NISQ-compatible quantum cryptography based on Parrondo dynamics in discrete-time quantum walks

TL;DR

It is shown that qubit selection and connectivity play a decisive role in determining fidelity and overall protocol performance, highlighting hardware-dependent trade-offs in NISQ implementations.

Abstract

Compatibility with noisy intermediate-scale quantum (NISQ) devices is crucial for the realistic implementation of quantum cryptographic protocols. We investigate a cryptographic scheme based on discrete-time quantum walks (DTQWs) on cyclic graphs that exploits Parrondo dynamics, wherein periodic evolution emerges from a deterministic sequence of individually chaotic coin operators. We construct an explicit quantum circuit realization tailored to NISQ architectures and analyze its performance through numerical simulations in Qiskit under both ideal and noisy conditions. Protocol performance is quantified using probability distributions, Hellinger fidelity, and total variation distance. To assess security at the circuit level, we model intercept-resend and man-in-the-middle attacks and evaluate the resulting quantum bit error rate. In the absence of adversarial intervention, the protocol enables reliable message recovery, whereas eavesdropping induces characteristic disturbances that disrupt the periodic reconstruction mechanism. We further examine hardware feasibility on contemporary NISQ processors, specifically $ibm\_torino$, incorporating qubit connectivity and state-transfer constraints into the circuit design. Our analysis demonstrates that communication between spatially separated logical modules increases circuit depth via SWAP operations, leading to cumulative noise effects. By exploring hybrid state-transfer strategies, we show that qubit selection and connectivity play a decisive role in determining fidelity and overall protocol performance, highlighting hardware-dependent trade-offs in NISQ implementations.

Figures (24)

• Figure 1: Schematic representation of the quantum circuit of the quantum cryptographic protocol.
• Figure 2: Algorithm 1: Parrondo's Paradox cyclic QW based Cryptographic Protocol on a 4-cycle graph (see, Fig. \ref{['f1']})
• Figure 3: Probability distribution for the public key generation on a 4-cycle graph with initial position $\ket{x} = |0\rangle$ and $\ket{l} = \ket{0}$ implemented in qiskit_aer with (0.03 depolarizing) and without noise for $10^5$ shots.
• Figure 4: Probability distribution for the Decrypted message, $k'$ for encoded message (a) $k = 0$, (b) $k = 1$, (c)$k = 2$, (d) $k = 3$ with initial position $\ket{x} = |0\rangle$ such that $k'=k$ implemented in qiskit_aer with depolarizing noise and without noise for $10^5$ shots on a 4-cycle graph.
• Figure 5: Hellinger Fidelity and total variance distance for different messages decrypted by Alice with initial position $\ket{x} = \ket{0}$ and coin $\ket{s} = \ket{0}$ implemented in qiskit_aer with depolarizing noise and without noise for $10^5$ shots on a 4-cycle graph.