QuantGraph Achieves 60% Search Space Reduction for Faster Graph Optimization

Graph-based optimisation problems underpin many areas of science and engineering, yet their complexity often limits the size of problems that can be solved efficiently. Pranav Vaidhyanathan, Aristotelis Papatheodorou, and colleagues from the University of Oxford and Hitachi Cambridge Laboratory present QuantGraph, a novel framework that tackles this challenge by combining the power of quantum computation with principles from control theory. This innovative approach casts graph optimisation as a search over possible trajectories, significantly reducing the computational burden and achieving a two-fold increase in precision for a given computational effort. By intelligently pruning the search space and embedding the quantum solver within a robust control scheme, QuantGraph represents a substantial advance in tackling complex optimisation challenges and opens new possibilities for applying quantum algorithms to real-world problems.

Graph Solver Optimizes Quantum System Control

QuantGraph is a new method for controlling quantum systems represented as networks of interconnected qubits, efficiently determining the control pulses needed to steer a system from a starting point to a desired target state. The method uses graph theory to represent system connections and employs a specialised optimisation algorithm to minimise deviations from the target state, ensuring control pulses are physically achievable and energy-efficient. QuantGraph breaks down the overall control task into a series of shorter, optimisable problems, repeatedly refining the solution to account for the system’s ongoing evolution. Evaluations on standard quantum control tasks, such as state transfer and entanglement generation, demonstrate QuantGraph’s ability to achieve high-fidelity control with reduced computational demands.

A key innovation is a novel graph-based representation that effectively captures system connectivity, facilitating efficient optimisation and enabling the solver to leverage the underlying structure of the quantum system. The method’s adaptive strategy enhances robustness and reliability, achieving 99.7% fidelity on a four-qubit system for a specific state transfer task, demonstrating potential for practical applications in quantum information processing.

Dynamic programming is a powerful technique for graph-based optimisation, but its computational demands increase rapidly with problem size. Researchers developed QuantGraph, a two-stage framework that casts optimisation problems as quantum searches over possible trajectories. The solver first identifies a sequence of locally optimal transitions, reducing the search space by up to 60% for certain examples, and then builds upon this reduced space to find the best overall solution.

Robotics Learns Optimal Control via Reinforcement

This research addresses the challenge of solving complex optimal control problems, particularly in robotics and physical systems. Traditional dynamic programming struggles with high-dimensional state spaces, limiting its applicability. The team proposes leveraging quantum computing to overcome these limitations and enable more sophisticated control strategies, introducing Metasym, a framework designed to represent and learn the dynamics of physical systems suitable for both classical and quantum computation. Symplectic geometry plays a crucial role, preserving the inherent structure of systems governed by energy conservation.

The core idea is to use quantum algorithms to accelerate key steps in the dynamic programming process, specifically value function approximation and policy optimisation. This involves a hybrid approach where classical computers handle data processing and system modelling, while quantum computers accelerate the most computationally intensive parts, utilising qubits to represent states and actions. The team intends to employ quantum algorithms such as Grover’s algorithm and quantum amplitude estimation to speed up the search for optimal solutions, potentially using Variational Quantum Eigensolver for optimisation within the control loop, and utilises Qiskit, IBM’s open-source quantum computing framework. This research has the potential to advance robotics, autonomous systems, and the optimal control of complex systems in areas such as aerospace, energy, and manufacturing. It could also optimise resource allocation in supply chains and logistics networks, and aid scientific discovery by modelling and controlling complex physical phenomena. The interdisciplinary nature of the work, combining quantum computing, control theory, machine learning, and robotics, is a significant strength, although challenges remain, including limitations of current quantum hardware and the scalability of the approach to high-dimensional state spaces.

Grover Search Boosts Optimisation Precision Twofold

QuantGraph represents a significant advance in graph-based optimisation, combining quantum computation with classical control techniques. Researchers successfully reformulated dynamic programming as a search over possible trajectories, employing a two-stage approach to enhance efficiency. The initial stage identifies promising trajectories and reduces the search space, while the subsequent stage, powered by Grover-adaptive-search, refines the solution with improved precision, achieving a two-fold increase in control-discretisation precision compared to existing methods for a given computational budget. The team’s work demonstrates a strong link between quantum optimisation and practical control applications, successfully applied to both linear and nonlinear dynamic systems like the double integrator and cart-pole. The framework’s integration with a receding-horizon model-predictive-control scheme not only stabilises the search process but also offers practical advantages for implementation on near-term quantum hardware by limiting circuit depth and mitigating decoherence. While the current implementation relies on discrete trajectory spaces, researchers acknowledge the potential for future work to incorporate quantum algorithms for continuous optimisation and further investigate nonlinear dynamics.