Experimental quantum end-to-end learning on a superconducting processor

Quantum computing offers the potential to revolutionize machine learning (ML) through quantum parallelism. While fault-tolerant quantum computers promise exponential speedups, even noisy intermediate-scale quantum (NISQ) devices hold promise for quantum advantage by enhancing model expressibility. A key challenge is creating parameterized quantum ansatzes trainable by classical optimizers. Most current approaches use quantum neural networks (QNNs) built from parameterized quantum gates, but their performance depends heavily on architecture and mapping to native gates, limiting their efficiency on NISQ devices. This paper explores a hardware-friendly end-to-end learning scheme, replacing gate-based QNNs with natural quantum dynamics driven by coherent control pulses. This eliminates the need for circuit design and compilation, making it more resource-efficient and potentially allowing for better exploitation of limited quantum coherence. The approach also involves jointly training a data encoder to transform classical data into quantum states via control pulses, simplifying the encoding process and introducing crucial nonlinearity. This pulse-based ansatz has shown promise in state preparation, optimization landscape investigation, and cloud-based training. The authors present an experimental demonstration of this end-to-end quantum machine learning on a superconducting processor, classifying handwritten digits from the MNIST dataset. The model achieved high accuracy (98% for two digits, 89% for four digits) without downsizing the image data, making it a promising approach for scaling to more complex real-world tasks.

The introduction thoroughly reviews existing literature on quantum machine learning, highlighting the potential for quantum speedup in high-dimensional and big data tasks. It discusses the limitations of gate-based quantum neural networks (QNNs) on NISQ devices, emphasizing the dependence on architecture design and circuit mapping. The authors cite numerous papers exploring different QNN architectures and applications in classification, clustering, and generative learning tasks. They also reference recent work proposing the hardware-friendly end-to-end learning scheme using pulse-based ansatzes, which directly parameterizes the quantum ansatz by physical control pulses applied to the qubits. The review sets the stage for the proposed end-to-end method by contrasting its advantages – simplicity, hardware friendliness, and efficiency – with the challenges of traditional gate-based methods.

The core of the methodology centers on an end-to-end quantum learning framework where the quantum ansatz is parameterized by physical control pulses, eliminating the need for gate-based QNNs and circuit compilation. The system uses a superconducting processor with six qubits, where a subset is used for the QNN. The quantum state evolves according to a time-dependent Hamiltonian driven by control pulses. A classical neural network acts as a data encoder, transforming the classical input data (MNIST digits) into control variables that steer the quantum state. The training process iteratively updates these control parameters based on the loss function (measured via quantum state readout). The loss function and its gradient are evaluated using a finite difference method, with the classical Adam optimizer updating model parameters to minimize the loss. The experiments involved two classification tasks: a 2-digit task ('0' and '2') using two qubits and a 4-digit task ('0', '2', '7', and '9') using three qubits. The encoding and inference blocks consisted of two layers each. The control parameters are the amplitudes of Gaussian-shaped microwave pulses applied to the qubits. The authors describe the experimental setup, including the superconducting processor's architecture, qubit control, and readout mechanism. The experimental results are compared with numerical simulations using the calibrated system Hamiltonian. Linear Discriminant Analysis (LDA) is used to visualize and analyze data distribution at different stages of the process.

The key findings demonstrate the successful experimental implementation of the quantum end-to-end learning framework on a superconducting processor. The model achieved high classification accuracy: 98.6 ± 0.1% for the 2-digit task and 89.4 ± 1.5% for the 4-digit task. These experimental results closely matched the simulation results (98.2% and 88.9%, respectively), validating the model and experimental setup. The analysis using LDA showed that the classical data encoder effectively compresses the high-dimensional input data, while the quantum neural network (QNN) performs the classification. The authors also investigated the impact of pulse length (coherence time) on the model's performance, finding an optimal range where entanglement benefits are balanced against decoherence losses. The data analysis shows a clear separation of data points for different digits in the final quantum states. The experimental results show that limited quantum resources on NISQ devices can be exploited more efficiently by end-to-end learning compared to traditional gate-based approaches.

The high accuracy achieved in the experiments validates the feasibility and efficiency of the end-to-end quantum machine learning framework. The results suggest that the pulse-based QNN approach leverages the limited quantum resources of NISQ devices more effectively than traditional gate-based quantum models. While the study does not claim a quantum advantage over classical ML algorithms, the enhanced expressivity of the quantum approach with more qubits and reduced noise offers promising prospects for surpassing classical methods. The simplicity and scalability of the pulse-based QNN make it suitable for implementation on larger quantum processors. The joint training of classical encoder and QNN provides a seamless combination of classical and quantum computing.

This work demonstrates the successful experimental implementation of a quantum end-to-end machine learning framework on a superconducting processor, achieving high accuracy in classifying handwritten digits. The pulse-based QNN approach offers a hardware-friendly and efficient method for leveraging limited quantum resources. While quantum advantage remains an ongoing pursuit, this work's scalability and potential for improved performance with more qubits offer a promising path for future applications in more complex real-world machine learning tasks.

The current study is limited by the number of qubits available in the superconducting processor. Scaling up to more complex tasks will require larger quantum processors with improved coherence times. The model's performance is also influenced by decoherence, as shown in the analysis of pulse length versus accuracy. Further research is needed to optimize the model for different task complexities and to explore advanced training algorithms. The current study focuses on a specific type of machine learning (supervised classification); extending the framework to other types of machine learning problems (unsupervised learning, reinforcement learning, generative models) is an important future direction.