Yang et al. (Phys. Rev. Lett. 133, 170601 (2024)) demonstrated a coupler-assisted leakage-reduction scheme on a 66-qubit two-dimensional tunable-coupler superconducting processor: coupler leakage is dissipated through readout resonators into a broadband Purcell filter (c-LRU), and state-selective parametric qubit-coupler swaps remove qubit leakage to the second and third excited states (f-LRU, h-LRU) with 98.1% efficiency and only 0.58% error on the computational subspace, suppressing time-correlated leakage errors in a weight-2 stabilizer circuit. Making the scheme scalable and performance-neutral in a full surface-code lattice remains open, with the authors themselves identifying the limitations that lead to this. Performance-neutrality here means that the per-cycle logical error rate of the lattice with the LRUs enabled does not exceed that of the identical lattice without LRUs (within the statistical uncertainty of the estimate). Three bottlenecks survive: (i) the coupler dissipation rate is limited by indirect coupling to the Purcell filter, and the proposed direct coupler-to-filter coupling, with its two-qubit-gate trade-offs, has not been implemented; (ii) simultaneous data- and ancilla-qubit LRUs across a 2D lattice lack a scalable calibration and control recipe that suppresses crosstalk and preserves computational-phase coherence; (iii) high-power readout can excite higher levels such as the third excited state, leaving residual leakage whose steady-state limit under realistic QEC operating points is unquantified, while LRU-induced computational-subspace errors (decoherence and conditional-phase accumulation) still need mitigation strategies validated at lattice scale.

Background

Superconducting quantum computers typically encode qubits in transmons — weakly anharmonic microwave oscillators whose lowest two levels |g⟩ and |e⟩ form the computational basis but which also possess higher levels |f⟩ (second excited) and |h⟩ (third excited). Gates and high-power dispersive readout occasionally populate these non-computational levels, an error type called leakage. The surface code — the leading quantum error correction (QEC) scheme for superconducting hardware — encodes a logical qubit in a 2D lattice of data qubits whose parity is repeatedly measured by ancilla qubits, and it assumes sparse, weakly correlated Pauli errors. Leakage violates this assumption: leaked population is long-lived, survives across cycles (time correlation), and can spread between neighboring qubits and couplers during two-qubit gates (space correlation), defeating the exponential suppression of logical error with code size. A leakage reduction unit (LRU) is an operation applied each QEC cycle that returns leaked population to the computational subspace, converting leakage into ordinary correctable Pauli errors. Two LRU families had been demonstrated before the source work: all-microwave LRUs, in which simultaneous drives on the transmon and its readout resonator empty the second and third excited states with about 99% efficacy in 220 ns and were run simultaneously in a weight-2 parity check (Marques et al., Phys. Rev. Lett. 130, 250602 (2023)); and swap-based data-qubit leakage removal, in which leaked population is swapped to dedicated neighboring qubits and reset, demonstrated with per-cycle leakage removal in distance-3 surface-code and distance-21 bit-flip codes on Google's Sycamore processor (Miao et al., Nature Physics 19, 1780 (2023)). Contemporary scalable superconducting processors, however, are built around tunable couplers — frequency-tunable intermediate transmons between every qubit pair that mediate entangling gates and are idle during measurement. The source work (Yang et al., Phys. Rev. Lett. 133, 170601 (2024)) turned these couplers into leakage conduits: the c-LRU tunes couplers near resonance with the readout resonators so that coupler leakage dissipates into the broadband Purcell filter (a coupled-resonator network that lets readout photons escape quickly while protecting qubit coherence), and the f-LRU and h-LRU use parametric frequency modulation of the coupler to activate state-selective qubit-coupler swaps that project |f⟩ and |h⟩ population back to |e⟩. On a 66-qubit 2D grid, the scheme removed coupler leakage within hundreds of nanoseconds, achieved 98.1% qubit-leakage reduction with 0.58% computational-subspace error measured by simultaneous interleaved randomized benchmarking (a protocol that compares randomized benchmarking decay with and without the LRU interleaved), and suppressed leakage-induced correlated errors in repeated weight-2 Z-stabilizer cycles. The couplers couple to the Purcell filter only indirectly, through a stray coupling to the readout resonators of roughly 30 MHz, which caps the coupler dissipation rate; the couplers are also weakly anharmonic and hence themselves prone to leakage, and adiabatically tuning a coupler close to its qubits to speed up the parametric interaction generates conditional-phase accumulation (unwanted two-qubit phases) and extra decoherence exposure, which the error budget identifies as the dominant LRU-induced computational-subspace errors. These are the specific bottlenecks the source authors leave open on the path from one stabilizer to a full surface-code lattice.

Problem Statement

How can the demonstrated coupler-assisted leakage-reduction scheme be extended from a single weight-2 stabilizer to a full two-dimensional surface-code lattice so that leakage is bounded and the scheme is performance-neutral? A complete answer must jointly deliver three linked results that constitute this single objective. Each result must be given as a concrete design or protocol with quantified predictions and explicit device parameters and assumptions; a rigorous analytical or numerical characterization may satisfy a deliverable in place of a physical demonstration. (1) Fast coupler dissipation: implement and characterize direct dissipative coupling between the tunable couplers and the broadband Purcell filter — bypassing the present indirect path through the readout resonators — and quantify the achievable increase in coupler dissipation rate for c-LRUs together with two-qubit gate performance under this hardware change; the untested design expectation is that gates are unaffected because couplers remain outside the dissipative regime during gate operations. (2) Parallel operation: demonstrate simultaneous application of LRUs to both data and ancilla qubits across a surface-code lattice, providing a calibration and control recipe that suppresses crosstalk when multiple adjacent couplers connected to the same qubit are tuned and modulated, and that preserves computational-phase coherence under parallel parametric modulation. (3) Bounded steady-state leakage under realistic operation: quantify the steady-state leakage population at realistic QEC operating points, including high-power ancilla readout that can excite higher levels such as |h⟩ beyond what the f-LRU plus c-LRU sequence removes, and establish mitigations (extended LRU sequences or readout strategies), while reducing LRU-induced computational-subspace errors — dominated by decoherence and conditional-phase accumulation during adiabatic coupler tuning, e.g. via faster LRUs, improved adiabatic profiles, or active phase compensation — to a level that meets the performance-neutral target.

References

  1. Xiaohan Yang, Ji Chu, Zechen Guo, Wenhui Huang, Yongqi Liang, Jiawei Liu, Jiawei Qiu, Xuandong Sun, Ziyu Tao, Jiawei Zhang, Jiajian Zhang, Libo Zhang, Yuxuan Zhou, Weijie Guo, Ling Hu, Ji Jiang, Yang Liu, Xiayu Linpeng, Tingyong Chen, Yuanzhen Chen, Jingjing Niu, Song Liu, Youpeng Zhong, Dapeng Yu, 'Coupler-Assisted Leakage Reduction for Scalable Quantum Error Correction with Superconducting Qubits', Physical Review Letters 133, 170601 (2024). DOI: 10.1103/PhysRevLett.133.170601; arXiv:2403.16155; https://doi.org/10.1103/PhysRevLett.133.170601
  2. Kevin C. Miao, Matt McEwen, Juan Atalaya, Dvir Kafri, Leonid P. Pryadko, Andreas Bengtsson, Alex Opremcak, Kevin J. Satzinger, Zijun Chen, Paul V. Klimov, et al. (Google Quantum AI), 'Overcoming leakage in scalable quantum error correction', Nature Physics 19, 1780-1786 (2023). DOI: 10.1038/s41567-023-02226-w; arXiv:2211.04728; https://doi.org/10.1038/s41567-023-02226-w
  3. J. F. Marques, H. Ali, B. M. Varbanov, M. Finkel, H. M. Veen, S. L. M. van der Meer, S. Valles-Sanclemente, N. Muthusubramanian, M. Beekman, N. Haider, B. M. Terhal, L. DiCarlo, 'All-microwave leakage reduction units for quantum error correction with superconducting transmon qubits', Physical Review Letters 130, 250602 (2023). DOI: 10.1103/PhysRevLett.130.250602; arXiv:2302.09876; https://doi.org/10.1103/PhysRevLett.130.250602
  4. Google Quantum AI and Collaborators, 'Quantum error correction below the surface code threshold', Nature 638, 920-926 (2025). DOI: 10.1038/s41586-024-08449-y; arXiv:2408.13687; https://doi.org/10.1038/s41586-024-08449-y
  5. Tan He, Weiping Lin, Rui Wang, Yuan Li, Jiahao Bei, et al. (USTC and collaborators), 'Experimental Quantum Error Correction below the Surface Code Threshold via All-Microwave Leakage Suppression', Physical Review Letters 135, 260601 (2025). DOI: 10.1103/rqkg-dw31; https://doi.org/10.1103/rqkg-dw31
  6. Yuejie Xin, Sean L. M. van der Meer, Marc Serra-Peralta, Tim H. F. Vroomans, Matvey Finkel, Hendrik M. Veen, Mark W. Beekman, Leonardo DiCarlo, 'Improved error correction with leakage reduction units built into qubit measurement in a superconducting quantum processor', arXiv:2511.17460 (2025). https://arxiv.org/abs/2511.17460
  7. Yong-Xi Xiao, Da'er Feng, Xu-Yang Gu, Gui-Han Liang, Ming-Chuan Wang, Zhen-Yu Peng, Bing-Jie Chen, Yu Yan, Zheng-Yang Mei, Si-Lu Zhao, Yi-Zhou Bu, Cheng-Lin Deng, Kai Yang, Ye Tian, Xiaohui Song, Dongning Zheng, Yu-Xiang Zhang, Yun-Hao Shi, Zhongcheng Xiang, Kai Xu, Heng Fan, 'Flexible Readout and Unconditional Reset for Superconducting Multiqubit Processors with Tunable Purcell Filters', Physical Review Letters 136, 070601 (2026). DOI: 10.1103/vwrv-x1kr; arXiv:2507.06988; https://doi.org/10.1103/vwrv-x1kr
  8. Xu-Yang Gu, Da'er Feng, Zhen-Yu Peng, Gui-Han Liang, Yang He, Yongxi Xiao, Ming-Chuan Wang, Yu Yan, Bing-Jie Chen, Zheng-Yang Mei, Yi-Zhou Bu, Jia-Chi Zhang, Jia-Cheng Song, Cheng-Lin Deng, Yun-Hao Shi, Xiaohui Song, Dongning Zheng, Kai Xu, Zhongcheng Xiang, Heng Fan, 'Multimode Purcell filter for superconducting-qubit reset and readout with intrinsic Purcell protection', Physical Review Applied 25, 044003 (2026). DOI: 10.1103/k398-k98j; arXiv:2507.04676; https://doi.org/10.1103/k398-k98j
  9. Hui Wang, Feng Bao, Yan-Jun Zhao, Xun-Wei Xu, 'Purcell-Engineered Hybrid Coupler for Leakage-Suppressed Robust CZ Gates', arXiv:2607.23463 (2026). https://arxiv.org/abs/2607.23463
  10. Taneli Tolppanen, Gonzalo Martín-Vázquez, Sasu Tuohino, Matti Silveri, 'Leakage Mobility and Passive Leakage Removal in Transmons with Tunable Couplers', arXiv:2607.00688 (2026). https://arxiv.org/abs/2607.00688
  11. Takeaki Miyamura, Zhiling Wang, Peter A. Spring, Hiroto Mukai, Kohei Matsuura, Jesper Ilves, Yoshiki Sunada, Yasunobu Nakamura, 'Heralded Leakage Detection with Preserved Computational-State Coherence in a Fixed-Frequency Transmon', arXiv:2607.17204 (2026). https://arxiv.org/abs/2607.17204
  12. Liran Shirizly, Dekel Meirom, Malcolm Carroll, Haggai Landa, 'Feedforward suppression of readout-induced faults in quantum error correction', Physical Review A 112, L050602 (2025). DOI: 10.1103/ght4-yqmb; https://doi.org/10.1103/ght4-yqmb
  13. Ting Lin, Zi-Hao Qin, Zheng-Yuan Xue, Tao Chen, 'Leakage Suppression in Quantum Control via Static Parameter Offsets', Physical Review A 113, 042623 (2026). DOI: 10.1103/lycw-g48q; arXiv:2604.03726; https://doi.org/10.1103/lycw-g48q