A bucket-brigade quantum random access memory

Nature Physics (2026)Cite this article Quantum random access memory (QRAM) enables efficient access to classical data for quantum computers and is a prerequisite for many quantum algorithms in achieving quantum speed-up. Despite various proposals, there have not been many experimental realizations of QRAM. Here we use a superconducting quantum processor to implement a circuit-based bucket-brigade QRAM, which uses a binary tree of quantum routers to enable efficient addressing of the stored information. To facilitate the experimental implementation, we introduce an efficient gate decomposition scheme for quantum routers, which effectively reduces the depth of the QRAM circuit compared with the conventional controlled-SWAP implementation. We further propose an error mitigation method to improve the query fidelity of the QRAM. With these techniques, we are able to experimentally implement the QRAM architectures for addressing four and eight classical bits, achieving query fidelities up to 0.809 ± 0.025 and 0.604 ± 0.005, respectively. Additionally, we study the error propagation mechanism and the scalability of our QRAM implementation, which provides experimental evidence for the noise resilience of the bucket-brigade architecture. Our results highlight the potential of superconducting quantum processors for realizing a scalable QRAM architecture.This is a preview of subscription content, access via your institution Access Nature and 54 other Nature Portfolio journals Get Nature+, our best-value online-access subscription $32.99 / 30 days cancel any timeSubscribe to this journal Receive 12 print issues and online access $259.00 per yearonly $21.58 per issueBuy this articleUSD 39.95Prices may be subject to local taxes which are calculated during checkoutThe data presented in the figures and that support the other findings of this study are publicly available via Zenodo at https://doi.org/10.5281/zenodo.18408759 (ref. 45.) Source data are provided with this paper.The data analysis and numerical simulation codes for this study are publicly available via Zenodo at https://doi.org/10.5281/zenodo.18408759 (ref. 45).Gupta, S. & Zia, R. Quantum neural networks. J. Comput. Syst. Sci. 63, 355–383 (2001).Article MathSciNet Google Scholar Rebentrost, P., Mohseni, M. & Lloyd, S. Quantum support vector machine for big data classification. Phys. Rev. Lett. 113, 130503 (2014).Article ADS Google Scholar Bang, J., Dutta, A., Lee, S.-W. & Kim, J. Optimal usage of quantum random access memory in quantum machine learning. Phys. Rev. A 99, 012326 (2019).Article ADS Google Scholar Phalak, K., Li, J. & Ghosh, S. Trainable PQC-based QRAM for quantum storage. IEEE Access 11, 51892 (2023).Article Google Scholar Liu, J. et al. Towards provably efficient quantum algorithms for large-scale machine-learning models. Nat. Commun. 15, 434 (2024).Article ADS Google Scholar Ciliberto, C. et al. Quantum machine learning: a classical perspective. Proc. R. Soc. A 474, 20170551 (2018).Article ADS MathSciNet Google Scholar Berry, D. W., Gidney, C., Motta, M., McClean, J. R. & Babbush, R. Qubitization of arbitrary basis quantum chemistry leveraging sparsity and low rank factorization. Quantum 3, 208 (2019).Article Google Scholar Babbush, R. et al. Encoding electronic spectra in quantum circuits with linear T complexity. Phys. Rev. X 8, 041015 (2018).

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Preprint at https://arxiv.org/abs/2405.08810 (2024).Van den Nest, M. Simulating quantum computers with probabilistic methods. Quant. Inf. Comp. 11, 784–812 (2011).MathSciNet Google Scholar Shen, F., Ji, Y. & Xiang, D. Source data and simulation code for ‘a bucket- bridge quantum random access memory’. Zenodo https://doi.org/10.5281/zenodo.18408759 (2026).Download referencesWe thank H. Wang for supporting the device and the experimental platform on which the experiment was carried out. The device was fabricated at the Micro-Nano Fabrication Center of Zhejiang University. We acknowledge support from the National Key Research and Development Program of China (Grant No. 2023YFB4502600), the Zhejiang Provincial Natural Science Foundation of China (Grant Nos. LR25F020002, LR24A040002 and LDQ23A040001), the National Natural Science Foundation of China (Grant Nos. 12174342, 12274368, 12274367, 12322414, 12404570, 12404574 and 92365301).These authors contributed equally: Fanhao Shen, Yujie Ji, Debin Xiang.School of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control, Zhejiang University, Hangzhou, ChinaFanhao Shen, Yujie Ji, Yanzhe Wang, Ke Wang, Chuanyu Zhang, Aosai Zhang, Yiren Zou, Yu Gao, Zhengyi Cui, Gongyu Liu, Jianan Yang, Yihang Han, Jinfeng Deng, Hekang Li, Qiujiang Guo, Pengfei Zhang, Chao Song & Zhen WangCollege of Computer Science, and ZJU-Ningbo Global Innovation Center, Zhejiang University, Hangzhou, ChinaDebin Xiang, Liqiang Lu & Jianwei YinChina Mobile (Suzhou) Software Technology Co. Ltd, Suzhou, ChinaAnbang Wang & Zhihong ZhangSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarC.S., L.L., Z.W. and J. Yin conceived the project. F.S. conducted the experiments under the supervision of C.S. Y.J. designed the experimental circuits and performed the theoretical analyses under the supervision of C.S. Y.J., F.S. and D.X. performed the simulations and analysed the experimental data under the supervision of C.S. and L.L. H.L. fabricated the device. C.S., Z.W., Q.G., H.L., P.Z., Y.W., K.W., C.Z., A.Z., Y.Z., Y.G., Z.C., G.L., J. Yang and Y.H. contributed to the experimental set-up. Y.J., F.S., D.X., L.L. and C.S. wrote the paper with input from all authors. All authors discussed the results and contributed to the final version of the paper.Correspondence to Chao Song, Liqiang Lu, Zhen Wang or Jianwei Yin.The authors declare no competing interests.Nature Physics thanks Connor Hann, Sébastien Léger and Hong Qiao for their contribution to the peer review of this work.Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.which provides a detailed explanation of Fig. 1d, elucidating the role of each physical qubit in every phase and the operations performed. Address preparation:The initial address state is prepared on the two address register qubits, a0 and a1. Address loading:The qubit originally holding a0 is reassigned as the router address qubit A. A quantum routing operation is then applied to load the information from a1 into the second-layer router address qubits A0 and A1. Finally, a SWAP gate moves A to the qubit originally occupied by a1. Data loading:The router data qubit D is initialized to \(|+\rangle\) to enable phase encoding during data writing. Its state is then loaded into the second-layer router data qubits D0 and D1 via a quantum routing operation. Data writing:Classical bits are encoded by selectively applying or omitting the quantum gates inside the dashed squares, depending on the bit value (1 or 0). Data retrieval:The quantum state is retrieved from D0 and D1 back to D via quantum routing. A Hadamard gate is applied to D to return the state to the computational basis. Quantum teleportation is then used to transfer the state from D to the data register qubit d. Address retrieval: A is swapped back to the qubit originally holding a0. The address information in A0 and A1 is then retrieved back to the qubit initially holding a1 via a quantum routing operation. Error mitigation and quantum state tomography (QST): QST is applied to a0, a1, and d, with the tomography operation on d reinterpreted via Pauli tracking (see Methods). Router qubits are also measured for post-selection error mitigation.In all figures, the proportion values represent the average value of the proportion of valid results across the 16 classical data configurations, with the error bar representing their standard deviation. a, The proportion of valid results after error mitigation for a two-layer bucket brigade QRAM under varying query addresses. b, The proportion of valid results for different error mitigation strategies under query addresses \(|0+\rangle\) and \(|1+\rangle\).Source dataa, Schematic of the three-layer bucket-brigade QRAM, which can query eight classical data bits, labeled from x000 to x111, according to the query address. b, Device layout for implementing the three-layer bucket-brigade QRAM. Physical qubits are labeled according to their assigned roles during operational phases from address loading to address retrieval. c, Quantum circuit for the error scaling experiment of the three-layer QRAM. As in the two-layer QRAM case, the router address qubit (A), router data qubit (D), and one ancilla qubit are reused as the address register a0, a1, and a2 at the beginning and end of the experiment. Instead of using quantum teleportation, here the data bus is directly transferred from the router data qubit D to the data register qubit d via two SWAP gates at the end of the data retrieval phase. a, Schematic of the three-layer bucket-brigade QRAM, which can query eight classical data bits, labeled from x000 to x111, according to the query address. b, Device layout for implementing the three-layer bucket-brigade QRAM. Physical qubits are labeled according to their assigned roles during operational phases from address loading to address retrieval. c, Quantum circuit for the error scaling experiment of the three-layer QRAM. As in the two-layer QRAM case, the router address qubit (A), router data qubit (D), and one ancilla qubit are reused as the address register a0, a1, and a2 at the beginning and end of the experiment. Instead of using quantum teleportation, here the data bus is directly transferred from the router data qubit D to the data register qubit d via two SWAP gates at the end of the data retrieval phase.The results are obtained via numerical simulations with address state \(|00+\rangle\) and the classic configuration 01010101. The percentage in parentheses represents the proportion of this error component in the total error. CZ: CZ gate depolarizing error, excluding the decoherence error during CZ gates; 1Q: Single-qubit gate depolarizing error, excluding the decoherence error during single-qubit gates; T1: Qubit energy relaxation error; Tφ: Qubit dephasing error.

See Supplementary Information for details on the error budget analysis.Source dataThe simulation data are fitted to 1 − F = A × pα, where F is the query fidelity and p is the two-qubit gate error rate. Only data points with infidelity below 0.1 are included in the fit. Experimental results for both two- and three-layer QRAM at p = 3.8 × 10−3 are marked by pentagrams. The discrepancy between the experimental and numerical results is mainly due to the over-simplification of the error models employed in the numerical simulation (see Method).Source dataSupplementary Figs. 1–12, Discussion and Tables I–III.Source data for supplementary figures.Simulation source data.Statistical source data and simulation source data.Statistical source data.Statistical source data and simulation source data.Statistical source data.Statistical source data.Statistical source data.Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.Reprints and permissionsShen, F., Ji, Y., Xiang, D. et al. A bucket-brigade quantum random access memory. Nat. Phys. (2026). https://doi.org/10.1038/s41567-026-03218-2Download citationReceived: 20 June 2025Accepted: 12 February 2026Published: 16 March 2026Version of record: 16 March 2026DOI: https://doi.org/10.1038/s41567-026-03218-2Anyone you share the following link with will be able to read this content:Sorry, a shareable link is not currently available for this article. Provided by the Springer Nature SharedIt content-sharing initiative