Efficient learning of quantum noise

John A. Smolin, Andrew W. Cross, Graeme Smith

Cambyse Rouzé, Daniel Stilck França

The unavoidable presence of noise is a crucial roadblock for the development of large-scale quantum computers and the ability to characterize quantum noise reliably and efficiently with high precision is essential to scale quantum technologies further. Although estimating an arbitrary quantum channel requires exponential resources, it is expected that physically relevant noise has some underlying local structure, for instance that errors across different qubits have a conditional independence structure. Previous works showed how it is possible to estimate Pauli noise channels with an efficient number of samples in a way that is robust to state preparation and measurement errors, albeit departing from a known conditional independence structure. We present a novel approach for learning Pauli noise channels over n qubits that addresses this shortcoming. Unlike previous works that focused on learning coefficients with a known conditional independence structure, our method learns both the coefficients and the underlying structure. We achieve our results by leveraging a groundbreaking result by Bresler for efficiently learning Gibbs measures and obtain an optimal sample complexity of O(log(n)) to learn the unknown structure of the noise acting on n qubits. This information can then be leveraged to obtain a description of the channel that is close in diamond distance from O(poly(n)) samples. Furthermore, our method is efficient both in the number of samples and postprocessing without giving up on other desirable features such as SPAM-robustness, and only requires the implementation of single qubit Cliffords. In light of this, our novel approach enables the large-scale characterization of Pauli noise in quantum devices under minimal experimental requirements and assumptions.

Daniele Cuomo

Senrui Chen, Zhihan Zhang, Liang Jiang +1 more

Understanding quantum noise is an essential step towards building practical quantum information processing systems. Pauli noise is a useful model that has been widely applied in quantum benchmarking, error mitigation, and error correction. Despite intensive study into Pauli noise learning, most existing works focus on learning Pauli channels associated with some specific gates rather than treating the gate set as a whole. A learning algorithm that is self-consistent, complete, and efficient at the same time has yet to be established. In this work, we study the task of , where a set of quantum gates, state preparation, and measurements all suffer from unknown Pauli noise channels with a customized noise ansatz. Using tools from algebraic graph theory, we analytically characterize the self-consistently learnable degrees of freedom for Pauli noise models with arbitrary linear ansatz, and design experiments to efficiently learn all the learnable information. Specifically, we show that all learnable information about the gate noise can be learned to relative precision, under mild assumptions on the noise ansatz. We then demonstrate the flexibility of our theory by applying it to concrete physically motivated ansatze (such as spatially local or quasi-local noise) and experimentally relevant gate sets (such as parallel CZ gates). These results not only enhance the theoretical understanding of quantum noise learning, but also provide a feasible recipe for characterizing existing and near-future quantum computing devices.

Xinfang Zhang, Zhihao Wu, Gregory A. L. White +12 more

The development of practical quantum processors relies on the ability to control and predict their functioning despite the presence of noise. This is particularly challenging for temporarily correlated noise. Here we propose a physics-inspired supervised machine learning approach to efficiently and accurately predict the functioning of quantum processors in the presence of correlated noise, which only requires data from randomized benchmarking experiments. To demonstrate the efficacy of our technique, we analyze the data from a superconducting quantum processor with tunable correlated noise. We produce training data by evolving the system for a number of time steps, and with this, we fully quantify the correlated noise and accurately predict the dynamics of the system for times beyond the training data. This approach shows a path towards efficient and effective learning of noisy quantum dynamics and optimally control quantum processors over long and complex computations even in the presence of correlated noise. Combining standard quantum benchmarking techniques with a physics-inspired supervised machine learning algorithm, the authors efficiently and accurately predict the functioning of a superconducting qubit in the presence of complex noise. The proposed approach opens a path towards a better control of current quantum devices.

Bhavna Bose