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Probabilistic Navigation with Quantum Circuits

Alberto Delgado

Published Mar 27, 2023• 0 citations
Publisher

Abstract

A probabilistic controller, for robot navigation with behaviors, is designed using the basic mathematical framework of quantum computing. The controller changes behavior probabilities following sensor readings, behaviors depend on arena and platform properties, not just obstacles, also controller gains can be programmed by direct external signals.

DOI
10.36227/techrxiv.22310284.v1

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A probabilistic controller, for robot navigation with behaviors, is designed using the basic mathematical framework of quantum computing. The controller changes behavior probabilities following sensor readings, behaviors depend on arena and platform properties, not just obstacles, also controller gains can be programmed by direct external signals.
In this paper studied are new concepts of robotic behaviors - deterministic and quantum probabilistic. In contrast to classical circuits, the quantum circuit can realize both of these behaviors. When applied to a robot, a quantum circuit controller realizes what we call quantum robot behaviors. We use automated methods to synthesize quantum behaviors (circuits) from the examples (examples are cares of the quantum truth table). The don't knows (minterms not given as examples) are then converted not only to deterministic cares as in the classical learning, but also to output values generated with various probabilities. The Occam Razor principle, fundamental to inductive learning, is satisfied in this approach by seeking circuits of reduced complexity. This is illustrated by the synthesis of single output quantum circuits, as we extended the logic synthesis approach to Inductive Machine Learning for the case of learning quantum circuits from behavioral examples.
This paper proposes a novel approach to quantum algorithm design by leveraging probabilistic programming. Traditional quantum algorithm design often relies on precise circuit specifications, which can be challenging due to the inherent uncertainty in quantum systems. We introduce a framework that allows users to define quantum algorithms as probability distributions, explicitly modeling the probabilistic nature of quantum computation. This framework enables the exploration of a wider range of potential solutions, facilitates optimization strategies based on probability, and provides a more intuitive way to design and understand quantum algorithms. The core concept is to represent quantum circuits not as deterministic operations, but as probability distributions over possible outcomes. This approach is particularly relevant for noisy intermediate-scale quantum (NISQ) devices where errors are unavoidable and inherent probability plays a crucial role. We outline the key components of this framework, including a probabilistic programming language extension and a mechanism for translating circuit descriptions into probability distributions. The work demonstrates the potential of probabilistic programming to overcome the limitations of traditional design methods and accelerate the development of practical quantum algorithms.
The design of optimal quantum circuits for specific tasks remains a significant challenge due to the exponentially growing complexity of possible circuit architectures. Traditional optimization methods struggle to navigate this vast design space effectively. This work proposes a novel approach leveraging probabilistic programming languages and Bayesian optimization to address this problem. We represent quantum circuits as probabilistic programs and utilize Bayesian optimization to efficiently explore the design space, driven by objective functions that quantify desired circuit properties such as fidelity and gate count. This approach allows for a systematic and data-driven exploration, moving beyond exhaustive search methods. The core contribution lies in the application of probabilistic programming to quantum circuit design, offering a scalable and adaptive framework for discovering high-performance circuits. The methodology presented provides a framework for efficient exploration of quantum circuit design space, which is critical for realizing the potential of quantum computing.
A quantum-inspired Q-learning (QIQL) algorithm is proposed for indoor robot navigation control. Q- learning is an action-dependent reinforcement learning method and has been widely used in robot navigation. Inspired by the fundamental characteristics of quantum computation, e.g. state superposition principle and quantum parallel computation, probability is introduced to Q-learning and along with the learning process the probability of each action to be selected at a certain state is updated, which leads to a natural exploration strategy instead of a pointed one with configured parameters. The simulated navigation experiments show that the proposed QIQL algorithm keeps a good balance of exploration and exploitation, which can avoid the local optimal policies and accelerate the learning process as well.