Quantum Search Approaches to Sampling-Based Motion Planning
arXiv:2304.06479 · doi:10.1109/ACCESS.2023.3307316
Abstract
In this paper, we present a novel formulation of traditional sampling-based motion planners as database-oracle structures that can be solved via quantum search algorithms. We consider two complementary scenarios: for simpler sparse environments, we formulate the Quantum Full Path Search Algorithm (q-FPS), which creates a superposition of full random path solutions, manipulates probability amplitudes with Quantum Amplitude Amplification (QAA), and quantum measures a single obstacle free full path solution. For dense unstructured environments, we formulate the Quantum Rapidly Exploring Random Tree algorithm, q-RRT, that creates quantum superpositions of possible parent-child connections, manipulates probability amplitudes with QAA, and quantum measures a single reachable state, which is added to a tree. As performance depends on the number of oracle calls and the probability of measuring good quantum states, we quantify how these errors factor into the probabilistic completeness properties of the algorithm. We then numerically estimate the expected number of database solutions to provide an approximation of the optimal number of oracle calls in the algorithm. We compare the q-RRT algorithm with a classical implementation and verify quadratic run-time speedup in the largest connected component of a 2D dense random lattice. We conclude by evaluating a proposed approach to limit the expected number of database solutions and thus limit the optimal number of oracle calls to a given number.
arXiv comment15 pages, 11 figures
References in corpus (19)
- Quantum Computation with Quantum Dots
- Elementary gates for quantum computation
- Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
- Quantum Convolutional Neural Networks
- Decoherence, the measurement problem, and interpretations of quantum mechanics
- Quantum Amplitude Amplification and Estimation
- Quantum computing for finance: overview and prospects
- Simulating Lattice Gauge Theories within Quantum Technologies
- Quantum reinforcement learning
- Computing prime factors with a Josephson phase qubit quantum processor
- Search via Quantum Walk
- Probabilities from Entanglement, Born's Rule from Envariance
- Quantum Counting
- Superconducting Qubits: A Short Review
- Quantum Navigation and Ranking in Complex Networks
- Quantum computing at the quantum advantage threshold: a down-to-business review
- Quantum annealing for systems of polynomial equations
- Percolation in Finite Matching Lattices
- Quantum Algorithms for Reinforcement Learning with a Generative Model