State preparation with parallel-sequential circuits
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AbstractWe introduce parallel-sequential (PS) circuits, a family of quantum circuit layouts that interpolate between brickwall and sequential circuits, which introduces control parameters governing a trade-off between the amount of entanglement and the maximum correlation range they can express. We provide numerical evidence that PS circuits can efficiently prepare many-body ground states in one dimension. On noisy devices, characterized through both idling errors and two-qubit gate errors, we show that in a wide parameter regime, PS circuits outperform brickwall, sequential, and the log-depth circuits from [Malz, Styliaris, Wei, Cirac, PRL 132, 040404 (2024)]. Additionally, we demonstrate that properly chosen noisy random PS circuits suppress error proliferation and, when employed as a variational ansatz, exhibit superior trainability.Popular summaryWe introduce parallel-sequential (PS) circuits, a class of quantum circuit layouts that unify and generalize brickwall and sequential circuits across arbitrary dimensions. Focusing on one-dimensional systems, we demonstrate that PS circuits efficiently prepare various classes of many-body ground states. Due to their optimized structure, we find that PS circuits outperform brickwall and sequential circuits on noisy quantum devices. Furthermore, appropriately selected noisy random PS circuits exhibit suppressed error proliferation, and superior trainability when used variationally. Our work thus offers a versatile and practically accessible strategy to improve performance across a wide array of quantum tasks on noisy quantum devices.► BibTeX data@article{Wei2026statepreparation, doi = {10.22331/q-2026-04-21-2079}, url = {https://doi.org/10.22331/q-2026-04-21-2079}, title = {State preparation with parallel-sequential circuits}, author = {Wei, Zhi-Yuan and Malz, Daniel}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2079}, month = apr, year = {2026} }► References [1] M A Nielsenand I L Chuang ``Quantum computation and quantum information'' Cambridge University Press (2000). [2] Guifré Vidal ``Efficient simulation of one-dimensional quantum many-body systems'' Physical Review Letters 93, 1–4 (2004). https://doi.org/10.1103/PhysRevLett.93.040502 [3] C. Schön, E. Solano, F. Verstraete, J. I. Cirac, and M. M. Wolf, ``Sequential generation of entangled multiqubit states'' Physical Review Letters 95, 1–4 (2005). https://doi.org/10.1103/PhysRevLett.95.110503 [4] M. C. Bañuls, D. Pérez-García, M. M. Wolf, F. Verstraete, and J. I. Cirac, ``Sequentially generated states for the study of two-dimensional systems'' Physical Review A 77, 1–9 (2008). https://doi.org/10.1103/PhysRevA.77.052306 [5] Michael P.
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Copyright remains with the original copyright holders such as the authors or their institutions. AbstractWe introduce parallel-sequential (PS) circuits, a family of quantum circuit layouts that interpolate between brickwall and sequential circuits, which introduces control parameters governing a trade-off between the amount of entanglement and the maximum correlation range they can express. We provide numerical evidence that PS circuits can efficiently prepare many-body ground states in one dimension. On noisy devices, characterized through both idling errors and two-qubit gate errors, we show that in a wide parameter regime, PS circuits outperform brickwall, sequential, and the log-depth circuits from [Malz, Styliaris, Wei, Cirac, PRL 132, 040404 (2024)]. Additionally, we demonstrate that properly chosen noisy random PS circuits suppress error proliferation and, when employed as a variational ansatz, exhibit superior trainability.Popular summaryWe introduce parallel-sequential (PS) circuits, a class of quantum circuit layouts that unify and generalize brickwall and sequential circuits across arbitrary dimensions. Focusing on one-dimensional systems, we demonstrate that PS circuits efficiently prepare various classes of many-body ground states. Due to their optimized structure, we find that PS circuits outperform brickwall and sequential circuits on noisy quantum devices. Furthermore, appropriately selected noisy random PS circuits exhibit suppressed error proliferation, and superior trainability when used variationally. Our work thus offers a versatile and practically accessible strategy to improve performance across a wide array of quantum tasks on noisy quantum devices.► BibTeX data@article{Wei2026statepreparation, doi = {10.22331/q-2026-04-21-2079}, url = {https://doi.org/10.22331/q-2026-04-21-2079}, title = {State preparation with parallel-sequential circuits}, author = {Wei, Zhi-Yuan and Malz, Daniel}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2079}, month = apr, year = {2026} }► References [1] M A Nielsenand I L Chuang ``Quantum computation and quantum information'' Cambridge University Press (2000). [2] Guifré Vidal ``Efficient simulation of one-dimensional quantum many-body systems'' Physical Review Letters 93, 1–4 (2004). https://doi.org/10.1103/PhysRevLett.93.040502 [3] C. Schön, E. Solano, F. Verstraete, J. I. Cirac, and M. M. Wolf, ``Sequential generation of entangled multiqubit states'' Physical Review Letters 95, 1–4 (2005). https://doi.org/10.1103/PhysRevLett.95.110503 [4] M. C. Bañuls, D. Pérez-García, M. M. Wolf, F. Verstraete, and J. I. Cirac, ``Sequentially generated states for the study of two-dimensional systems'' Physical Review A 77, 1–9 (2008). https://doi.org/10.1103/PhysRevA.77.052306 [5] Michael P.
Zaleteland Frank Pollmann ``Isometric Tensor Network States in Two Dimensions'' Physical Review Letters 124, 37201 (2020). https://doi.org/10.1103/PhysRevLett.124.037201 [6] Zhi Yuan Wei, Daniel Malz, and J Ignacio Cirac, ``Sequential Generation of Projected Entangled-Pair States'' Physical Review Letters 128, 1–14 (2022). https://doi.org/10.1103/PhysRevLett.128.010607 [7] Yu-Jie Liu, Kirill Shtengel, Adam Smith, and Frank Pollmann, ``Methods for Simulating String-Net States and Anyons on a Digital Quantum Computer'' PRX Quantum 3, 040315 (2022). https://doi.org/10.1103/PRXQuantum.3.040315 [8] Xie Chen, Arpit Dua, Michael Hermele, David T Stephen, Nathanan Tantivasadakarn, Robijn Vanhove, and Jing-Yu Zhao, ``Sequential quantum circuits as maps between gapped phases'' Physical Review B 109, 075116 (2024). https://doi.org/10.1103/PhysRevB.109.075116 [9] Y. Y. Shi, L. M. Duan, and G Vidal, ``Classical simulation of quantum many-body systems with a tree tensor network'' Physical Review A 74, 1–4 (2006). https://doi.org/10.1103/PhysRevA.74.022320 [10] Adam Smith, Bernhard Jobst, Andrew G Green, and Frank Pollmann, ``Crossing a topological phase transition with a quantum computer'' Physical Review Research 4, L022020 (2022). https://doi.org/10.1103/PhysRevResearch.4.L022020 [11] Shi Ju Ran ``Encoding of matrix product states into quantum circuits of one- A nd two-qubit gates'' Physical Review A 101, 1–7 (2020). https://doi.org/10.1103/PhysRevA.101.032310 [12] Sheng-Hsuan Lin, Rohit Dilip, Andrew G Green, Adam Smith, and Frank Pollmann, ``Real-and imaginary-time evolution with compressed quantum circuits'' PRX Quantum 2, 10342 (2021). https://doi.org/10.1103/PRXQuantum.2.010342 [13] Reza Haghshenas, Johnnie Gray, Andrew C Potter, and Garnet Kin-Lic Chan, ``Variational power of quantum circuit tensor networks'' Physical Review X 12, 11047 (2022). https://doi.org/10.1103/PhysRevX.12.011047 [14] Manuel S Rudolph, Jing Chen, Jacob Miller, Atithi Acharya, and Alejandro Perdomo-Ortiz, ``Decomposition of matrix product states into shallow quantum circuits'' Quantum Science and Technology 9, 015012 (2023). https://doi.org/10.1088/2058-9565/ad04e6 [15] Marco Cerezo, Andrew Arrasmith, Ryan Babbush, Simon C Benjamin, Suguru Endo, Keisuke Fujii, Jarrod R McClean, Kosuke Mitarai, Xiao Yuan, Lukasz Cincio, and Others, ``Variational quantum algorithms'' Nature Reviews Physics 3, 625–644 (2021). https://doi.org/10.1038/s42254-021-00348-9 [16] Kishor Bharti, Alba Cervera-Lierta, Thi Ha Kyaw, Tobias Haug, Sumner Alperin-Lea, Abhinav Anand, Matthias Degroote, Hermanni Heimonen, Jakob S Kottmann, Tim Menke, and Others, ``Noisy intermediate-scale quantum algorithms'' Reviews of Modern Physics 94, 15004 (2022). https://doi.org/10.1103/RevModPhys.94.015004 [17] Jules Tilly, Hongxiang Chen, Shuxiang Cao, Dario Picozzi, Kanav Setia, Ying Li, Edward Grant, Leonard Wossnig, Ivan Rungger, and George H Booth, ``The variational quantum eigensolver: a review of methods and best practices'' Physics Reports 986, 1–128 (2022). https://doi.org/10.1016/j.physrep.2022.08.003 [18] Matthew B Hastings ``An area law for one-dimensional quantum systems'' Journal of Statistical Mechanics: Theory and Experiment 2007, P08024 (2007). https://doi.org/10.1088/1742-5468/2007/08/P08024 [19] Jens Eisert, Marcus Cramer, and Martin B Plenio, ``Colloquium: Area laws for the entanglement entropy'' Reviews of modern physics 82, 277 (2010). https://doi.org/10.1103/RevModPhys.82.277 [20] M. B. Hastings ``Locality in Quantum and Markov Dynamics on Lattices and Networks'' Phys. Rev. Lett. 93, 140402 (2004). https://doi.org/10.1103/PhysRevLett.93.140402 [21] Daniel Malz, Georgios Styliaris, Zhi-Yuan Wei, and J Ignacio Cirac, ``Preparation of matrix product states with log-depth quantum circuits'' Physical Review Letters 132, 040404 (2024). https://doi.org/10.1103/PhysRevLett.132.040404 [22] Silvano Garnerone, Thiago R de Oliveira, Stephan Haas, and Paolo Zanardi, ``Statistical properties of random matrix product states'' Physical Review A 82, 052312 (2010). https://doi.org/10.1103/PhysRevA.82.052312 [23] Jonas Haferkamp, Christian Bertoni, Ingo Roth, and Jens Eisert, ``Emergent statistical mechanics from properties of disordered random matrix product states'' PRX Quantum 2, 40308 (2021). https://doi.org/10.1103/PRXQuantum.2.040308 [24] Cécilia Lancienand David Pérez-Garcia ``Correlation length in random MPS and PEPS'' Annales Henri Poincaré 23, 141–222 (2022). https://doi.org/10.1007/s00023-021-01087-4 [25] D Perez-Garcia, F Verstraete, M M Wolf, and J I Cirac, ``Matrix Product State Representations'' Quantum Info. Comput. 7, 401–430 (2007). https://doi.org/10.26421/QIC7.5-6-1 [26] Michael M. Wolf, Gerardo Ortiz, Frank Verstraete, and J. Ignacio Cirac, ``Quantum phase transitions in matrix product systems'' Physical Review Letters 97, 1–4 (2006). https://doi.org/10.1103/PhysRevLett.97.110403 [27] Carlos Bravo-Prieto, Josep Lumbreras-Zarapico, Luca Tagliacozzo, and José I. 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