Related papers: Analysis of the Non-variational Quantum Walk-based…
We present a detailed analysis of continuous time quantum walks (CTQW) with both position and transition defects defined at a single point in the line. Analytical solutions of both traveling waves or bound states are obtained, which provide…
In this study, we propose a new method for constrained combinatorial optimization using variational quantum circuits. Quantum computers are considered to have the potential to solve large combinatorial optimization problems faster than…
Quantum computing offers an alternative paradigm for addressing combinatorial optimization problems compared to classical computing. Despite recent hardware improvements, the execution of empirical quantum optimization experiments at scales…
A promising approach to useful computational quantum advantage is to use variational quantum algorithms for optimisation problems. Crucial for the performance of these algorithms is to ensure that the algorithm converges with high…
The variational principle serves as a fundamental framework for describing equilibrium states of physical systems via the minimization or extremization of an energy-like functional. While quantum algorithms have demonstrated promising…
Quantum walks are the quantum-mechanical analog of random walks, in which a quantum `walker' evolves between initial and final states by traversing the edges of a graph, either in discrete steps from node to node or via continuous evolution…
The execution of quantum algorithms on modern hardware is often constrained by noise and qubit decoherence, limiting the circuit depth and the number of gates that can be executed. Circuit optimization techniques help mitigate these…
Variational quantum algorithms (VQA) have emerged as a promising quantum alternative for solving optimization and machine learning problems using parameterized quantum circuits (PQCs). The design of these circuits influences the ability of…
We consider a parametric quasi-variational inequality (QVI) without any convexity assumption. Using the concept of \emph{optimal value function}, we transform the problem into that of solving a nonsmooth system of inequalities. Based on…
This work shows that minimizing the depth of a quantum circuit composed of commuting operations reduces to a vertex coloring problem on an appropriately constructed graph, where gates correspond to vertices and edges encode…
Proposed hybrid algorithms encode a combinatorial cost function into a problem Hamiltonian and optimize its energy by varying over a set of states with low circuit complexity. Classical processing is typically only used for the choice of…
Challenging combinatorial optimization problems are ubiquitous in science and engineering. Several quantum methods for optimization have recently been developed, in different settings including both exact and approximate solvers. Addressing…
Solving combinatorial optimization problems on near-term quantum devices has gained a lot of attraction in recent years. Currently, most works have focused on single-objective problems, whereas many real-world applications need to consider…
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…
Many-particle continuous-time quantum walks (CTQWs) represent a resource for several tasks in quantum technology, including quantum search algorithms and universal quantum computation. In order to design and implement CTQWs in a realistic…
Quantum walks have proven to be a universal model for quantum computation and to provide speed-up in certain quantum algorithms. The discrete-time quantum walk (DTQW) model, among others, is one of the most suitable candidates for circuit…
Computing using a continuous-time evolution, based on the natural interaction Hamiltonian of the quantum computer hardware, is a promising route to building useful quantum computers in the near-term. Adiabatic quantum computing, quantum…
This paper introduces weighted-BMP, a variant of the Bandwidth Minimization Problem (BMP), with a significant application in optimizing quantum emulation. Weighted-BMP optimizes particles ordering to reduce the emulation costs, by designing…
Markov Chain Monte Carlo (MCMC) methods are algorithms for sampling probability distributions, commonly applied to the Boltzmann distribution in physical and chemical models such as protein folding and the Ising model. These methods enable…
We introduce a quantum algorithm that produces approximate solutions for combinatorial optimization problems. The algorithm depends on a positive integer p and the quality of the approximation improves as p is increased. The quantum circuit…