Evaluating the noise resilience of variational quantum algorithms (2011.01125v3)

Abstract: We simulate the effects of different types of noise in state preparation circuits of variational quantum algorithms. We first use a variational quantum eigensolver to find the ground state of a Hamiltonian in presence of noise, and adopt two quality measures in addition to the energy, namely fidelity and concurrence. We then extend the task to the one of constructing, with a layered quantum circuit ansatz, a set of general random target states. We determine the optimal circuit depth for different types and levels of noise, and observe that the variational algorithms mitigate the effects of noise by adapting the optimised parameters. We find that the inclusion of redundant parameterised gates makes the quantum circuits more resilient to noise. For such overparameterised circuits different sets of parameters can result in the same final state in the noiseless case, which we denote as parameter degeneracy. Numerically, we show that this degeneracy can be lifted in the presence of noise, with some states being significantly more resilient to noise than others. We also show that the average deviation from the target state is linear in the noise level, as long as this is small compared to a circuit-dependent threshold. In this region the deviation is well described by a stochastic model. Above the threshold, the optimisation can converge to states with largely different physical properties from the true target state, so that for practical applications it is critical to ensure that noise levels are below this threshold.

Evaluating the Impact of Noise on Variational Quantum Algorithms

Variational Quantum Algorithms (VQAs) hold significant promise for noisy intermediate-scale quantum (NISQ) computing, combining quantum subroutines with classical optimization to explore complex quantum problems. In the paper titled "Evaluating the Noise Resilience of Variational Quantum Algorithms," the authors provide a meticulous paper on the adaptability of VQAs in the presence of diverse noise types and levels. This investigation is strategically conducted using variational quantum eigensolver (VQE) simulations and fidelity maximization for general target states.

Noise Models on Quantum Circuits

The paper analyzes the impact of three noise channels: phase damping, amplitude damping, and symmetric depolarising noise. These noise channels capture the primary decoherence phenomena present in NISQ devices. For each noise model, the paper dissects VQAs' performance by exploring variations in circuit configurations and optimizing quantum gates' parameters to assess noise resilience. In doing so, the work underscores the necessity of robust noise models as they directly affect resistance to quantum state deviations.

Circuit Ansätze and Parameter Degeneracies

By employing different circuit ansätze for 2-qubit and 4-qubit systems, the authors investigate how layout variations impact noise resilience. A particular focus is placed on overparameterised circuits, which have redundant parameters that are shown to lift degeneracy in noisy environments. These redundant parameters provide alternative paths in parameter space that lead to more noise-resilient states under specific noise conditions. The exploration of parameter degeneracies reveals critical insights into quantum circuit design, emphasizing that strategic placement and redundancy can significantly enhance noise mitigation.

Simulations on Random Target States

The paper furthers its exploration through simulations designed to optimize fidelity with random target states. In this general setting, the work evaluates how noise interferes with a circuit's ability to recreate desired quantum states, introducing a linear noise model to predict relative infidelity for low noise levels. Notably, this linear model factors each noise channel's additive effect, allowing for an insightful approximation of how noise propagates through quantum circuits. The results indicate that the model successfully captures the average infidelity trends, providing a foundational understanding of noise influence over complex systems.

Implications and Future Directions

This comprehensive examination of noise resilience in VQAs offers valuable knowledge that can inform both theoretical and practical directions in quantum computing. Practically, the findings emphasize the importance of optimizing quantum circuit designs to account for noise types specific to quantum hardware. Theoretically, the paper promotes further investigation into how parameter degeneracies and circuit overparameterisation can be exploited systematically to improve quantum algorithms' robustness against noise.

Looking ahead, expanding this research to include shot noise and readout errors could refine strategies for deploying VQAs on real-world quantum devices. Moreover, exploring how these findings scale with circuit complexity and different quantum architectures could unlock new potentials in VQE applications, ultimately guiding future innovations in quantum algorithm resilience and efficiency.

In summary, this paper provides a compelling probe into the nuanced behaviors of VQAs under noisy conditions, advancing our understanding and shaping future quantum algorithm development in NISQ technologies.