Blind quantum machine learning with quantum bipartite correlator

TL;DR

Novel blind quantum machine learning protocols based on the quantum bipartite correlator algorithm are introduced, introducing robust algorithm-specific privacy-preserving mechanisms with low computational overhead that do not require complex cryptographic techniques.

Abstract

Distributed quantum computing is a promising computational paradigm for performing computations that are beyond the reach of individual quantum devices. Privacy in distributed quantum computing is critical for maintaining confidentiality and protecting the data in the presence of untrusted computing nodes. In this work, we introduce novel blind quantum machine learning protocols based on the quantum bipartite correlator algorithm. Our protocols have reduced communication overhead while preserving the privacy of data from untrusted parties. We introduce robust algorithm-specific privacy-preserving mechanisms with low computational overhead that do not require complex cryptographic techniques. We then validate the effectiveness of the proposed protocols through complexity and privacy analysis. Our findings pave the way for advancements in distributed quantum computing, opening up new possibilities for privacy-aware machine learning applications in the era of quantum technologies.

Figures (3)

• Figure 1: Diagram for blind QBC with untrusted server. The upper diagram shows the quantum counting algorithm consisting Grover phase oracles $\hat{G}_{\vec{x},\vec{y}}$ and inverse QFT, while the lower box panel shows the realization details of each phase oracle. Compared to the original QBC algorithm, we introduce an ancillary qubit $o_3$ on client's side to add a phase $g_i$ during the computation process. The phase can be introduced via applying a phase gate on qubit $o_3$, which encodes a bitstring that is random and unknown to the server. The detailed phase encoding rule is explained in the text. The quantum state at the star point is shown in the inset of the figure. After the server finishes the quantum circuit, it sends the extracted modified bipartite correlation $\frac{1}{N}\sum_i^N (x_i y_i +g_i)$ to the client via a classical communication channel. We omit the $1/\sqrt{N}$ normalization factor for index qubit states $\sum_i^N \ket{i}$ in the figures hereafter for simplicity.
• Figure 2: Grover operator $\hat{H}^{\otimes n}(2|0\rangle_n \langle 0|_n-\hat{I})\hat{H}^{\otimes n} \hat{O}_{f}$ for blind quantum bipartite correlator protocol to hide server data $\boldsymbol{X}$ from client. The operator starts with an oracle held by server (Alice) that encodes $\boldsymbol{X}$ with random basis (oracle $\hat{U}_{X_1}$). After receiving the state returned by client (Bob), the server extracts the desired phase term $(-1)^{x_i y_i}$ ($\hat{U}_{X_2}$) and return an encoded state back to client ($\hat{U}_{X_3}$) to remove the phase in $o_1$ qubit that the server does not know. Finally, the server reaches the target state $\frac{1}{\sqrt{N}}\sum_i^N (-1)^{x_i y_i} \ket{i}_n$ by decoupling $o_1$ qubit with index qubits ($\hat{U}_{X_4}$).
• Figure 3: Circuit diagram for implementing $U_{\Vec{X_2}}$ with the help of an ancilla qubit $o_a$. The first control line shows the classical control decided by the random number $R_i, i = 1, ... N$.