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arXiv · 2309.02863

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

Edward H. Chen·Guo-Yi Zhu·Ruben Verresen·Alireza Seif·Elisa Bäumer·David Layden·Nathanan Tantivasadakarn·Guanyu Zhu·Sarah Sheldon·Ashvin Vishwanath·Simon Trebst·Abhinav Kandala
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Abstract

Preparing quantum states across many qubits is necessary to unlock the full potential of quantum computers. However, a key challenge is to realize efficient preparation protocols which are stable to noise and gate imperfections. Here, using a measurement-based protocol on a 127 superconducting qubit device, we study the generation of the simplest long-range order -- Ising order, familiar from Greenberger-Horne-Zeilinger (GHZ) states and the repetition code -- on 54 system qubits. Our efficient implementation of the constant-depth protocol and classical decoder shows higher fidelities for GHZ states compared to size-dependent, unitary protocols. By experimentally tuning coherent and incoherent error rates, we demonstrate stability of this decoded long-range order in two spatial dimensions, up to a critical point which corresponds to a 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 -- locking the effective temperature and disorder driving this transition. Our study exemplifies how measurement-based state preparation can be meaningfully explored on quantum processors beyond a hundred qubits.

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Edward H. Chen, Guo-Yi Zhu, Ruben Verresen, Alireza Seif, Elisa Bäumer, David Layden, Nathanan Tantivasadakarn, Guanyu Zhu, Sarah Sheldon, Ashvin Vishwanath, Simon Trebst, Abhinav Kandala. 2023-09-06. Realizing the Nishimori transition across the error threshold for constant-depth quantum circuits. https://doi.org/10.1038/s41567-024-02696-6

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