Photon-number conserved universal quantum logic employing continuous-time quantum walk on dual-rail qubit arrays

npj | quantum information Article Published in partnership with The University of New South Wales https://doi.org/10.1038/s41534-025-01147-1 Photon-number conserved universal quantum logic employing continuous-time quantum walk on dual-rail qubit arrays Check for updates 1,2,5 1234567890():,; 1234567890():,; Hao-Yu Guan 3,5 , Yifei Li 1,2,4 & Xiu-Hao Deng We demonstrate a synergy between dual-rail qubit encoding and continuous-time quantum walks (CTQW) to realize universal quantum logic in superconducting circuits. Utilizing the photon-numberconserving dynamics of CTQW on dual-rail transmons, which systematically transform leakage and relaxation into erasure events, our architecture facilitates the suppression of population leakage and the implementation of high-fidelity quantum gates. We construct single-, two-, and three-qubit operations that preserve dual-rail encoding, facilitated by tunable coupler strengths compatible with current superconducting qubit platforms. Numerical simulations confirm robust behavior against dephasing, relaxation, and imperfections in coupling, underscoring the erasure-friendly nature of the system. This hardware-efficient scheme thus provides a practical pathway to early fault-tolerant quantum computation, laying the groundwork for scalable gate implementations and advanced errorcorrection strategies. In quantum information processing, high-fidelity control and error correction are vital, as superconducting architectures often suffer from leakage out of the logical subspace or relaxation to lower-energy states. A promising path to address these issues is converting leakage or relaxation events into erasure errors, which explicitly flag themselves for correction1,2. Recent studies on dual-rail qubits encode information in a single photon-number excitation distributed across two resonantly coupled transmons, enabling efficient leakage detection and improving error-correction thresholds3–10. Despite these advances in error detection capabilities, a critical gap persists in developing universal quantum logical gates that inherently preserve the dual-rail encoding during operation. This fundamental limitation currently constrains the practical implementation of fault-tolerant quantum computation using this promising architecture. In parallel, continuous-time quantum walks (CTQW) provide a powerful framework that preserves the total number of excitations, making them a natural match for dual-rail encoding. By confining the walker–a single excitation–to a well-defined subspace, CTQW safeguards against leakage while enabling potential quantum speedups in hitting and mixing processes11–14. These features have spurred experimental demonstrations across various integrated qubit systems, such as superconducting qubits15–17. Beyond single-particle dynamics, interactions between multiple walkers introduce richer correlated behavior18,19 and can support robust quantum search20–23 and error correction24. From a theoretical standpoint, multi-walkers CTQW can construct universal quantum logic25,26, supported by proposals demonstrating high-fidelity controlled-phase (CPhase) gates27 or leveraging two internal states of the walker on a directed graph28. A controlled-NOT (CNOT) gate has been constructed for both noninteracting bosons–realized by photons in waveguide lattices–and for interacting bosons using ultra-cold atoms29. All these advancements highlight the potential of CTQW in universal quantum computing. By integrating the dual-rail transmon encoding with CTQW, it is possible to harness the advantages of both methodologies: robust error management via erasure conversion and the preservation of photonnumber properties inherent to CTQW. This integration enhances the efficiency of erasure error correction in quantum computing architectures built upon this framework. In this study, we propose a foundational framework to implement universal quantum logic based on the operation of correlated CTQW within the structure of dual-rail encoded qubit arrays. We present explicit constructions of single- and two-qubit gates, such as the controlledZ (CZ) and iSWAP gates, alongside three-qubit gates, maintaining the dualrail encoding by the end of the quantum evolution. Our analysis encompasses both transverse and longitudinal connections within a superconducting qubit array, deriving parameter regimes that align with current experimental methodologies utilizing tunable transmon couplers. Additionally, we investigate the behavior of these gate constructions under realistic noise conditions, including dephasing, relaxation, and imperfections in 1 International Quantum Academy, Shenzhen, China. 2Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, China. 3Cuiying Honors College, Lanzhou University, Lanzhou, China. 4Shenzhen Branch, Hefei National Laboratory, Shenzhen, China. 5These authors e-mail: contributed equally: Hao-Yu Guan, Yifei Li. npj Quantum Information | (2026)12:17 1 Article https://doi.org/10.1038/s41534-025-01147-1 coupler strengths or detunings. Our results suggest that the intrinsic properties of dual-rail transmons, in conjunction with the excitationconserving attributes of CTQW, render this approach not only feasible but potentially robust against prevalent hardware imperfections. This comprehensive perspective holds promise for advancing early efforts in faulttolerant quantum computation by providing both practical means for gate synthesis and a stable encoding architecture for superconducting circuits. Results Continuous-time quantum walks on the extended BoseHubbard model The extended Bose-Hubbard model (EBHM) serves as a nontrivial model for studying quantum walks. There is no additional interaction energy when there is a single walker on graphs; when multiple walkers are on the same graphs, they interact with each other and exhibit correlated quantum walks29. These quantum walks go beyond simple hopping, incorporating local phase shifts, on-site interactions, and nearest-neighbor correlations associated with EBHM. This subsection introduces the EBHM and its graph-based interpretation as a platform for describing such nontrivial CTQWs. The EBHM incorporates additional interactions beyond the standard Bose-Hubbard framework, enabling the study of diverse quantum phenomena30. It has been experimentally realized in ultracold atoms in optical lattices31, Rydberg atom arrays32,33, superconducting circuits5,34, and dipolar excitons35. In this work, we implement the EBHM using a two-dimensional superconducting circuit composed of transmons and tunable couplers, as illustrated in Fig. 1(a). Starting from the full circuit Hamiltonian, we derive an effective Hamiltonian by decoupling the coupler. This effective Hamiltonian is then transformed into the rotating frame. The full description of (a) T C C T C T T C T C C Q T T C Coupler C Q C C C C T Q Transmon 2 C (...truncated)