Nishimori transition across the error threshold for constant-depth quantum circuits

Creators: Chen, Edward H.^{1, 2}; Zhu, Guo-Yi³; Verresen, Ruben⁴; Seif, Alireza⁵; Bäumer, Elisa⁶; Layden, David^{1, 5}; Tantivasadakarn, Nathanan^{4, 7}; Zhu, Guanyu⁵; Sheldon, Sarah⁵; Vishwanath, Ashvin⁴; Trebst, Simon³; Kandala, Abhinav⁵

1. IBM Research - Almaden
2. IBM Quantum, Research Triangle Park, NC, USA
3. University of Cologne
4. Harvard University
5. IBM Research - Thomas J. Watson Research Center
6. IBM Research - Zurich
7. California Institute of Technology

Abstract

Quantum computing involves the preparation of entangled states across many qubits. This requires efficient preparation protocols that are stable to noise and gate imperfections. Here we demonstrate the generation of the simplest long-range order—Ising order—using a measurement-based protocol on 54 system qubits in the presence of coherent and incoherent errors. We implement a constant-depth preparation protocol that uses classical decoding of measurements to identify long-range order that is otherwise hidden by the randomness of quantum measurements. By experimentally tuning the error rates, we demonstrate the stability of this decoded long-range order in two spatial dimensions, up to a critical phase transition belonging to the unusual Nishimori universality class. Although in classical systems Nishimori physics requires fine-tuning multiple parameters, here it arises as a direct result of the Born rule for measurement probabilities. Our study demonstrates the emergent phenomena that can be explored on quantum processors beyond a hundred qubits.

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Acknowledgement

We thank M. Ware, P. Jurcevic, Y. Kim, A. Eddins, H. Nayfeh, I. Lauer, D. McKay, G. Jones and J. Summerour for assistance with performing experiments and B. Mitchell, D. Zajac, J. Wootton, L. Govia, X. Wei, R. Gupta, T. Yoder, T. Soejima, K. Siva, M. Motta, Z. Minev, S. Pappalardi, S. Garratt, E. Altman, F. Valenti and H. Nishimori for thoughtful discussions. We thank H. Nishimori for careful reading of the paper. The Cologne group was partially funded by the Deutsche Forschungsgemeinschaft under Germany’s Excellence Strategy – Cluster of Excellence Matter and Light for Quantum Computing (ML4Q) EXC 2004/1 – 390534769 and within the CRC network TR 183 (project grant no. 277101999: G.-Y.Z. and S.T.) as part of projects A04 and B01. The classical simulations were performed on the JUWELS cluster at the Forschungszentrum Juelich. R.V. is supported by the Harvard Quantum Initiative Postdoctoral Fellowship in Science and Engineering. A.V. is supported by a Simons Investigator grant and by NSF-DMR 2220703. A.V. and R.V. are supported by the Simons Collaboration on Ultra-Quantum Matter, which is a grant from the Simons Foundation (618615, A.V.). G.Z. is supported by the US Department of Energy, Office of Science, National Quantum Information Science Research Centers, Co-design Center for Quantum Advantage (C2QA) under contract number DE-SC0012704. We acknowledge the use of IBM Quantum services for this work.

Data Availability

The data supporting the findings of this study can be found via figshare at https://doi.org/10.6084/m9.figshare.24293524

Supplemental Material

Supplemental Figs. 1–13, Discussion and Tables 1–4: Supplementary Information

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