@article{chapman_high--off-ratio_2023,
	title = {High-On-Off-Ratio Beam-Splitter Interaction for Gates on Bosonically Encoded Qubits},
	volume = {4},
	issn = {2691-3399},
	url = {https://link.aps.org/doi/10.1103/PRXQuantum.4.020355},
	doi = {10.1103/PRXQuantum.4.020355},
	pages = {020355},
	number = {2},
	journaltitle = {{PRX} Quantum},
	shortjournal = {{PRX} Quantum},
	author = {Chapman, Benjamin J. and De Graaf, Stijn J. and Xue, Sophia H. and Zhang, Yaxing and Teoh, James and Curtis, Jacob C. and Tsunoda, Takahiro and Eickbusch, Alec and Read, Alexander P. and Koottandavida, Akshay and Mundhada, Shantanu O. and Frunzio, Luigi and Devoret, M.H. and Girvin, S.M. and Schoelkopf, R.J.},
	urldate = {2023-11-02},
	date = {2023-06-28},
	langid = {english},
	file = {Chapman et al. - 2023 - High-On-Off-Ratio Beam-Splitter Interaction for Ga.pdf:/Users/shiv/Zotero/storage/9KHNWBPR/Chapman et al. - 2023 - High-On-Off-Ratio Beam-Splitter Interaction for Ga.pdf:application/pdf},
}


@article{Poboiko_2025,
   title={Measurement-induced transitions for interacting fermions},
   volume={111},
   ISSN={2469-9969},
   url={http://dx.doi.org/10.1103/PhysRevB.111.024204},
   DOI={10.1103/physrevb.111.024204},
   number={2},
   journal={Physical Review B},
   publisher={American Physical Society (APS)},
   author={Poboiko, Igor and Pöpperl, Paul and Gornyi, Igor V. and Mirlin, Alexander D.},
   year={2025},
   month=jan }



@article{Alberton_2021,
   title={Entanglement Transition in a Monitored Free-Fermion Chain: From Extended Criticality to Area Law},
   volume={126},
   ISSN={1079-7114},
   url={http://dx.doi.org/10.1103/PhysRevLett.126.170602},
   DOI={10.1103/physrevlett.126.170602},
   number={17},
   journal={Physical Review Letters},
   publisher={American Physical Society (APS)},
   author={Alberton, O. and Buchhold, M. and Diehl, S.},
   year={2021},
   month=apr }


@article{cao2019entanglement,
  title={Entanglement in a fermion chain under continuous monitoring},
  author={Cao, Xiangyu and Tilloy, Antoine and De Luca, Andrea},
  journal={SciPost Physics},
  volume={7},
  number={2},
  pages={024},
  year={2019}
}


@article{Fava_2023,
   title={Nonlinear Sigma Models for Monitored Dynamics of Free Fermions},
   volume={13},
   ISSN={2160-3308},
   url={http://dx.doi.org/10.1103/PhysRevX.13.041045},
   DOI={10.1103/physrevx.13.041045},
   number={4},
   journal={Physical Review X},
   publisher={American Physical Society (APS)},
   author={Fava, Michele and Piroli, Lorenzo and Swann, Tobias and Bernard, Denis and Nahum, Adam},
   year={2023},
   month=dec }




@article{Yokomizo_2025,
   title={Measurement-induced phase transition in free bosons},
   volume={111},
   ISSN={2469-9969},
   url={http://dx.doi.org/10.1103/y5r3-tv78},
   DOI={10.1103/y5r3-tv78},
   number={23},
   journal={Physical Review B},
   publisher={American Physical Society (APS)},
   author={Yokomizo, Kazuki and Ashida, Yuto},
   year={2025},
   month=jun }

@article{Guo_2025,
   title={Field theory of monitored interacting fermion dynamics with charge conservation},
   volume={112},
   ISSN={2469-9969},
   url={http://dx.doi.org/10.1103/gdxd-pw8v},
   DOI={10.1103/gdxd-pw8v},
   number={6},
   journal={Physical Review B},
   publisher={American Physical Society (APS)},
   author={Guo, Haoyu and Foster, Matthew S. and Jian, Chao-Ming and Ludwig, Andreas W. W.},
   year={2025},
   month=aug }

@article{poboiko2023theory,
  title={Theory of free fermions under random projective measurements},
  author={Poboiko, Igor and P{\"o}pperl, Paul and Gornyi, Igor V and Mirlin, Alexander D},
  journal={Physical Review X},
  volume={13},
  number={4},
  pages={041046},
  year={2023},
  publisher={APS}
}



@article{Minoguchi_2022,
   title={Continuous gaussian measurements of the free boson CFT: A model for  exactly solvable and detectable measurement-induced dynamics},
   volume={12},
   ISSN={2542-4653},
   url={http://dx.doi.org/10.21468/SciPostPhys.12.1.009},
   DOI={10.21468/scipostphys.12.1.009},
   number={1},
   journal={SciPost Physics},
   publisher={Stichting SciPost},
   author={Minoguchi, Yuri and Rabl, Peter and Buchhold, Michael},
   year={2022},
   month=jan }

@article{PhysRevResearch.6.043246,
  title = {Monitored fermions with conserved $U(1)$ charge},
  author = {Fava, Michele and Piroli, Lorenzo and Bernard, Denis and Nahum, Adam},
  journal = {Phys. Rev. Res.},
  volume = {6},
  issue = {4},
  pages = {043246},
  numpages = {21},
  year = {2024},
  month = {Dec},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevResearch.6.043246},
  url = {https://link.aps.org/doi/10.1103/PhysRevResearch.6.043246}
}



@article{Liu_2024,
   title={Entanglement of bosonic systems under monitored evolution},
   volume={110},
   ISSN={2469-9934},
   url={http://dx.doi.org/10.1103/PhysRevA.110.022208},
   DOI={10.1103/physreva.110.022208},
   number={2},
   journal={Physical Review A},
   publisher={American Physical Society (APS)},
   author={Liu, Quancheng and Ziegler, Klaus},
   year={2024},
   month=aug }

@article{Li_2025,
   title={Emergent deterministic entanglement dynamics in monitored infinite-range bosonic systems},
   volume={112},
   ISSN={2469-9969},
   url={http://dx.doi.org/10.1103/bhst-127b},
   DOI={10.1103/bhst-127b},
   number={10},
   journal={Physical Review B},
   publisher={American Physical Society (APS)},
   author={Li, Zejian and Delmonte, Anna and Fazio, Rosario},
   year={2025},
   month=sep }

@article{Zabalo-2022,
  title = {Operator Scaling Dimensions and Multifractality at Measurement-Induced Transitions},
  author = {Zabalo, A. and Gullans, M. J. and Wilson, J. H. and Vasseur, R. and Ludwig, A. W. W. and Gopalakrishnan, S. and Huse, David A. and Pixley, J. H.},
  journal = {Phys. Rev. Lett.},
  volume = {128},
  issue = {5},
  pages = {050602},
  numpages = {6},
  year = {2022},
  month = {Feb},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.128.050602},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.128.050602}
}


@article{Kamakari-2025,
  title = {Experimental Demonstration of Scalable Cross-Entropy Benchmarking to Detect Measurement-Induced Phase Transitions on a Superconducting Quantum Processor},
  author = {Kamakari, Hirsh and Sun, Jiace and Li, Yaodong and Thio, Jonathan J. and Gujarati, Tanvi P. and Fisher, Matthew P. A. and Motta, Mario and Minnich, Austin J.},
  journal = {Phys. Rev. Lett.},
  volume = {134},
  issue = {12},
  pages = {120401},
  numpages = {9},
  year = {2025},
  month = {Mar},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.134.120401},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.134.120401}
}


@misc{AshidafreeBoson,
      title={Measurement-Induced Phase Transition in Free Bosons}, 
      author={Kazuki Yokomizo and Yuto Ashida},
      year={2024},
      eprint={2405.19768},
      archivePrefix={arXiv},
      primaryClass={quant-ph},
      url={https://arxiv.org/abs/2405.19768}, 
}

@article{chakram_seamless_2021,
	title = {Seamless High- Q Microwave Cavities for Multimode Circuit Quantum Electrodynamics},
	volume = {127},
	issn = {0031-9007, 1079-7114},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.127.107701},
	doi = {10.1103/PhysRevLett.127.107701},
	pages = {107701},
	number = {10},
	journaltitle = {Physical Review Letters},
	shortjournal = {Phys. Rev. Lett.},
	author = {Chakram, Srivatsan and Oriani, Andrew E. and Naik, Ravi K. and Dixit, Akash V. and He, Kevin and Agrawal, Ankur and Kwon, Hyeokshin and Schuster, David I.},
	urldate = {2024-05-23},
	date = {2021-08-31},
	langid = {english},
	file = {Chakram et al. - 2021 - Seamless High- Q Microwave Cavities for Multimode .pdf:/Users/shiv/Zotero/storage/VUWLR8AI/Chakram et al. - 2021 - Seamless High- Q Microwave Cavities for Multimode .pdf:application/pdf},
}

@article{chakram_multimode_2022,
	title = {Multimode photon blockade},
	volume = {18},
	rights = {2022 The Author(s), under exclusive licence to Springer Nature Limited},
	issn = {1745-2481},
	url = {https://www.nature.com/articles/s41567-022-01630-y},
	doi = {10.1038/s41567-022-01630-y},
	abstract = {Interactions are essential for the creation of correlated quantum many-body states. Although two-body interactions underlie most natural phenomena, three- and four-body interactions are important for the physics of nuclei1, exotic few-body states in ultracold quantum gases2, the fractional quantum Hall effect3, quantum error correction4 and holography5,6. Recently, a number of artificial quantum systems have emerged as simulators for many-body physics, featuring the ability to engineer strong interactions. However, the interactions in these systems have largely been limited to the two-body paradigm and require building up multibody interactions by combining two-body forces. Here we implement a scheme to create a higher-order interaction between photons stored in multiple electromagnetic modes of a microwave cavity. The system is dressed such that there is collectively no interaction until a target total photon number is reached across multiple distinct modes, at which point the photons interact strongly. In our demonstration, we create interactions involving up to three bodies and across up to five modes. We harness the interaction to prepare single-mode Fock states and multimode W states, which we verify by introducing a multimode Wigner tomography method.},
	pages = {879--884},
	number = {8},
	journaltitle = {Nature Physics},
	shortjournal = {Nat. Phys.},
	author = {Chakram, Srivatsan and He, Kevin and Dixit, Akash V. and Oriani, Andrew E. and Naik, Ravi K. and Leung, Nelson and Kwon, Hyeokshin and Ma, Wen-Long and Jiang, Liang and Schuster, David I.},
	urldate = {2024-05-23},
	date = {2022-08},
	langid = {english},
	note = {Publisher: Nature Publishing Group},
	keywords = {Quantum information, Quantum mechanics, Quantum simulation, Qubits, Single photons and quantum effects},
	file = {Full Text PDF:/Users/shiv/Zotero/storage/2IFDG3VK/Chakram et al. - 2022 - Multimode photon blockade.pdf:application/pdf},
}



@article{Dehghani_2023,
   title={Neural-network decoders for measurement induced phase transitions},
   volume={14},
   ISSN={2041-1723},
   url={http://dx.doi.org/10.1038/s41467-023-37902-1},
   DOI={10.1038/s41467-023-37902-1},
   number={1},
   journal={Nature Communications},
   publisher={Springer Science and Business Media LLC},
   author={Dehghani, Hossein and Lavasani, Ali and Hafezi, Mohammad and Gullans, Michael J.},
   year={2023},
   month=may }

@article{Ippoliti_2024,
   title={Learnability Transitions in Monitored Quantum Dynamics via Eavesdropper’s Classical Shadows},
   volume={5},
   ISSN={2691-3399},
   url={http://dx.doi.org/10.1103/PRXQuantum.5.020304},
   DOI={10.1103/prxquantum.5.020304},
   number={2},
   journal={PRX Quantum},
   publisher={American Physical Society (APS)},
   author={Ippoliti, Matteo and Khemani, Vedika},
   year={2024},
   month=apr }

@misc{akhtar2023,
      title={Measurement-Induced Criticality is Tomographically Optimal}, 
      author={Ahmed A. Akhtar and Hong-Ye Hu and Yi-Zhuang You},
      year={2023},
      eprint={2308.01653},
      archivePrefix={arXiv},
      primaryClass={quant-ph},
      url={https://arxiv.org/abs/2308.01653} 
}

@misc{kim2025,
      title={Learning measurement-induced phase transitions using attention}, 
      author={Hyejin Kim and Abhishek Kumar and Yiqing Zhou and Yichen Xu and Romain Vasseur and Eun-Ah Kim},
      year={2025},
      eprint={2508.15895},
      archivePrefix={arXiv},
      primaryClass={quant-ph},
      url={https://arxiv.org/abs/2508.15895}, 
}

@article{McGinley_2024,
   title={Postselection-Free Learning of Measurement-Induced Quantum Dynamics},
   volume={5},
   ISSN={2691-3399},
   url={http://dx.doi.org/10.1103/PRXQuantum.5.020347},
   DOI={10.1103/prxquantum.5.020347},
   number={2},
   journal={PRX Quantum},
   publisher={American Physical Society (APS)},
   author={McGinley, Max},
   year={2024},
   month=may }





@article{milul_superconducting_2023,
	title = {Superconducting Cavity Qubit with Tens of Milliseconds Single-Photon Coherence Time},
	volume = {4},
	url = {https://link.aps.org/doi/10.1103/PRXQuantum.4.030336},
	doi = {10.1103/PRXQuantum.4.030336},
	abstract = {Storing quantum information for an extended period of time is essential for running quantum algorithms with low errors. Currently, superconducting quantum memories have coherence times of a few milliseconds, and surpassing this performance has remained an outstanding challenge. In this work, we report a single-photon qubit encoded in a novel superconducting cavity with a coherence time of 34 ms, representing an order of magnitude improvement compared to previous demonstrations. We use this long-lived quantum memory to store a Schrödinger cat state with a record size of 1024 photons, indicating the cavity’s potential for bosonic quantum error correction.},
	pages = {030336},
	number = {3},
	journaltitle = {{PRX} Quantum},
	shortjournal = {{PRX} Quantum},
	author = {Milul, Ofir and Guttel, Barkay and Goldblatt, Uri and Hazanov, Sergey and Joshi, Lalit M. and Chausovsky, Daniel and Kahn, Nitzan and Çiftyürek, Engin and Lafont, Fabien and Rosenblum, Serge},
	urldate = {2024-05-23},
	date = {2023-09-14},
	note = {Publisher: American Physical Society},
	file = {APS Snapshot:/Users/shiv/Zotero/storage/UTRV6247/PRXQuantum.4.html:text/html;Full Text PDF:/Users/shiv/Zotero/storage/AJU9UUAK/Milul et al. - 2023 - Superconducting Cavity Qubit with Tens of Millisec.pdf:application/pdf},
}

@article{reagor_quantum_2016,
	title = {Quantum memory with millisecond coherence in circuit {QED}},
	volume = {94},
	url = {https://link.aps.org/doi/10.1103/PhysRevB.94.014506},
	doi = {10.1103/PhysRevB.94.014506},
	abstract = {Significant advances in coherence render superconducting quantum circuits a viable platform for fault-tolerant quantum computing. To further extend capabilities, highly coherent quantum systems could act as quantum memories for these circuits. A useful quantum memory must be rapidly addressable by Josephson-junction-based artificial atoms, while maintaining superior coherence. We demonstrate a superconducting microwave cavity architecture that is highly robust against major sources of loss that are encountered in the engineering of circuit {QED} systems. The architecture allows for storage of quantum superpositions in a resonator on the millisecond scale, while strong coupling between the resonator and a transmon qubit enables control, encoding, and readout at {MHz} rates. This extends the maximum available coherence time attainable in superconducting circuits by almost an order of magnitude compared to earlier hardware. Our design is an ideal platform for studying coherent quantum optics and marks an important step towards hardware-efficient quantum computing in Josephson-junction-based quantum circuits.},
	pages = {014506},
	number = {1},
	journaltitle = {Physical Review B},
	shortjournal = {Phys. Rev. B},
	author = {Reagor, Matthew and Pfaff, Wolfgang and Axline, Christopher and Heeres, Reinier W. and Ofek, Nissim and Sliwa, Katrina and Holland, Eric and Wang, Chen and Blumoff, Jacob and Chou, Kevin and Hatridge, Michael J. and Frunzio, Luigi and Devoret, Michel H. and Jiang, Liang and Schoelkopf, Robert J.},
	urldate = {2024-05-23},
	date = {2016-07-08},
	note = {Publisher: American Physical Society},
	file = {APS Snapshot:/Users/shiv/Zotero/storage/Y2IETT6K/PhysRevB.94.html:text/html;Full Text PDF:/Users/shiv/Zotero/storage/ZTD7PS55/Reagor et al. - 2016 - Quantum memory with millisecond coherence in circu.pdf:application/pdf},
}

@article{heeres_cavity_2015,
	title = {Cavity State Manipulation Using Photon-Number Selective Phase Gates},
	volume = {115},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.115.137002},
	doi = {10.1103/PhysRevLett.115.137002},
	abstract = {The large available Hilbert space and high coherence of cavity resonators make these systems an interesting resource for storing encoded quantum bits. To perform a quantum gate on this encoded information, however, complex nonlinear operations must be applied to the many levels of the oscillator simultaneously. In this work, we introduce the selective number-dependent arbitrary phase (snap) gate, which imparts a different phase to each Fock-state component using an off-resonantly coupled qubit. We show that the snap gate allows control over the quantum phases by correcting the unwanted phase evolution due to the Kerr effect. Furthermore, by combining the snap gate with oscillator displacements, we create a one-photon Fock state with high fidelity. Using just these two controls, one can construct arbitrary unitary operations, offering a scalable route to performing logical manipulations on oscillator-encoded qubits.},
	pages = {137002},
	number = {13},
	journaltitle = {Physical Review Letters},
	shortjournal = {Phys. Rev. Lett.},
	author = {Heeres, Reinier W. and Vlastakis, Brian and Holland, Eric and Krastanov, Stefan and Albert, Victor V. and Frunzio, Luigi and Jiang, Liang and Schoelkopf, Robert J.},
	urldate = {2024-05-23},
	date = {2015-09-22},
	note = {Publisher: American Physical Society},
	file = {APS Snapshot:/Users/shiv/Zotero/storage/J3M4ZBBD/PhysRevLett.115.html:text/html;Full Text PDF:/Users/shiv/Zotero/storage/S422YW2M/Heeres et al. - 2015 - Cavity State Manipulation Using Photon-Number Sele.pdf:application/pdf},
}

@article{Chan_2019,
   title={Unitary-projective entanglement dynamics},
   volume={99},
   ISSN={2469-9969},
   url={http://dx.doi.org/10.1103/PhysRevB.99.224307},
   DOI={10.1103/physrevb.99.224307},
   number={22},
   journal={Physical Review B},
   publisher={American Physical Society (APS)},
   author={Chan, Amos and Nandkishore, Rahul M. and Pretko, Michael and Smith, Graeme},
   year={2019},
   month=jun }

@inbook{Potter_2022,
   title={Entanglement Dynamics in Hybrid Quantum Circuits},
   ISBN={9783031039980},
   ISSN={2364-9062},
   url={http://dx.doi.org/10.1007/978-3-031-03998-0_9},
   DOI={10.1007/978-3-031-03998-0_9},
   booktitle={Entanglement in Spin Chains},
   publisher={Springer International Publishing},
   author={Potter, Andrew C. and Vasseur, Romain},
   year={2022},
   pages={211–249} }



@article{noel2022measurement,
  title={Measurement-induced quantum phases realized in a trapped-ion quantum computer},
  author={Noel, Crystal and Niroula, Pradeep and Zhu, Daiwei and Risinger, Andrew and Egan, Laird and Biswas, Debopriyo and Cetina, Marko and Gorshkov, Alexey V and Gullans, Michael J and Huse, David A and others},
  journal={Nature Physics},
  volume={18},
  number={7},
  pages={760--764},
  year={2022},
  publisher={Nature Publishing Group UK London}
}

@article{Wang_2020,
   title={Efficient Multiphoton Sampling of Molecular Vibronic Spectra on a Superconducting Bosonic Processor},
   volume={10},
   ISSN={2160-3308},
   url={http://dx.doi.org/10.1103/PhysRevX.10.021060},
   DOI={10.1103/physrevx.10.021060},
   number={2},
   journal={Physical Review X},
   publisher={American Physical Society (APS)},
   author={Wang, Christopher S. and Curtis, Jacob C. and Lester, Brian J. and Zhang, Yaxing and Gao, Yvonne Y. and Freeze, Jessica and Batista, Victor S. and Vaccaro, Patrick H. and Chuang, Isaac L. and Frunzio, Luigi and Jiang, Liang and Girvin, S. M. and Schoelkopf, Robert J.},
   year={2020},
   month=jun }



@article{gullans2020,
  title = {Scalable Probes of Measurement-Induced Criticality},
  author = {Gullans, Michael J. and Huse, David A.},
  journal = {Phys. Rev. Lett.},
  volume = {125},
  issue = {7},
  pages = {070606},
  numpages = {6},
  year = {2020},
  month = {Aug},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.125.070606},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.125.070606}
}

@article{Tianciboson,
  title = {Nonunitary entanglement dynamics in continuous-variable systems},
  author = {Zhou, Tianci and Chen, Xiao},
  journal = {Phys. Rev. B},
  volume = {104},
  issue = {18},
  pages = {L180301},
  numpages = {6},
  year = {2021},
  month = {Nov},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevB.104.L180301},
  url = {https://link.aps.org/doi/10.1103/PhysRevB.104.L180301}
}


@article{Jian_2020,
   title={Measurement-induced criticality in random quantum circuits},
   volume={101},
   ISSN={2469-9969},
   url={http://dx.doi.org/10.1103/PhysRevB.101.104302},
   DOI={10.1103/physrevb.101.104302},
   number={10},
   journal={Physical Review B},
   publisher={American Physical Society (APS)},
   author={Jian, Chao-Ming and You, Yi-Zhuang and Vasseur, Romain and Ludwig, Andreas W. W.},
   year={2020},
   month=mar }

@misc{li2025cascaded,
      title={A Cascaded Random Access Quantum Memory}, 
      author={Ziqian Li and Eesh Gupta and Fang Zhao and Riju Banerjee and Yao Lu and Tanay Roy and Andrew Oriani and Andrei Vrajitoarea and Srivatsan Chakram and David I. Schuster},
      year={2025},
      eprint={2503.13953},
      archivePrefix={arXiv},
      primaryClass={quant-ph},
      url={https://arxiv.org/abs/2503.13953}, 
}

@article{supp,
	journal = {See Supplemental Material for additional details}}


@article{koh_measurement-induced_2023,
	title = {Measurement-induced entanglement phase transition on a superconducting quantum processor with mid-circuit readout},
	volume = {19},
	rights = {2023 The Author(s), under exclusive licence to Springer Nature Limited},
	issn = {1745-2481},
	url = {https://www.nature.com/articles/s41567-023-02076-6},
	doi = {10.1038/s41567-023-02076-6},
	abstract = {Quantum many-body systems subjected to unitary evolution with the addition of interspersed measurements exhibit a variety of dynamical phases that do not occur under pure unitary evolution. However, these systems remain challenging to investigate on near-term quantum hardware owing to the need for numerous ancilla qubits or repeated high-fidelity mid-circuit measurements, a capability that has only recently become available. Here we report the realization of a measurement-induced entanglement phase transition with a hybrid random circuit on up to 14 superconducting qubits with mid-circuit readout capability. We directly observe extensive and sub-extensive scaling of entanglement entropy in the volume- and area-law phases, respectively, by varying the rate of the measurements. We also demonstrate phenomenological critical behaviour by performing a data collapse of the measured entanglement entropy. Our work establishes the use of mid-circuit measurement as a powerful resource for quantum simulation on near-term quantum computers.},
	pages = {1314--1319},
	number = {9},
	journaltitle = {Nature Physics},
	shortjournal = {Nat. Phys.},
	author = {Koh, Jin Ming and Sun, Shi-Ning and Motta, Mario and Minnich, Austin J.},
	urldate = {2024-01-11},
	date = {2023-09},
	langid = {english},
	note = {Number: 9
Publisher: Nature Publishing Group},
	keywords = {Condensed-matter physics, Phase transitions and critical phenomena, Quantum information, Quantum physics, Quantum simulation},
	file = {Full Text PDF:/Users/shiv/Zotero/storage/S3I5L9AG/Koh et al. - 2023 - Measurement-induced entanglement phase transition .pdf:application/pdf},
}


@article{gullansDynamical2020,
   title={Dynamical Purification Phase Transition Induced by Quantum Measurements},
   volume={10},
   ISSN={2160-3308},
   url={http://dx.doi.org/10.1103/PhysRevX.10.041020},
   DOI={10.1103/physrevx.10.041020},
   number={4},
   journal={Physical Review X},
   publisher={American Physical Society (APS)},
   author={Gullans, Michael J. and Huse, David A.},
   year={2020},
   month=oct }

@misc{singh2025,
      title={Mixed-state learnability transitions in monitored noisy quantum dynamics}, 
      author={Hansveer Singh and Romain Vasseur and Andrew C. Potter and Sarang Gopalakrishnan},
      year={2025},
      eprint={2503.10308},
      archivePrefix={arXiv},
      primaryClass={quant-ph},
      url={https://arxiv.org/abs/2503.10308}, 
}

@article{li2019measurement,
  title={Measurement-driven entanglement transition in hybrid quantum circuits},
  author={Li, Yaodong and Chen, Xiao and Fisher, Matthew PA},
  journal={Physical Review B},
  volume={100},
  number={13},
  pages={134306},
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  publisher={APS}
}

@article{qutip5,
  title = {QuTiP 5: The Quantum Toolbox in {Python}},
  author = {
    Lambert, Neill and Gigu{`e}re, Eric and Menczel, Paul and Li, Boxi and
    Hopf, Patrick and Su{'a}rez, Gerardo and Gali, Marc and Lishman, Jake and
    Gadhvi, Rushiraj and Agarwal, Rochisha and Galicia, Asier and Shammah, Nathan and
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    Pitchford, Alexander and Nori, Franco
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  journal = {Physics Reports},
  volume = {1153},
  pages = {1-62},
  year = {2026},
  issn = {0370-1573},
  doi = {10.1016/j.physrep.2025.10.001},
  url = {https://www.sciencedirect.com/science/article/pii/S0370157325002704},
}

@article{johansson2013qutip,
      title = {QuTiP 2: A Python framework for the dynamics of open quantum systems},
      journal = {Computer Physics Communications},
      volume = {184},
      number = {4},
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      year = {2013},
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      url = {https://www.sciencedirect.com/science/article/pii/S0010465512003955},
      author = {J.R. Johansson and P.D. Nation and Franco Nori},
      keywords = {Open quantum systems, Lindblad, Bloch–Redfield, Floquet–Markov, Master equation, Quantum Monte Carlo, Python}
}

@article{johansson2012qutip,
      title = {QuTiP: An open-source Python framework for the dynamics of open quantum systems},
      journal = {Computer Physics Communications},
      volume = {183},
      number = {8},
      pages = {1760-1772},
      year = {2012},
      issn = {0010-4655},
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      url = {https://www.sciencedirect.com/science/article/pii/S0010465512000835},
      author = {J.R. Johansson and P.D. Nation and Franco Nori},
      keywords = {Open quantum systems, Lindblad master equation, Quantum Monte Carlo, Python}
}

@article{Gertler_2021,
   title={Protecting a bosonic qubit with autonomous quantum error correction},
   volume={590},
   ISSN={1476-4687},
   url={http://dx.doi.org/10.1038/s41586-021-03257-0},
   DOI={10.1038/s41586-021-03257-0},
   number={7845},
   journal={Nature},
   publisher={Springer Science and Business Media LLC},
   author={Gertler, Jeffrey M. and Baker, Brian and Li, Juliang and Shirol, Shruti and Koch, Jens and Wang, Chen},
   year={2021},
   month=feb, pages={243–248} }

@article{Rosenblum_2018,
   title={Fault-tolerant detection of a quantum error},
   volume={361},
   ISSN={1095-9203},
   url={http://dx.doi.org/10.1126/science.aat3996},
   DOI={10.1126/science.aat3996},
   number={6399},
   journal={Science},
   publisher={American Association for the Advancement of Science (AAAS)},
   author={Rosenblum, S. and Reinhold, P. and Mirrahimi, M. and Jiang, Liang and Frunzio, L. and Schoelkopf, R. J.},
   year={2018},
   month=jul, pages={266–270} }

@article{chou_superconducting_2024,
	title = {A superconducting dual-rail cavity qubit with erasure-detected logical measurements},
	volume = {20},
	copyright = {2024 The Author(s), under exclusive licence to Springer Nature Limited},
	issn = {1745-2481},
	url = {https://www.nature.com/articles/s41567-024-02539-4},
	doi = {10.1038/s41567-024-02539-4},
	language = {english},
	number = {9},
	urldate = {2026-03-12},
	journal = {Nature Physics},
	author = {Chou, Kevin S. and Shemma, Tali and McCarrick, Heather and Chien, Tzu-Chiao and Teoh, James D. and Winkel, Patrick and Anderson, Amos and Chen, Jonathan and Curtis, Jacob C. and de Graaf, Stijn J. and Garmon, John W. O. and Gudlewski, Benjamin and Kalfus, William D. and Keen, Trevor and Khedkar, Nishaad and Lei, Chan U. and Liu, Gangqiang and Lu, Pinlei and Lu, Yao and Maiti, Aniket and Mastalli-Kelly, Luke and Mehta, Nitish and Mundhada, Shantanu O. and Narla, Anirudh and Noh, Taewan and Tsunoda, Takahiro and Xue, Sophia H. and Yuan, Joseph O. and Frunzio, Luigi and Aumentado, José and Puri, Shruti and Girvin, Steven M. and Moseley, S. Harvey and Schoelkopf, Robert J.},
	month = sep,
	year = {2024},
	note = {Publisher: Nature Publishing Group},
	keywords = {Quantum information, Qubits},
	pages = {1454--1460},
}

@article{de_graaf_mid-circuit_2025,
	title = {A mid-circuit erasure check on a dual-rail cavity qubit using the joint-photon number-splitting regime of circuit {QED}},
	volume = {11},
	copyright = {2025 The Author(s)},
	issn = {2056-6387},
	url = {https://www.nature.com/articles/s41534-024-00944-4},
	doi = {10.1038/s41534-024-00944-4},
	language = {english},
	number = {1},
	urldate = {2026-03-12},
	journal = {npj Quantum Inf},
	author = {de Graaf, Stijn J. and Xue, Sophia H. and Chapman, Benjamin J. and Teoh, James D. and Tsunoda, Takahiro and Winkel, Patrick and Garmon, John W. O. and Chang, Kathleen M. and Frunzio, Luigi and Puri, Shruti and Schoelkopf, Robert J.},
	month = jan,
	year = {2025},
	note = {Publisher: Nature Publishing Group},
	keywords = {Quantum information, Qubits},
	pages = {1},
}

@article{teoh2023dual,
  title={Dual-rail encoding with superconducting cavities},
  author={Teoh, James D and Winkel, Patrick and Babla, Harshvardhan K and Chapman, Benjamin J and Claes, Jahan and de Graaf, Stijn J and Garmon, John WO and Kalfus, William D and Lu, Yao and Maiti, Aniket and others},
  journal={Proceedings of the National Academy of Sciences},
  volume={120},
  number={41},
  pages={e2221736120},
  year={2023},
  publisher={National Academy of Sciences}
}

@article{mai2026biased,
  title={A biased-erasure cavity qubit with hardware-efficient quantum error detection},
  author={Mai, Jiasheng and Liu, Qiyu and Deng, Xiaowei and Cai, Yanyan and Ni, Zhongchu and Zhang, Libo and Hu, Ling and Zheng, Pan and Liu, Song and Xu, Yuan and others},
  journal={arXiv preprint arXiv:2601.21616},
  year={2026}
}