Quantum time dynamics mediated by the Yang-Baxter equation and artificial neural networks

2024-01-30

AI Summary

Quantum time-evolution simulation on Noisy Intermediate-Scale Quantum (NISQ) devices suffers from high noise sensitivity and error accumulation. Method: This work proposes a synergistic error-mitigation framework integrating the Yang–Baxter equation (YBE) with artificial neural networks (ANNs). YBE generates physically faithful, symmetry-preserving controllable noisy training data and enables quantum circuit compression; ANNs learn the noise-induced dynamical mapping and correct the output quantum states. Contribution/Results: To our knowledge, this is the first approach to leverage integrable-model-derived YBE for joint noise modeling and circuit optimization. Evaluated on Heisenberg XY spin-chain simulation, the framework significantly improves state fidelity on real NISQ hardware. It exhibits linear scalability and supports flexible deployment—either full-circuit or partial-circuit—demonstrating practical efficacy for medium-scale quantum systems.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Sampling/Simulation-based Search
• Intelligent Robots: State Estimation

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Quantum computing shows great potential, but errors pose a significant challenge. This study explores new strategies for mitigating quantum errors using artificial neural networks (ANN) and the Yang-Baxter equation (YBE). Unlike traditional error mitigation methods, which are computationally intensive, we investigate artificial error mitigation. We developed a novel method that combines ANN for noise mitigation combined with the YBE to generate noisy data. This approach effectively reduces noise in quantum simulations, enhancing the accuracy of the results. The YBE rigorously preserves quantum correlations and symmetries in spin chain simulations in certain classes of integrable lattice models, enabling effective compression of quantum circuits while retaining linear scalability with the number of qubits. This compression facilitates both full and partial implementations, allowing the generation of noisy quantum data on hardware alongside noiseless simulations using classical platforms. By introducing controlled noise through the YBE, we enhance the dataset for error mitigation. We train an ANN model on partial data from quantum simulations, demonstrating its effectiveness in mitigating errors in time-evolving quantum states, providing a scalable framework to enhance quantum computation fidelity, particularly in noisy intermediate-scale quantum (NISQ) systems. We demonstrate the efficacy of this approach by performing quantum time dynamics simulations using the Heisenberg XY Hamiltonian on real quantum devices.

Problem

• Mitigating quantum errors using neural networks and Yang-Baxter equation.
• Reducing noise in quantum simulations to enhance result accuracy.
• Improving quantum computation fidelity in NISQ systems.

Innovation

• Combines ANN with YBE for noise mitigation
• YBE preserves quantum correlations and symmetries
• Trains ANN on partial quantum simulation data