Benchmarking of quantum protocols

Abstract

Quantum network protocols offer new functionalities such as enhanced security to communication and computational systems. Despite the rapid progress in quantum hardware, it has not yet reached a level of maturity that enables execution of many quantum protocols in practical settings. To develop quantum protocols in real world, it is necessary to examine their performance considering the imperfections in their practical implementation using simulation platforms. In this paper, we consider several quantum protocols that enable promising functionalities and services in near-future quantum networks. The protocols are chosen from both areas of quantum communication and quantum computation as follows: quantum money, W-state based anonymous transmission, verifiable blind quantum computation, and quantum digital signature. We use NetSquid simulation platform to evaluate the effect of various sources of noise on the performance of these protocols, considering different figures of merit. We find that to enable quantum money protocol, the decoherence time constant of the quantum memory must be at least three times the storage time of qubits. Furthermore, our simulation results for the w-state based anonymous transmission protocol show that to achieve an average fidelity above 0.8 in this protocol, the storage time of sender's and receiver's particles in the quantum memory must be less than half of the decoherence time constant of the quantum memory. We have also investigated the effect of gate imperfections on the performance of verifiable blind quantum computation. We find that with our chosen parameters, if the depolarizing probability of quantum gates is equal to or greater than 0.05, the security of the protocol cannot be guaranteed. Lastly, our simulation results for quantum digital signature protocol show that channel loss has a significant effect on the probability of repudiation.

Figure 1

c versus client wait time, T. The blue dashed line shows the security threshold 0.875.

Figure 2

(a) $P_{\mathrm{correct}}$ versus number of qubit pairs for $T=0.01\mathrm{s}$ and $T=0.1\mathrm{s}$. (b) $P_{\mathrm{forge}}$ versus number of qubit pairs for $T=0.01\mathrm{s}$ and $T=0.1\mathrm{s}$.

Figure 3

General description of W-state based anonymous transmission protocol. Solid arrows represent quantum communication, while dotted arrows represent classical communication. QM quantum memory, BSM Bell state measurement.

Figure 4

Average fidelity of the teleported state for different values of $q_1$ and $q_2$.

Figure 5

Average fidelity of the teleported state versus q.

Figure 6

Probability of protocol failure versus transmission loss for different number of users.

Figure 7

Probability of failure of a test run for different values of depolarizing probability in quantum gates. The blue dashed line represents the threshold 0.25 for w/t.