Fraunhofer IIS, Fraunhofer Institute for Integrated Circuits IIS, Division Positioning and Networks, Nuremberg, Germany
Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.
Abstract
Circuit cutting, the decomposition of a quantum circuit into independent partitions, has become a promising avenue towards experiments with larger quantum circuits in the noisy-intermediate scale quantum (NISQ) era. While previous work focused on cutting qubit wires or two-qubit gates, in this work we introduce a method for cutting multi-controlled Z gates. We construct a decomposition and prove the upper bound $mathcal{O}(6^{2K})$ on the associated sampling overhead, where $K$ is the number of cuts in the circuit. This bound is independent of the number of control qubits but can be further reduced to $mathcal{O}(4.5^{2K})$ for the special case of CCZ gates. Furthermore, we evaluate our proposal on IBM hardware and experimentally show noise resilience due to the strong reduction of CNOT gates in the cut circuits.
► BibTeX data
► References
[1] M. A. Nielsen and I. L. Chuang. “Quantum computation and quantum information: 10th anniversary edition”. Cambridge University Press. (2010).
https://doi.org/10.1017/CBO9780511976667
[2] J. Preskill. “Quantum Computing in the NISQ era and beyond”. Quantum 2, 79 (2018).
https://doi.org/10.22331/q-2018-08-06-79
[3] P.W. Shor. “Algorithms for quantum computation: discrete logarithms and factoring”. In Proceedings 35th Annual Symposium on Foundations of Computer Science. Page 124. IEEE Comput. Soc. Press (1994).
https://doi.org/10.1109/SFCS.1994.365700
[4] L. K. Grover. “A fast quantum mechanical algorithm for database search”. In Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing. Page 212. New York, NY, USA (1996). Association for Computing Machinery.
https://doi.org/10.1145/237814.237866
[5] E. Farhi, J. Goldstone, and S. Gutmann. “A quantum approximate optimization algorithm” (2014). arXiv:1411.4028.
arXiv:1411.4028
[6] “IBM Development Roadmap 2022”. https://www.ibm.com/quantum/roadmap. Accessed: 2023-01-02.
https://www.ibm.com/quantum/roadmap
[7] T. Peng, A. W. Harrow, M. Ozols, and X. Wu. “Simulating large quantum circuits on a small quantum computer”. Phys. Rev. Lett. 125, 150504 (2020).
https://doi.org/10.1103/PhysRevLett.125.150504
[8] M. A. Perlin, Z. H. Saleem, M. Suchara, and J. C. Osborn. “Quantum circuit cutting with maximum-likelihood tomography”. NPJ Quantum Inf. 7, 64 (2021).
https://doi.org/10.1038/s41534-021-00390-6
[9] G. Uchehara, T. M. Aamodt, and O. Di Matteo. “Rotation-inspired circuit cut optimization”. In 2022 IEEE/ACM Third International Workshop on Quantum Computing Software (QCS). Page 50. Los Alamitos, CA, USA (2022). IEEE Computer Society.
https://doi.org/10.1109/QCS56647.2022.00011
[10] D. Chen, B. Baheri, V. Chaudhary, Q. Guan, N. Xie, and S. Xu. “Approximate quantum circuit reconstruction”. In 2022 IEEE International Conference on Quantum Computing and Engineering (QCE). Page 509. (2022).
https://doi.org/10.1109/QCE53715.2022.00073
[11] C. Ying, B. Cheng, Y. Zhao, H.-L. Huang, Y.-N. Zhang, M. Gong, Y. Wu, S. Wang, F. Liang, J. Lin, Y. Xu, H. Deng, H. Rong, C.-Z. Peng, M.-H. Yung, X. Zhu, and J.-W. Pan. “Experimental simulation of larger quantum circuits with fewer superconducting qubits”. Phys. Rev. Lett. 130, 110601 (2023).
https://doi.org/10.1103/PhysRevLett.130.110601
[12] T. Ayral, F.-M. Le Régent, Z. Saleem, Y. Alexeev, and M. Suchara. “Quantum divide and compute: Hardware demonstrations and noisy simulations”. In 2020 IEEE Computer Society Annual Symposium on VLSI (ISVLSI). Page 138. (2020).
https://doi.org/10.1109/ISVLSI49217.2020.00034
[13] T. Ayral, F.-M. Le Régent, Z. Saleem, Y. Alexeev, and M. Suchara. “Quantum divide and compute: Exploring the effect of different noise sources”. SN comput. sci. 2, 132 (2021).
https://doi.org/10.1007/s42979-021-00508-9
[14] J. Liu, A. Gonzales, and Z. H. Saleem. “Classical simulators as quantum error mitigators via circuit cutting” (2022). arXiv:2212.07335.
arXiv:2212.07335
[15] R. Majumdar and C. J. Wood. “Error mitigated quantum circuit cutting” (2022). arXiv:2211.13431.
arXiv:2211.13431
[16] W. Tang, T. Tomesh, M. Suchara, J. Larson, and M. Martonosi. “CutQC: Using small quantum computers for large quantum circuit evaluations”. In Proceedings of the 26th ACM International Conference on Architectural Support for Programming Languages and Operating Systems. Page 473. ASPLOS 2021New York, NY, USA (2021). Association for Computing Machinery.
https://doi.org/10.1145/3445814.3446758
[17] W. Tang and M. Martonosi. “ScaleQC: A scalable framework for hybrid computation on quantum and classical processors” (2022). arXiv:2207.00933.
arXiv:2207.00933
[18] T. Chatterjee, A. Das, S. I. Mohtashim, A. Saha, and A. Chakrabarti. “Qurzon: A prototype for a divide and conquer-based quantum compiler for distributed quantum systems”. SN Computer Science 3, 323 (2022).
https://doi.org/10.1007/s42979-022-01207-9
[19] K. Mitarai and K. Fujii. “Methodology for replacing indirect measurements with direct measurements”. Phys. Rev. Research 1, 013006 (2019).
https://doi.org/10.1103/PhysRevResearch.1.013006
[20] K. Mitarai and K. Fujii. “Constructing a virtual two-qubit gate by sampling single-qubit operations”. New J. Phys. 23, 023021 (2021).
https://doi.org/10.1088/1367-2630/abd7bc
[21] K. Mitarai and K. Fujii. “Overhead for simulating a non-local channel with local channels by quasiprobability sampling”. Quantum 5, 388 (2021).
https://doi.org/10.22331/q-2021-01-28-388
[22] K. Temme, S. Bravyi, and J. M. Gambetta. “Error mitigation for short-depth quantum circuits”. Phys. Rev. Lett. 119, 180509 (2017).
https://doi.org/10.1103/PhysRevLett.119.180509
[23] C. Piveteau, D. Sutter, and S. Woerner. “Quasiprobability decompositions with reduced sampling overhead”. NPJ Quantum Inf. 8, 12 (2022).
https://doi.org/10.1038/s41534-022-00517-3
[24] C. Piveteau. “Advanced methods for quasiprobabilistic quantum error mitigation”. Master’s thesis. ETH Zurich. (2021). url: https://www.research-collection.ethz.ch/handle/20.500.11850/504508.
https://www.research-collection.ethz.ch/handle/20.500.11850/504508
[25] H. Pashayan, J. J. Wallman, and S. D. Bartlett. “Estimating outcome probabilities of quantum circuits using quasiprobabilities”. Phys. Rev. Lett. 115, 070501 (2015).
https://doi.org/10.1103/PhysRevLett.115.070501
[26] C. Piveteau and D. Sutter. “Circuit knitting with classical communication” (2022). arXiv:2205.00016.
arXiv:2205.00016
[27] G. Vidal and R. Tarrach. “Robustness of entanglement”. Phys. Rev. A 59, 141 (1999).
https://doi.org/10.1103/PhysRevA.59.141
[28] A. Lowe, M. Medvidović, A. Hayes, L. J. O’Riordan, T. R. Bromley, J. M. Arrazola, and N. Killoran. “Fast quantum circuit cutting with randomized measurements”. Quantum 7, 934 (2023).
https://doi.org/10.22331/q-2023-03-02-934
[29] Z. H. Saleem, T. Tomesh, M. A. Perlin, P. Gokhale, and M. Suchara. “Divide and conquer for combinatorial optimization and distributed computing” (2021). arXiv:2107.07532.
arXiv:2107.07532
[30] S. Hadfield. “Quantum algorithms for scientific computing and approximate optimization” (2018). arXiv:1805.03265.
arXiv:1805.03265
[31] T. Yamamoto and R. Ohira. “Error suppression by a virtual two-qubit gate”. J. Appl. Phys. 133, 174401 (2023).
https://doi.org/10.1063/5.0151037
[32] S. C. Marshall, C. Gyurik, and V. Dunjko. “High Dimensional Quantum Machine Learning With Small Quantum Computers”. Quantum 7, 1078 (2023).
https://doi.org/10.22331/q-2023-08-09-1078
[33] B. Coecke and R. Duncan. “Interacting quantum observables: categorical algebra and diagrammatics”. New J. Phys. 13, 043016 (2011).
https://doi.org/10.1088/1367-2630/13/4/043016
[34] B. Coecke and R. Duncan. “Interacting quantum observables”. In L. Aceto, I. Damgård, L. A. Goldberg, M. M. Halldórsson, A. Ingólfsdóttir, and I. Walukiewicz, editors, Automata, Languages and Programming. Page 298. Berlin, Heidelberg (2008). Springer Berlin Heidelberg.
https://doi.org/10.1007/978-3-540-70583-3_25
[35] J. van de Wetering. “ZX-calculus for the working quantum computer scientist” (2020). arXiv:2012.13966.
arXiv:2012.13966
[36] A. Kissinger and J. van de Wetering. “Simulating quantum circuits with zx-calculus reduced stabiliser decompositions”. Quantum Sci. Technol. 7, 044001 (2022).
https://doi.org/10.1088/2058-9565/ac5d20
[37] A. Kissinger, J. van de Wetering, and R. Vilmart. “Classical simulation of quantum circuits with partial and graphical stabiliser decompositions”. In F.s Le Gall and T. Morimae, editors, 17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022). Volume 232 of Leibniz International Proceedings in Informatics (LIPIcs), page 5:1. Dagstuhl, Germany (2022).
https://doi.org/10.4230/LIPIcs.TQC.2022.5
[38] M. Backens and A. Kissinger. “ZH: A complete graphical calculus for quantum computations involving classical non-linearity”. Electron. Proc. Theor. Comput. Sci. 287, 23 (2019).
https://doi.org/10.4204/eptcs.287.2
[39] “van de Wetering, J.”. Private communication.
[40] “IBM Quantum”. https://quantum-computing.ibm.com/. Accessed: 2023-01-23.
https://quantum-computing.ibm.com/
[41] A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter. “Elementary gates for quantum computation”. Phys. Rev. A 52, 3457 (1995).
https://doi.org/10.1103/PhysRevA.52.3457
[42] S. Bravyi, G. Smith, and J. A. Smolin. “Trading classical and quantum computational resources”. Phys. Rev. X 6, 021043 (2016).
https://doi.org/10.1103/PhysRevX.6.021043
[43] “Github repository MCZ-gate cutting”. https://github.com/ChristianUfrecht/MCZgate_cutting.
https://github.com/ChristianUfrecht/MCZgate_cutting
[44] E. van den Berg, Z. K. Minev, and K. Temme. “Model-free readout-error mitigation for quantum expectation values”. Phys. Rev. A 105, 032620 (2022).
https://doi.org/10.1103/PhysRevA.105.032620
Cited by
[1] Hiroyuki Harada, Kaito Wada, and Naoki Yamamoto, “Optimal parallel wire cutting without ancilla qubits”, arXiv:2303.07340, (2023).
[2] Sebastian Brandhofer, Ilia Polian, and Kevin Krsulich, “Optimal Partitioning of Quantum Circuits using Gate Cuts and Wire Cuts”, arXiv:2308.09567, (2023).
[3] Ryo Nagai, Shu Kanno, Yuki Sato, and Naoki Yamamoto, “Quantum channel decomposition with preselection and postselection”, Physical Review A 108 2, 022615 (2023).
[4] Tuomas Laakkonen, Konstantinos Meichanetzidis, and John van de Wetering, “Picturing Counting Reductions with the ZH-Calculus”, arXiv:2304.02524, (2023).
[5] Shikun Zhang, Zheng Qin, Yang Zhou, Rui Li, Chunxiao Du, and Zhisong Xiao, “Single Entanglement Connection Architecture between Multi-Layer HEA for Distributed VQE”, arXiv:2307.12323, (2023).
The above citations are from SAO/NASA ADS (last updated successfully 2023-10-23 15:53:56). 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 2023-10-23 15:53:54: Could not fetch cited-by data for 10.22331/q-2023-10-23-1147 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.
- SEO Powered Content & PR Distribution. Get Amplified Today.
- PlatoData.Network Vertical Generative Ai. Empower Yourself. Access Here.
- PlatoAiStream. Web3 Intelligence. Knowledge Amplified. Access Here.
- PlatoESG. Carbon, CleanTech, Energy, Environment, Solar, Waste Management. Access Here.
- PlatoHealth. Biotech and Clinical Trials Intelligence. Access Here.
- Source: https://quantum-journal.org/papers/q-2023-10-23-1147/
