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Routing Codes: High-Rate Quantum LDPC Codes with Short, Parallel Non-Local Connectivity
Authors:
Jiaxuan Zhang,
Zhao-Yun Chen,
Peng Duan,
Jia-Ning Li,
Tian-Hao Wei,
Qing-Yang Hou,
Wei-Cheng Kong,
Yu-Chun Wu,
Guo-Ping Guo
Abstract:
Quantum low-density parity-check (qLDPC) codes are promising candidates for realizing large-scale fault-tolerant quantum computing. Although many codes with favorable theoretical parameters have been developed, their practical adoption must take hardware implementability into account. For mainstream quantum platforms such as superconductors and neutral atoms, the connectivity, the length of non-lo…
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Quantum low-density parity-check (qLDPC) codes are promising candidates for realizing large-scale fault-tolerant quantum computing. Although many codes with favorable theoretical parameters have been developed, their practical adoption must take hardware implementability into account. For mainstream quantum platforms such as superconductors and neutral atoms, the connectivity, the length of non-local couplings, and the complexity of wiring or atom rearrangement are key factors that dictate the difficulty of hardware realization. Here, we propose a new family of qLDPC codes, termed routing codes. Within this family, we find explicit instances whose encoding rates are competitive to those of bivariate bicycle (BB) codes, while systematically reducing qubit connectivity, shortening the length of non-local couplings, and, crucially, making all non-local couplings mutually parallel. This parallelism translates into quantifiable benefits, substantially reducing wiring crossings in superconducting multi-layer architectures and simplifying the scheduling of atom movement in neutral-atom arrays. The weight-7 routing codes maintain a high threshold of 0.7\% and reduce the physical qubit overhead by approximately a factor of 8, compared to surface codes achieving a same logical error rate. Further increasing the weight to 11 yields a [[200, 24, 14]] and [[200, 16, 17]] codes with an encoding rate over 23 times that of the surface code, at the cost of a higher logical error rate. These results establish routing codes as a hardware-centric qLDPC family that bridges the gap between theoretical optimality and near-term physical feasibility.
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Submitted 9 August, 2026; v1 submitted 23 June, 2026;
originally announced June 2026.
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Phase coding semi-quantum key distribution system based on the Single-state protocol
Authors:
Si-Ying Huang,
Qin-Cheng Hou,
Tian-Ming Zhao,
Jin-Dong Wang,
Nai-Da Mo,
Zheng-JunWei,
Ya-Fei Yu,
Zhi-Ming Zhang
Abstract:
Semi-quantum key distribution (SQKD) allows sharing random keys between a quantum user and a classical user, which significantly saves user resources, especially when using the Single-state protocol. However, the operation of the classical user, which involves measurement and resending using the Single-state protocol, presents technical difficulties in experiment and there is a security vulnerabil…
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Semi-quantum key distribution (SQKD) allows sharing random keys between a quantum user and a classical user, which significantly saves user resources, especially when using the Single-state protocol. However, the operation of the classical user, which involves measurement and resending using the Single-state protocol, presents technical difficulties in experiment and there is a security vulnerability of "tagged" attack in theory. To solve these problems, in our work, based on the Single-state protocol, we propose the "selective modulation" method and successfully implement a phase-encoded semi-quantum key distribution system. The system operates at a frequency of 100MHz and an average photon number of 0.1. The interference contrast achieved 97.45%, the average quantum bit error rate was 1.20%, and the raw key rate reached 88Kbps. Our experimental results demonstrate the feasibility and stability of the proposed phase-encoded SQKD system. Furthermore, we conducted an analysis of the "selective modulation" scheme in terms of quantum state evolution to assess the security of our system and ultimately proved that it can resist "tagged" attack. The classical user of our system requires only two optical devices and operates without relying on full quantum capabilities, thereby enhancing its application potential in quantum networks. This work validates the feasibility of SQKD experiments and provides ideas for future research on SQKD experiments and security studies.
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Submitted 23 May, 2026; v1 submitted 13 May, 2024;
originally announced May 2024.
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Active robustness against the detuning-error for Rydberg quantum gates
Authors:
Qing-Ling Hou,
Han Wang,
Jing Qian
Abstract:
Error suppression to the experimental imperfections is a central challenge for useful quantum computing. Recent studies have shown the advantages of using single-modulated pulses based on optimal control which can realize high-fidelity two-qubit gates in neutral-atom arrays. However, typical optimization only minimizes the ideal gate error in the absence of any decay, which allows the gate to be p…
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Error suppression to the experimental imperfections is a central challenge for useful quantum computing. Recent studies have shown the advantages of using single-modulated pulses based on optimal control which can realize high-fidelity two-qubit gates in neutral-atom arrays. However, typical optimization only minimizes the ideal gate error in the absence of any decay, which allows the gate to be passively influenced by all error sources leading to an exponential increase of sensitivity when the error becomes larger. In the present work, we propose the realization of two-qubit CZ gates with active robustness against two-photon detuning errors. Our method depends on a modified cost function in numerical optimization for shaping gate pulses, which can minimize, not only the ideal gate error but also the fluctuations of gate infidelity over a wide error range. We introduce a family of Rydberg blockade gates with active robustness towards the impacts of versatile noise sources such as Doppler dephasing and ac Stark shifts. The resulting gates with robust pulses can significantly increase the insensitivity to any type of errors acting on the two-photon detuning, benefiting from a relaxed requirement of colder atomic temperatures or more stable lasers for current experimental technology.
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Submitted 4 September, 2024; v1 submitted 17 April, 2024;
originally announced April 2024.
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Partial transpose of permutation matrices
Authors:
Qing-Hu Hou,
Toufik Mansour,
Simone Severini
Abstract:
The partial transpose of a block matrix M is the matrix obtained by transposing the blocks of M independently. We approach the notion of partial transpose from a combinatorial point of view. In this perspective, we solve some basic enumeration problems concerning the partial transpose of permutation matrices. More specifically, we count the number of permutations matrices which are equal to thei…
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The partial transpose of a block matrix M is the matrix obtained by transposing the blocks of M independently. We approach the notion of partial transpose from a combinatorial point of view. In this perspective, we solve some basic enumeration problems concerning the partial transpose of permutation matrices. More specifically, we count the number of permutations matrices which are equal to their partial transpose and the number of permutation matrices whose partial transpose is still a permutation. We solve these problems also when restricted to symmetric permutation matrices only.
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Submitted 22 March, 2008; v1 submitted 21 September, 2007;
originally announced September 2007.