Multimodal Deep Representation Learning for Quantum Cross-Platform Verification

Efficient learning for linear properties of bounded-gate quantum circuits

The vast and complicated many-qubit state space forbids us to comprehensively capture the dynamics of modern quantum computers via classical simulations or quantum tomography. Recent progress in quantum learning theory prompts a crucial question: can linear properties of a many-qubit circuit with d tunable RZ gates and G - d Clifford gates be efficiently learned from measurement data generated by varying classical inputs? In this work, we prove that the sample complexity scaling linearly in d is required to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d. To address this challenge, we propose a kernel-based method leveraging classical shadows and truncated trigonometric expansions, enabling a controllable trade-off between prediction accuracy and computational overhead. Our results advance two crucial realms in quantum computation: the exploration of quantum algorithms with practical utilities and learning-based quantum system certification. We conduct numerical simulations to validate our proposals across diverse scenarios, encompassing quantum information processing protocols, Hamiltonian simulation, and variational quantum algorithms up to 60 qubits.

Noise-agnostic quantum error mitigation with data augmented neural models

Quantum error mitigation, a data processing technique for recovering the statistics of target processes from their noisy version, is a crucial task for near-term quantum technologies. Most existing methods require prior knowledge of the noise model or the noise parameters. Deep neural networks have the potential to lift this requirement, but current models require training data produced by ideal processes in the absence of noise. Here we build a neural model that achieves quantum error mitigation without any prior knowledge of the noise and without training on noise-free data. To achieve this feature, we introduce a quantum augmentation technique for error mitigation. Our approach applies to quantum circuits and to the dynamics of many-body and continuous-variable quantum systems, accommodating various types of noise models. We demonstrate its effectiveness by testing it both on simulated noisy circuits and on real quantum hardware.

Learning quantum properties from short-range correlations using multi-task networks

Characterizing multipartite quantum systems is crucial for quantum computing and many-body physics. The problem, however, becomes challenging when the system size is large and the properties of interest involve correlations among a large number of particles. Here we introduce a neural network model that can predict various quantum properties of many-body quantum states with constant correlation length, using only measurement data from a small number of neighboring sites. The model is based on the technique of multi-task learning, which we show to offer several advantages over traditional single-task approaches. Through numerical experiments, we show that multi-task learning can be applied to sufficiently regular states to predict global properties, like string order parameters, from the observation of short-range correlations, and to distinguish between quantum phases that cannot be distinguished by single-task networks. Remarkably, our model appears to be able to transfer information learnt from lower dimensional quantum systems to higher dimensional ones, and to make accurate predictions for Hamiltonians that were not seen in the training.