear system algorithms. The first scheme, more similar to a classical solution algorithm, computes an inexact…
Variational Quantum Circuits (VQCs) have emerged as a promising paradigm for quantum machine learning in the NISQ era. While parameter sharing in VQCs can reduce the parameter space dimensionality and potentially mitigate the barren plateau…