Quantum Walks Boost Security on Early Computers

Scientists are increasingly focused on developing quantum cryptographic protocols compatible with near-term, noisy intermediate-scale quantum (NISQ) devices. Aditi Rath, Dinesh Kumar Panda, and Colin Benjamin, all from the National Institute of Science Education and Research, Bhubaneswar, Homi Bhabha National Institute, detail a novel scheme leveraging discrete-time quantum walks and Parrondo dynamics on cyclic graphs.

This research is significant because it constructs a practical quantum circuit specifically tailored for NISQ architectures and rigorously assesses its security against common attacks, modelling intercept-resend and man-in-the-middle scenarios. Through numerical simulations and analysis of hardware feasibility, the authors demonstrate how connectivity and state-transfer strategies critically impact fidelity and performance, offering valuable insights into the trade-offs inherent in deploying quantum cryptography on contemporary processors. Scientists are edging closer to unhackable communications with a quantum cryptography method designed for today’s limited quantum computers. This advance tackles a critical challenge by working with imperfect, noisy hardware than waiting for fully-fledged quantum machines. The technique promises secure data transmission even before large-scale quantum networks become a reality. Compatibility with noisy intermediate-scale quantum (NISQ) devices is paramount for realising practical quantum cryptographic protocols. This work investigates a novel cryptographic scheme founded on discrete-time quantum walks (DTQWs) on cyclic graphs, harnessing the intriguing Parrondo dynamics, a phenomenon where periodic behaviour arises from a sequence of individually chaotic operations. Researchers have constructed a dedicated quantum circuit design optimised for NISQ architectures and rigorously analysed its performance using numerical simulations within the Qiskit framework, both under idealised conditions and with realistic noise modelling. Protocol efficacy is quantified through detailed analysis of probability distributions, Hellinger fidelity, and total variation distance, providing a comprehensive assessment of its capabilities. To rigorously evaluate security, the study models common adversarial attacks, specifically, intercept-resend and man-in-the-middle scenarios, and quantifies the resulting quantum bit error rate. The protocol reliably recovers transmitted messages in the absence of eavesdropping. However, any attempt at interception introduces detectable disturbances that disrupt the crucial periodic reconstruction mechanism inherent to the scheme. This sensitivity to disturbance forms the basis of its security. Further analysis focuses on hardware feasibility, utilising the contemporary NISQ processor, ibm torino, and explicitly incorporating qubit connectivity and state-transfer limitations into the circuit design. The simulations reveal that communication between logically separated modules necessitates SWAP operations, which accumulate noise and degrade performance. By exploring hybrid state-transfer strategies, the researchers demonstrate that careful qubit selection and connectivity optimisation are decisive factors in achieving high fidelity and overall protocol performance, highlighting the critical hardware-dependent trade-offs inherent in NISQ implementations. This work establishes a pathway towards practical quantum cryptography tailored for near-term quantum devices. Fidelity and noise sensitivity in cyclic graph quantum cryptography Initial simulations of the quantum cryptographic protocol, conducted under ideal conditions, demonstrated near-perfect message recovery across various cyclic graphs. Specifically, the protocol achieved a fidelity of 0.999 for message decryption on a 4-cycle graph, indicating minimal information loss during the encryption-decryption process. This high fidelity was maintained across multiple message encodings, confirming the reliability of the scheme in a noise-free environment. Further analysis revealed that the protocol’s performance is critically dependent on the precise implementation of the Parrondo sequence, a deterministic combination of chaotic coin operators. The research then investigated the impact of noise on protocol performance, simulating realistic conditions on a contemporary NISQ processor, ibm torino. Introducing noise resulted in a measurable decrease in fidelity, with values dropping to 0.88 on the 4-cycle graph. This reduction highlights the sensitivity of the protocol to hardware imperfections and the need for error mitigation strategies. Detailed modelling of intercept-resend and man-in-the-middle attacks revealed that Eve’s intervention consistently disrupted the walk periodicity essential for decryption. The quantum bit error rate, a key metric for assessing security, increased significantly, reaching 0.12, when an eavesdropper attempted to intercept and resend the message. To assess hardware feasibility, the study explored hybrid state-transfer strategies, combining SWAP operations and SWAP-teleportation operations to connect logically separated qubit modules on the ibm torino processor. The analysis showed that communication between these modules increased circuit depth, introducing cumulative noise effects. Specifically, a 5-qubit implementation required an average of 12 SWAP operations, contributing significantly to the overall error rate. However, careful selection of qubit choice and transpilation strategy proved decisive in mitigating these effects, demonstrating that hardware-dependent trade-offs are crucial for successful NISQ implementations.

Simulating Quantum Communication with Virtual Modules on a Single NISQ Processor A module-based approach to quantum cryptography forms the basis of this work, simulating communication via quantum state transfer across virtual modules within a single noisy intermediate-scale quantum (NISQ) device. Rather than utilising physically separate quantum processors, Alice and Bob are each assigned disjoint sets of qubits, functioning as their respective modules. Information exchange between these modules is emulated through sequences of SWAP gates, allowing for the preparation, transmission, and recovery of encoded messages entirely within the confines of a single NISQ processor. Alice initiates the process with three qubits designated for a 4-cycle graph, serving as her position and coin registers, and prepares an initial state using coin rotations and conditional shift operators to generate her public key state. To transfer this state to Bob, a series of SWAP gates are applied, moving the qubits into Bob’s designated register. This simulates a quantum communication channel without requiring physical transmission. Bob then encodes his message, k, by applying spatial translation operators, Tk, to the received public key state. Following encoding, another sequence of SWAP gates returns the modified quantum state to Alice’s qubits. Alice subsequently decrypts the message by applying an operator that is the inverse of her initial public key operation, and measures the position qubits to recover the original message. The core of the protocol relies on discrete-time quantum walks (DTQWs) on cyclic graphs, exploiting Parrondo dynamics, where periodic evolution arises from a deterministic sequence of chaotic coin operators. To optimise the quantum circuit realisation for NISQ architectures, the time evolution operator is expressed using Quantum Fourier Transform (QFT) matrices, reducing the circuit complexity by utilising only one pair of QFT and inverse QFT (IQFT) operations. This method leverages the unitarity condition, simplifying the implementation and enhancing efficiency. The diagonalised forms of the shift operators, Tk, are implemented via single-qubit phase rotation gates, further streamlining the circuit design. Resilient quantum key distribution using discrete-time walks on noisy intermediate-scale quantum devices The relentless pursuit of secure communication in an age of increasingly sophisticated cyber threats has led researchers to explore the seemingly paradoxical realm of quantum cryptography. This work represents a valuable step towards building practical quantum systems tolerant of the imperfections inherent in current technology. For years, the promise of unbreakable quantum keys has been hampered by the fragility of quantum states and the sheer difficulty of scaling up quantum devices.

This research tackles that challenge head-on, focusing on a cryptographic scheme built on discrete-time quantum walks, a method that appears more resilient to the noise present in near-term quantum computers. What distinguishes this approach is its explicit design for noisy intermediate-scale quantum (NISQ) devices. Rather than striving for ideal conditions, the team directly addresses the limitations of existing hardware, modelling the impact of realistic errors and connectivity constraints. The exploration of hybrid state-transfer strategies, balancing circuit depth with fidelity, is a particularly pragmatic move. It acknowledges that perfect quantum communication isn’t immediately achievable and that clever engineering can mitigate the worst effects of imperfect components. The trade-offs identified, specifically, the increased circuit depth caused by communication between modules, highlight a persistent bottleneck. While the protocol demonstrates reliable message recovery in the absence of attack, and detectable disturbances under eavesdropping, scaling this up to a truly useful key distribution rate remains a significant hurdle. Future work will likely focus on optimising these hybrid strategies, perhaps incorporating error correction techniques tailored to the specific noise profiles of different quantum processors. Beyond this, we can anticipate a broader effort to map quantum cryptographic protocols onto diverse hardware platforms, recognising that a one-size-fits-all solution is unlikely to emerge. 👉 More information 🗞 NISQ-compatible quantum cryptography based on Parrondo dynamics in discrete-time quantum walks 🧠 ArXiv: https://arxiv.org/abs/2602.14678 Tags: