Quantum Hamiltonian Learning Using Imperfect Quantum Resources (1311.5269v2)

Abstract: Identifying an accurate model for the dynamics of a quantum system is a vexing problem that underlies a range of problems in experimental physics and quantum information theory. Recently, a method called quantum Hamiltonian learning has been proposed by the present authors that uses quantum simulation as a resource for modeling an unknown quantum system. This approach can, under certain circumstances, allow such models to be efficiently identified. A major caveat of that work is the assumption of that all elements of the protocol are noise-free. Here, we show that quantum Hamiltonian learning can tolerate substantial amounts of depolarizing noise and show numerical evidence that it can tolerate noise drawn from other realistic models. We further provide evidence that the learning algorithm will find a model that is maximally close to the true model in cases where the hypothetical model lacks terms present in the true model. Finally, we also provide numerical evidence that the algorithm works for non-commuting models. This work illustrates that quantum Hamiltonian learning can be performed using realistic resources and suggests that even imperfect quantum resources may be valuable for characterizing quantum systems.

Quantum Hamiltonian Learning Using Imperfect Quantum Resources

The paper "Quantum Hamiltonian Learning Using Imperfect Quantum Resources" provides an insightful discussion on the challenges and methodologies involved in modeling quantum systems through Hamiltonian learning using quantum simulators. The primary focus is on the quantum Hamiltonian learning (QHL) algorithm which leverages Bayesian inference and quantum resources to efficiently estimate Hamiltonian parameters of uncharacterized quantum systems, even with the presence of realistic noise.

Overview of Quantum Hamiltonian Learning

Identifying an accurate Hamiltonian model of a quantum system is crucial for understanding its dynamics, which is particularly challenging for large quantum systems. Traditional approaches such as tomography become computationally infeasible as the system size increases. Quantum Hamiltonian learning offers a promising alternative by using a trusted quantum simulator to simulate the dynamics of the proposed Hamiltonian, thereby bypassing classical computational limits.

The methodology employs Bayesian inference, providing an efficient way to integrate prior knowledge with new data to update confidence in specific Hamiltonian models. The likelihood function, crucial to Bayesian inference, is calculated using quantum simulations which are adept at processing complex quantum data. This paper investigates the robustness of such simulations when subjected to imperfect quantum resources, including noise.

Key Results

1. Robustness to Noise: The paper systematically explores the impact of depolarizing noise on the QHL algorithm and demonstrates that even significant levels of such noise do not prevent effective Hamiltonian learning. The QHL algorithm is shown to maintain its learning capability with minimal degradation in performance even when noise levels are substantial.
2. Handling Non-commuting Models: Quantum Hamiltonian learning is adaptable to non-commuting models by adjusting initial state preparations and measurement strategies. While more challenging, the algorithm still provides efficient learning rates demonstrating its applicability beyond simple commuting systems.
3. Model Selection and Error Management: The paper highlights the algorithm's ability to effectively select the best model from competing hypotheses, even when the true Hamiltonian is not within the modeled hypothesis space. It uses Bayesian model selection to discern between overfitting and underfitting, optimizing the complexity of inferred Hamiltonians.

Implications and Future Directions

This research underscores the potential utility of quantum simulators not just for computation but for characterization tasks that are essential for advancing quantum technologies. By proving robust in scenarios with realistic noise, the QHL algorithm opens the way for accurate characterization of quantum processors, thereby enabling improved design and functioning of quantum systems.

The paper suggests that future research could optimize the QHL methodology by incorporating more advanced quantum algorithms for experiment selection and likelihood computation. Additionally, exploring the integration of quantum computing resources beyond simulation, such as quantum gradient estimation, could further enhance algorithm efficiency.

In conclusion, "Quantum Hamiltonian Learning Using Imperfect Quantum Resources" provides a comprehensive exploration into making quantum Hamiltonian characterization feasible with current quantum technologies. Its insights and methodologies present a significant step toward effective quantum system modeling, promising enhanced quantum processor developments.