Measurement-based quantum machine learning

TL;DR

This paper develops a measurement-based quantum machine learning (MB-QML) framework centered on MuTA, a universal quantum neural network built from MBQC resource states. MuTA delivers determinism via flow, universality via single-qubit gates and entangling Ising XX interactions, and monotonic expressivity with bias engineering, all while remaining scalable in parameter count. The authors demonstrate MuTA’s capabilities through learning universal gate sets, classifying quantum states using QFI, implementing a learnable quantum teleportation instrument, and constructing MBQC-based kernels for classical data; they also address hardware constraints by proposing heuristic training methods for photonic GKP MBQC. The work highlights MBQC’s potential advantages—reduced time complexity and compatibility with classical co-processing—for practical QML on near-term devices and outlines paths for future MB-QML advances and dataset applications.

Abstract

Quantum machine learning (QML) leverages quantum computing for classical inference, furnishes the processing of quantum data with machine-learning methods, and provides quantum algorithms adapted to noisy devices. Typically, QML proposals are framed in terms of the circuit model of quantum computation. The alternative measurement-based quantum computing (MBQC) paradigm can exhibit lower circuit depths, is naturally compatible with classical co-processing of mid-circuit measurements, and offers a promising avenue towards error correction. Despite significant progress on MBQC devices, QML in terms of MBQC has been hardly explored. We propose the multiple-triangle ansatz (MuTA), a universal quantum neural network assembled from MBQC neurons featuring bias engineering, monotonic expressivity, tunable entanglement, and scalable training. We numerically demonstrate that MuTA can learn a universal set of gates in the presence of noise, a quantum-state classifier, as well as a quantum instrument, and classify classical data using a quantum kernel tailored to MuTA. Finally, we incorporate hardware constraints imposed by photonic Gottesman-Kitaev-Preskill qubits. Our framework lays the foundation for versatile quantum neural networks native to MBQC, allowing to explore MBQC-specific algorithmic advantages and QML on MBQC devices.

Figures (11)

• Figure 1: Illustrations of the multiple-triangle ansatz (MuTA) architecture: (a) A MuTA for three qubits, showing input qubits $I$ on the left, output qubits $O$ on the right (in blue), with arrows indicating the flow of $(G,I,O)$; (b) A $(2,0)$-MuTA layer.
• Figure 2: A MuTA layer implementing the same connectivity as a classical NN. (a) Layers $l$ and $l+1$ of a feed-forward NN with connectivity between neurons in nodes $i$ and $J = \{i-1, i+2\}$. (b) A MuTA layer $(n,i)$ with connectivity $(i,J)$. Quantizing the same classical NN yields several MuTAs---neurons in subsequent layers can either share a wire or not.
• Figure 3: Learning curves for (a) single-qubit Haar-random unitaries on the first qubit and (b) an $\text{Ising}X\!X\left(\pi/2\right)$ gate, averaged over $20$ runs. The shaded region is the standard deviation.
• Figure 4: Stability of MB-QML under noise affecting the training dataset. The testing curves are obtained using noiseless data. Models are trained for $60$ and $200$ steps for Brownian and Bitflip noise, respectively. Each datapoint is an average over $5$ runs, each of which uses a different Haar-random dataset. The dataset size is $N=20$ for Brownian noise and $N=100$ for bit-flip noise. In both cases, the data are split evenly between training and testing.
• Figure 5: Learned surface to classify states of high $({>2})$ and low (${<2}$) QFI. The surface is defined by a degree two polynomial, and the position of each point on the surface is defined by the measurement pattern. The scattered points correspond to Haar-random states.

Theorems & Definitions (14)

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• Definition A.1: Classical artificial neuron
• Definition A.2: Classical neural network