arXiv subjects

Bao Yan

Publications and source records attributed to Bao Yan.

6 recordsLinked to original sources

arXiv2025

Space-Optimized and Experimental Implementations of Regev's Quantum Factoring Algorithm

The integer factorization problem (IFP) underpins the security of RSA, yet becomes efficiently solvable on a quantum computer through Shor's algorithm. Regev's recent high-dimensional variant reduces the circuit size through lattice-based post-processing, but introduces substantial space overhead and lacks practical implementations. Here, we propose a qubit reuse method by intermediate-uncomputation that significantly reduces the space complexity of Regev's algorithm, inspired by reversible computing. Our basic strategy lowers the cost from $ O(n^{3/2}) $ to $ O(n^{5/4}) $, and refined strategies achieve $ O(n \log n) $which is a space lower bound within this model. Simulations demonstrate the resulting time-space trade-offs and resource scaling. Moreover, we construct and compile quantum circuits that factor $ N = 35 $, verifying the effectiveness of our method through noisy simulations. A more simplified experimental circuit for Regev's algorithm is executed on a superconducting quantum computer, with lattice-based post-processing successfully retrieving the factors. These results advance the practical feasibility of Regev-style quantum factoring and provide guidance for future theoretical and experimental developments.

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arXiv2025

Evidence of scaling advantage on an NP-Complete problem with enhanced quantum solvers

Achieving quantum advantage remains a key milestone in the noisy intermediate-scale quantum era. Without rigorous complexity proofs, scaling advantage-where quantum resource requirements grow more slowly than their classical counterparts-serves as the primary indicator. However, direct applications of quantum optimization algorithms to classically intractable problems have yet to demonstrate this advantage. To address this challenge, we develop enhanced quantum solvers for the NP-complete one-in-three Boolean satisfiability problem. We propose a restricting space reduction algorithm (RSRA) that achieves optimal search space dimensionality, thereby reducing both qubits and time complexity for various quantum solvers. Extensive numerical investigations on problem instances with up to 65 variables demonstrate that our enhanced quantum approximate optimization algorithm (QAOA) and quantum adiabatic algorithm (QAA)-based solvers outperform state-of-the-art classical solvers, with the QAA-based solver providing a lower bound for our method while exhibiting scaling advantage. Furthermore, we experimentally implement our enhanced solvers on a superconducting quantum processor with 13 qubits, confirming the predicted performance improvements. Collectively, our results provide empirical evidence of quantum speedup for an NP-complete problem.

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arXiv2024

Quantum-Classical Hybrid Algorithm for Solving the Learning-With-Errors Problem on NISQ Devices

The Learning-With-Errors (LWE) problem is a fundamental computational challenge with implications for post-quantum cryptography and computational learning theory. Here we propose a quantum-classical hybrid algorithm with Ising model to address LWE, transforming it into the Shortest Vector Problem and using variable qubits to encode lattice vectors into an Ising Hamiltonian. By identifying low-energy Hamiltonian levels, the solution is extracted, making the method suitable for noisy intermediate-scale quantum devices. The required number of qubits is less than $m(m+1)$, where $m$ is the number of samples. Our heuristic algorithm's time complexity depends on the specific quantum eigensolver used to find low-energy levels, and the performance when using the Quantum Approximate Optimization Algorithm is investigated. We validate the algorithm by solving a $2$-dimensional LWE problem on a $5$-qubit quantum device, demonstrating its potential for solving meaningful LWE instances on near-term quantum devices.

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arXiv2022

Factoring integers with sublinear resources on a superconducting quantum processor

Shor's algorithm has seriously challenged information security based on public key cryptosystems. However, to break the widely used RSA-2048 scheme, one needs millions of physical qubits, which is far beyond current technical capabilities. Here, we report a universal quantum algorithm for integer factorization by combining the classical lattice reduction with a quantum approximate optimization algorithm (QAOA). The number of qubits required is O(logN/loglog N), which is sublinear in the bit length of the integer $N$, making it the most qubit-saving factorization algorithm to date. We demonstrate the algorithm experimentally by factoring integers up to 48 bits with 10 superconducting qubits, the largest integer factored on a quantum device. We estimate that a quantum circuit with 372 physical qubits and a depth of thousands is necessary to challenge RSA-2048 using our algorithm. Our study shows great promise in expediting the application of current noisy quantum computers, and paves the way to factor large integers of realistic cryptographic significance.

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arXiv2018

Fair Efficiency Comparisons of Decoy-state Quantum Key Distribution Protocols

Secure key rate of decoy-state quantum key distribution protocols has been improved with biased basis choice, however, the security standards and parameters of current protocols are different. As a result, we cannot give an accurate key rate comparison between different kinds of protocols. Taking the schemes based on different formula of secure key rate as examples, we give a fair comparison between typical protocols under universal composable security standard. Through analyzing the relationship of security parameters in post-processing stage and final secure key, we achieve the unified quantification between protocols based on Gottesman-Lo-Lutkenhaus-Preskill formula and the ones under universal composable security. Based on the above research, the impact of different sending length and secure parameters on secure key rate is investigated, meanwhile, we give the dependent relationship between secure key rate and sending length under different secure parameters. Besides, we analyze the importance and conditions of fair comparison. For the first time we give a fair comparison between the protocols based on GLLP formula and smooth entropy, and taking Raymond protocol and Toshiba protocol as examples, we analyze the way for improving secure key rate in the light intensity choice and the single bit error rate estimation method.

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arXiv2016

Universally-composable finite-key analysis for efficient four-intensity decoy-state quantum key distribution

We propose an efficient four-intensity decoy-state BB84 protocol and derive concise security bounds for this protocol with the universally composable finite-key analysis method. Comparing with the efficient three-intensity protocol, we find that our efficient four-intensity protocol can increase the secret key rate by at least $30\%$. Particularly, this increasing rate of secret key rate will be raised as the transmission distance increases. At a large transmission distance, our efficient four-intensity protocol can improve the performance of quantum key distribution profoundly.

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