Distribution alignment based transfer fusion frameworks on quantum devices for seeking quantum advantages

TL;DR

Two transfer fusion frameworks are proposed in this paper to predict the labels of a target domain data by aligning its distribution to a different but related labelled source domain on quantum devices through a quantum information infusion channel.

Abstract

The scarcity of labelled data is specifically an urgent challenge in the field of quantum machine learning (QML). Two transfer fusion frameworks are proposed in this paper to predict the labels of a target domain data by aligning its distribution to a different but related labelled source domain on quantum devices. The frameworks fuses the quantum data from two different, but related domains through a quantum information infusion channel. The predicting tasks in the target domain can be achieved with quantum advantages by post-processing quantum measurement results. One framework, the quantum basic linear algebra subroutines (QBLAS) based implementation, can theoretically achieve the procedure of transfer fusion with quadratic speedup on a universal quantum computer. In addition, the other framework, a hardware-scalable architecture, is implemented on the noisy intermediate-scale quantum (NISQ) devices through a variational hybrid quantum-classical procedure. Numerical experiments on the synthetic and handwritten digits datasets demonstrate that the variatioinal transfer fusion (TF) framework can reach state-of-the-art (SOTA) quantum DA method performance.

Figures (6)

• Figure 1: The schematic diagram of the procedure of the DDA. The source domain data $X_{s}$ and the target domain data $X_{t}$ are different in both the marginal and conditional distributions. The DDA attempts to align the distributions of the two domains to achieve the procedure of TL.
• Figure 2: The schematic notaion of the basic quantum gates. (a)Pauli-X gate; (b)Pauli-Y gate; (c)Pauli-Z gate; (d)Hadamard gate; (e)Controlled-$U$ gate; (f)Quantum measurement.
• Figure 3: The schematic diagram of the distribution alignment based quantum transfer fusion framework.
• Figure 4: The corresponding quantum circuits of the QBLAS-based TF. (a) The quantum circuits for predicting the target labels through the procedure of QBLAS-based TF where $U_{w}$ is the quantum information fusion channel with $QPCA$ represents the quantum principal component analysis operation; (b) The quantum circuits of $\textbf{U}_{SP}(M, K, \lambda)$; (c) The quantum circuits of $\textbf{U}_{P}(M, f(\lambda))$ where $QFT$ and $QFT^{\dagger}$ are the quantum Fourier transform and its inverse respectively.
• Figure 5: The illustrative diagram of the VQTF