Related papers: Quantum Hamiltonian Descent
Gaussian processes are widely known for their ability to provide probabilistic predictions in supervised machine learning models. Their non-parametric nature and flexibility make them particularly effective for regression tasks. However,…
Quantum state tomography (QST) is a widely employed technique for characterizing the state of a quantum system. However, it is plagued by two fundamental challenges: computational and experimental complexity grows exponentially with the…
The recent emergence of novel computational devices, such as quantum computers, coherent Ising machines, and digital annealers presents new opportunities for hardware-accelerated hybrid optimization algorithms. Unfortunately, demonstrations…
We initiate the study of online quantum state tomography (QST), where the matrix representation of an unknown quantum state is reconstructed by sequentially performing a batch of measurements and updating the state estimate using only the…
Hard Attention Mechanisms (HAMs) effectively filter essential information discretely and significantly boost the performance of machine learning models on large datasets. Nevertheless, they confront the challenge of non-differentiability,…
Within the context of hybrid quantum-classical optimization, gradient descent based optimizers typically require the evaluation of expectation values with respect to the outcome of parameterized quantum circuits. In this work, we explore…
Quantum annealing is a heuristic optimization algorithm that exploits quantum evolution to approximately find lowest energy states. Quantum annealers have scaled up in recent years to tackle increasingly larger and more highly connected…
We propose an efficient quantum algorithm for simulating the dynamics of general Hamiltonian systems. Our technique is based on a power series expansion of the time-evolution operator in its off-diagonal terms. The expansion decouples the…
Machine learning techniques have achieved impressive results in recent years and the possibility of harnessing the power of quantum physics opens new promising avenues to speed up classical learning methods. Rather than viewing classical…
Gradient Descent (GD) is a ubiquitous algorithm for finding the optimal solution to an optimization problem. For reduced computational complexity, the optimal solution $\mathrm{x^*}$ of the optimization problem must be attained in a minimum…
Classical algorithms are often not effective for solving nonconvex optimization problems where local minima are separated by high barriers. In this paper, we explore possible quantum speedups for nonconvex optimization by leveraging the…
We present an efficient quantum algorithm aiming to find the negative curvature direction for escaping the saddle point, which is the critical subroutine for many second-order non-convex optimization algorithms. We prove that our algorithm…
Quantum coherence, rooted in the superposition principle of quantum mechanics, is a crucial quantum resource. Various measures, operational interpretations, and generalizations of quantum coherence have been proposed. In recent years, its…
We demonstrate provable (sub)exponential quantum speedups in both discrete and continuous optimization, achieved through simple and natural quantum optimization algorithms, namely the quantum adiabatic algorithm for discrete optimization…
Using the methods of quantum trajectories we investigate the effects of dissipative decoherence in a quantum computer algorithm simulating dynamics in various regimes of quantum chaos including dynamical localization, quantum ergodic regime…
The Harrow-Hassidim-Lloyd (HHL) quantum algorithm for sampling from the solution of a linear system provides an exponential speed-up over its classical counterpart. The problem of solving a system of linear equations has a wide scope of…
We present a quantum algorithm for finding the minimum of a function based on multistep quantum computation and apply it for optimization problems with continuous variables, in which the variables of the problem are discretized to form the…
When applying quantum computing to machine learning tasks, one of the first considerations is the design of the quantum machine learning model itself. Conventionally, the design of quantum machine learning algorithms relies on the…
Deep learning has been shown to be able to recognize data patterns better than humans in specific circumstances or contexts. In parallel, quantum computing has demonstrated to be able to output complex wave functions with a few number of…
This paper introduces a vision for Quantum Software Development lifecycle, proposing a hybrid full-stack iterative model that integrates quantum and classical computing. Addressing the current challenges in Quantum Computing (QC) such as…