Classical multiparty computation using quantum resources

In this work, we demonstrate a way to perform classical multiparty computing among parties with limited computational resources. Our method harnesses quantum resources to increase the computational power of the individual parties. We show how a set of clients restricted to linear classical processing are able to jointly compute a nonlinear multivariable function that lies beyond their individual capabilities. The clients are only allowed to perform classical xor gates and single-qubit gates on quantum states. We also examine the type of security that can be achieved in this limited setting. Finally, we provide a proof-of-concept implementation using photonic qubits that allows four clients to compute a specific example of a multiparty function, the pairwise and.

Figure 1

A sketch of our scheme for multiparty computation, where a server computes a Boolean function $f(x_1,x_2,...,x_n)$ with inputs $x_i$ from different clients. The server generates simple computational resources, such as single qubits, and sends them consecutively to a number of different clients. Each client manipulates the computational resources by performing single-qubit gates. At the end, the server measures the output state. The result of this measurement is sent to the clients, who can deduce the result of the computation.

Figure 2

Protocol for delegated multiparty computation. For a description of the protocol, see the main text.

Figure 3

Experimental scheme. The server generates heralded, horizontally polarized photons, which are sent to the clients' side. Each client uses a pair of half-wave plates for applying the gates $V^{r_i}$ and $U^{x_i}$. If $x_i$ or $r_i$ are equal to zero, the setting of the respective half-wave plate is chosen to be zero. If $x_i$ or $r_i$ are equal to one, the corresponding half-wave plate is rotated by an angle $\theta$ with respect to the horizontal polarization state, where $\theta$ is given in the figure. Finally, one of the clients performs a final conditional rotation dependent on ${\oplus }_i{x}_i$. The photon is sent back to the server, where a measurement in the computational basis is performed; this has been implemented using a Wollaston prism and two single-photon Avalanche photodiodes (APDs).

Figure 4

(a) Measured outcomes of the computation after decoding $r\oplus (r\oplus f)$ for a sample subset $(x_1,x_2,x_3,x_4)$ of the input bits tested (horizontal axis). (b) Measured outcomes of the computation before decoding $(r\oplus f)$, averaged over all possible combinations of $r_i$, $i=1,...,4$. For each data point, we integrated over 15 s, yielding an overall statistics of about 3000 counts for each computation performed. (c) Long-term stability of our experiment. The graph shows the probability of obtaining the correct outcome measured over 13 h of data acquirement. Every point of the plot corresponds to the average over 1 h of measurement time. The combination of the clients' input bits used here is $(x_1,x_2,x_3,x_4)$ = (1,1,1,1).