Efficient State Preparation for Quantum Machine Learning

TL;DR

Efficient State Preparation for Quantum Machine Learning addresses the data-encoding bottleneck in quantum machine learning by employing Matrix Product States (MPS) to construct low-depth, approximate encodings that preserve classification performance. The authors outline how to build MPS from classical input via reshaping and singular value decomposition, and how to translate the MPS into practical, shallower state-preparation circuits. They integrate this encoding approach with Quantum Variational Classifiers and demonstrate that approximate inputs can maintain high accuracy while increasing robustness to classical adversarial attacks, including demonstrations on MNIST/FMNIST and a small superconducting-device experiment. The work highlights that bespoke, structure-aware encodings can reduce circuit depth and enhance security against perturbations, suggesting a pathway toward scalable and robust QML pipelines. Open questions remain on the persistence of these advantages when adversaries also have quantum resources or full knowledge of the encoding scheme.

Abstract

One of the key considerations in the development of Quantum Machine Learning (QML) protocols is the encoding of classical data onto a quantum device. In this chapter we introduce the Matrix Product State representation of quantum systems and show how it may be used to construct circuits which encode a desired state. Putting this in the context of QML we show how this process may be modified to give a low depth approximate encoding and crucially that this encoding does not hinder classification accuracy and is indeed exhibits an increased robustness against classical adversarial attacks. This is illustrated by demonstrations of adversarially robust variational quantum classifiers for the MNIST and FMNIST dataset, as well as a small-scale experimental demonstration on a superconducting quantum device.

Figures (6)

• Figure 1: The state preparation circuits resulting from the procedure outlined in Section \ref{['sec:state_prep']}. (a) uses the conventional procedure as described with $k=2$ where as (b) is seeking to minimise the depth of the each individual layer. Note that in (b) the "disentangled" qubit is the top qubit for unitaries acting on the first four qubit and the bottom qubit elsewhere and that $U_4^0$ and $U_5^0$ are two qubit unitaries acting on the top and bottom qubits only.
• Figure 2: Test Accuracy for 500 images of the MNIST dataset mnist in the presence of random perturbations to the input amplitudes on a trained QVC with many layers. Note that the test accuracy only dips after the input fidelity drops below $60\%$. Reprint from drastic
• Figure 3: Example images from the Fashion MNIST dataset upon approximate encoding using the MPS assisted protocol. Note that the vertical stripes that result from the encoding as per Equation \ref{['eq:compr']}. Reprint from drastic
• Figure 4: The training accuracy for a deep nine qubit QVC using both an exact encoding and MPS assisted encoding with a threshold accuracy of $60\%$. Figure adapted from Supplemental Material of drastic
• Figure 5: CNOT gate count for $500$ MNIST and FMNIST input states using the MPS method with a target fidelity of $60\%$, as well as the Qiskit qiskit exact state preparation function based off shende. Note that the MPS method results in a circuit with significantly fewer CNOT gates, suggesting that at most only seven iterations of the algorithm are required to rearch the target fidelity. Figure adapted from drastic