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Quantum Information Processing

Dynamic full quantum one-way function based on quantum circuit mapping

Yao Tang, Tao Shang, Jianwei Liu

Published Aug 26, 2023• 6 citations
Publisher
DOI
10.1007/s11128-023-04065-3

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One-way functions are fundamental tools for cryptography. Until now, quantum one-way functions have several input-output categories such as “classical-to-classical,” “classical-to-quantum,” and “quantum-to-classical,” which are used for postquantum cryptography or quantum cryptography. However, there are still no intrinsic “quantum-to-quantum” quantum one-way functions. In this article, we propose the full quantum one-way function to design full quantum cryptographic schemes. By concatenating the “quantum-classical” one-way function and the rotation operation of single qubit, the full quantum one-way function has the input and output of quantum states. We prove its one-way property from “easy computation” and “computationally difficult to invert.” Then we apply the full quantum one-way function to quantum identity authentication. Security analysis shows that the proposed quantum identity authentication scheme based on the full quantum one-way function is secure even under active attacks.
Quantum one-way function (QOWF) was proposed for quantum cryptography, which was computable but almost irreversible in quantum polynomial time. Full quantum one-way function (F-QOWF) is one of the most important models of QOWF, which deals with quantum states. Although the universal construction of full quantum one-way function has been proposed, there is still little further discussion on the entangled input, specific function instantiation and application scenarios of F-QOWF. In this paper, we introduce quantum hypergraph states into the universal construction of F-QOWF. Quantum hypergraph states are highly entangled multi-party states constructed from the hypergraph. By applying quantum hypergraph states to the new F-QOWF, we generalize the universal construction of F-QOWF to entangled states. The application to quantum aggregate signature shows that quantum hypergraph states help the new F-QOWF be well applied to quantum multi-party cryptographic protocols.
As Quantum Computers continue to increase in size, throughput has not increased proportionally [1]. Errors in qubit measurement and gate operations continue to increase with circuit width and depth. In order to maximize machine throughput, researchers have begun exploring ways of parallelizing circuit execution [2]–[9]. Due to the noisyness of quantum computers, this requires new algorithms for efficient resource allocation, qubit mapping, and scheduling. We improve on existing greedy algorithms by formulating the mapping search as a Binary Integer Non-Linear Programming (BINLP) problem. We model practical constraints and propose new heuristics for determining the goodness of a mapping. We evaluate our mappings on several sets of benchmark circuits and investigate the usefulness of parallel execution for circuit cutting, QAOAs, and deep circuits. We observe similar fidelity compared to Qiskit's transpiler for circuit cutting and throughput benchmarks. We observe greater fidelity over Qiskit's transpiler for dense QAOA ansatzes. Finally, we find that parallel circuit cutting provides greater fidelity than full-circuit execution.