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RandomMeas.jl: A Julia Package for Randomized Measurements in Quantum Devices

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RandomMeas.jl: A Julia Package for Randomized Measurements in Quantum Devices

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AbstractWe introduce $\texttt{RandomMeas.jl}$, a modular and high-performance open-source software package written in Julia for implementing and analyzing randomized measurement protocols in quantum computing. Randomized measurements provide a powerful framework for extracting properties of quantum states and processes such as expectation values, entanglement, and fidelities using simple experimental procedures combined with classical post-processing, most prominently via the classical shadow formalism. RandomMeas.jl covers the full randomized measurement workflow, from the generation of measurement settings for use on a quantum computer, the optional classical simulation of randomized measurements with tensor networks, to a suite of estimators for physical properties based on classical shadows. The package includes advanced features such as robust and shallow shadow techniques, batch estimators, and built-in statistical uncertainty estimation. Its unified, composable design enables the scalable application and further development of randomized measurements protocols across theoretical and experimental contexts.Featured image: RandomMeas.jl overview. The Julia package provides an end-to-end, modular workflow for randomized-measurement experiments—generating measurement settings, loading or simulating measurement data, constructing classical shadows, and computing scalable estimators with uncertainty quantification.Popular summaryRandomized measurement protocols provide an efficient quantum-to-classical conversion: by performing a series of randomly chosen measurements, one obtains a compact classical dataset (bitstrings) that can later be reprocessed to estimate many properties of the underlying quantum state, without redesigning the experiment for each new question. RandomMeas.jl is an open-source Julia package developed to make these methods broadly accessible and scalable. It offers a unified workflow—from generating randomized measurement settings, to handling measurement data, to computing classical-shadow-based estimators with uncertainty quantification—and is designed to be modular and extensible, so that new protocols and analysis routines can be incorporated and shared across theory and experiments.► BibTeX data@article{Elben2026randommeasjljulia, doi = {10.22331/q-2026-04-28-2086}, url = {https://doi.org/10.22331/q-2026-04-28-2086}, title = {Random{M}eas.jl: {A} {J}ulia {P}ackage for {R}andomized {M}easurements in {Q}uantum {D}evices}, author = {Elben, Andreas and Vermersch, Benoit}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2086}, month = apr, year = {2026} }► References [1] Andreas Elben, Steven T. 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SciPost Physics 12, 106 (2022). https://doi.org/10.21468/SciPostPhys.12.3.106 [62] Christian Kokail, Christine Maier, Rick van Bijnen, Tiff Brydges, Manoj K. Joshi, Petar Jurcevic, Christine A. Muschik, Pietro Silvi, Rainer Blatt, Christian F. Roos, and Peter Zoller. ``Self-Verifying Variational Quantum Simulation of the Lattice Schwinger Model''. Nature 569, 355–360 (2019). https://doi.org/10.1038/s41586-019-1177-4 [63] Tiff Brydges, Andreas Elben, Petar Jurcevic, Benoît Vermersch, Christine Maier, Ben P. Lanyon, Peter Zoller, Rainer Blatt, and Christian F. Roos. ``Probing Rényi Entanglement Entropies via Randomized Measurements''. https://zenodo.org/records/2527010 (2018). https://zenodo.org/records/2527010~Cited by[1] Akash Vijay, Ayush Raj, Jonah Kudler-Flam, Benoît Vermersch, Andreas Elben, and Laimei Nie, "Analytically Continuing the Randomized Measurement Toolbox", arXiv:2511.02912, (2025). [2] Matteo Votto, Marko Ljubotina, Cécilia Lancien, J. Ignacio Cirac, Peter Zoller, Maksym Serbyn, Lorenzo Piroli, and Benoît Vermersch, "Learning Mixed Quantum States in Large-Scale Experiments", Physical Review Letters 136 9, 090801 (2026). [3] Jihyeon Park, Collin C. D. Frink, and Matthew Otten, "CANOE: Classically Assisted Non-Orthogonal Eigensolver", arXiv:2603.13188, (2026). The above citations are from SAO/NASA ADS (last updated successfully 2026-04-28 08:21:26). The list may be incomplete as not all publishers provide suitable and complete citation data.Could not fetch Crossref cited-by data during last attempt 2026-04-28 08:21:25: Could not fetch cited-by data for 10.22331/q-2026-04-28-2086 from Crossref. This is normal if the DOI was registered recently.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. AbstractWe introduce $\texttt{RandomMeas.jl}$, a modular and high-performance open-source software package written in Julia for implementing and analyzing randomized measurement protocols in quantum computing. Randomized measurements provide a powerful framework for extracting properties of quantum states and processes such as expectation values, entanglement, and fidelities using simple experimental procedures combined with classical post-processing, most prominently via the classical shadow formalism. RandomMeas.jl covers the full randomized measurement workflow, from the generation of measurement settings for use on a quantum computer, the optional classical simulation of randomized measurements with tensor networks, to a suite of estimators for physical properties based on classical shadows. The package includes advanced features such as robust and shallow shadow techniques, batch estimators, and built-in statistical uncertainty estimation. Its unified, composable design enables the scalable application and further development of randomized measurements protocols across theoretical and experimental contexts.Featured image: RandomMeas.jl overview. The Julia package provides an end-to-end, modular workflow for randomized-measurement experiments—generating measurement settings, loading or simulating measurement data, constructing classical shadows, and computing scalable estimators with uncertainty quantification.Popular summaryRandomized measurement protocols provide an efficient quantum-to-classical conversion: by performing a series of randomly chosen measurements, one obtains a compact classical dataset (bitstrings) that can later be reprocessed to estimate many properties of the underlying quantum state, without redesigning the experiment for each new question. RandomMeas.jl is an open-source Julia package developed to make these methods broadly accessible and scalable. It offers a unified workflow—from generating randomized measurement settings, to handling measurement data, to computing classical-shadow-based estimators with uncertainty quantification—and is designed to be modular and extensible, so that new protocols and analysis routines can be incorporated and shared across theory and experiments.► BibTeX data@article{Elben2026randommeasjljulia, doi = {10.22331/q-2026-04-28-2086}, url = {https://doi.org/10.22331/q-2026-04-28-2086}, title = {Random{M}eas.jl: {A} {J}ulia {P}ackage for {R}andomized {M}easurements in {Q}uantum {D}evices}, author = {Elben, Andreas and Vermersch, Benoit}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2086}, month = apr, year = {2026} }► References [1] Andreas Elben, Steven T. Flammia, Hsin-Yuan Huang, Richard Kueng, John Preskill, Benoît Vermersch, and Peter Zoller. ``The randomized measurement toolbox''. Nat. Rev. Phys. 5, 9–24 (2022). https://doi.org/10.1038/s42254-022-00535-2 [2] Hsin-Yuan Huang, Richard Kueng, and John Preskill. ``Predicting Many Properties of a Quantum System from Very Few Measurements''. Nat. Phys. 16, 1050–1057 (2020). https://doi.org/10.1038/s41567-020-0932-7 [3] Tiff Brydges, Andreas Elben, Petar Jurcevic, Benoît Vermersch, Christine Maier, Ben P. Lanyon, Peter Zoller, Rainer Blatt, and Christian F. Roos. ``Probing entanglement entropy via randomized measurements''. Science 364, 260–263 (2019). https://doi.org/10.1126/science.aau4963 [4] Manoj K. Joshi, Andreas Elben, Benoı̂t Vermersch, Tiff Brydges, Christine Maier, Peter Zoller, Rainer Blatt, and Christian F. Roos. ``Quantum Information Scrambling in a Trapped-Ion Quantum Simulator with Tunable Range Interactions''. Phys. Rev. Lett. 124, 240505 (2020). https://doi.org/10.1103/PhysRevLett.124.240505 [5] D. Zhu, Z. P. Cian, C. Noel, A. Risinger, D. Biswas, L. Egan, Y. Zhu, A. M. Green, C. Huerta Alderete, N. H. Nguyen, Q. Wang, A. Maksymov, Y. Nam, M. Cetina, N. M. Linke, M. Hafezi, and C. Monroe. ``Cross-platform comparison of arbitrary quantum states''. Nature Communications 13 (2022). https://doi.org/10.1038/s41467-022-34279-5 [6] Lata Kh. Joshi, Johannes Franke, Aniket Rath, Filiberto Ares, Sara Murciano, Florian Kranzl, Rainer Blatt, Peter Zoller, Benoît Vermersch, Pasquale Calabrese, Christian F. Roos, and Manoj K. Joshi. ``Observing the Quantum Mpemba Effect in Quantum Simulations''. Phys. Rev. Lett. 133, 010402 (2024). https://doi.org/10.1103/PhysRevLett.133.010402 [7] Ting Zhang, Jinzhao Sun, Xiao-Xu Fang, Xiao-Ming Zhang, Xiao Yuan, and He Lu. ``Experimental quantum state measurement with classical shadows''. Phys. Rev. Lett. 127, 200501 (2021). https://doi.org/10.1103/PhysRevLett.127.200501 [8] G.I. Struchalin, Ya. A. Zagorovskii, E.V. Kovlakov, S.S. Straupe, and S.P. Kulik. ``Experimental estimation of quantum state properties from classical shadows''. PRX Quantum 2 (2021). https://doi.org/10.1103/prxquantum.2.010307 [9] K. J. et al Satzinger. ``Realizing topologically ordered states on a quantum processor''. Science 374, 1237–1241 (2021). https://doi.org/10.1126/science.abi8378 [10] Vittorio Vitale, Aniket Rath, Petar Jurcevic, Andreas Elben, Cyril Branciard, and Benoît Vermersch. ``Robust Estimation of the Quantum Fisher Information on a Quantum Processor''. PRX Quantum 5, 030338 (2024). https://doi.org/10.1103/PRXQuantum.5.030338 [11] Hong-Ye Hu, Andi Gu, Swarnadeep Majumder, Hang Ren, Yipei Zhang, Derek S. Wang, Yi-Zhuang You, Zlatko Minev, Susanne F. Yelin, and Alireza Seif. ``Demonstration of robust and efficient quantum property learning with shallow shadows''. Nat. Comm. 16, 2943 (2025). https://doi.org/10.1038/s41467-025-57349-w [12] Hang Dong, Pengfei Zhang, Ceren B. Dağ, Yu Gao, Ning Wang, Jinfeng Deng, Xu Zhang, Jiachen Chen, Shibo Xu, Ke Wang, Yaozu Wu, Chuanyu Zhang, Feitong Jin, Xuhao Zhu, Aosai Zhang, Yiren Zou, Ziqi Tan, Zhengyi Cui, Zitian Zhu, Fanhao Shen, Tingting Li, Jiarun Zhong, Zehang Bao, Hekang Li, Zhen Wang, Qiujiang Guo, Chao Song, Fangli Liu, Amos Chan, Lei Ying, and H. Wang. ``Measuring the spectral form factor in many-body chaotic and localized phases of quantum processors''.

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RandomMeas.jl: A Julia Package for Randomized Measurements in Quantum Devices

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