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

TL;DR

This work tackles quantum errors in time-dependent quantum simulations on NISQ devices by marrying artificial neural networks (ANN) with Yang-Baxter equation (YBE) based circuit compression. YBE enables constant-depth circuit compression that preserves essential quantum correlations, while ANN learns to map noisy observables to their noiseless counterparts using data generated from partially compressed circuits. The authors demonstrate effective error mitigation for time evolution under the XY spin-chain Hamiltonian on real IBM hardware, requiring only modest training data and enabling scalable mitigation in larger systems. This approach offers a practical pathway to improve quantum fidelity in time-dependent simulations and could extend to broader Hamiltonians and hardware platforms.

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.

Figures (12)

• Figure 1: Different variation of performing folding of gates. Top diagram shows the global folding where the whole unitary, $U$ is folded. The bottom diagram shows local folding where each part of whole unitary is folded individually.
• Figure 2: Pulse stretching to increase noise in a physical device
• Figure 3: Quantum circuit representation of the YBE for three qubits.
• Figure 4: (A) Quantum circuit representation of the YBE for three qubits. (B) Reflection symmetry is achieved by using the YBE four times on four qubits (action of YBE on which triplets is shown by black dots)
• Figure 5: Compression scheme for 4 qubits. Reflection symmetry exists with two layers of alternative gates. Addition of a third layer can be absorbed into the two layers by recursive usage of reflection symmetry (red bracket) via the YBE and merge identity.