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

• URL: http://arxiv.org/abs/2309.02863v2
• Date: Fri, 8 Dec 2023 13:18:52 GMT
• Title: Realizing the Nishimori transition across the error threshold for constant-depth quantum circuits
• Authors: Edward H. Chen, Guo-Yi Zhu, Ruben Verresen, Alireza Seif, Elisa B\"aumer, David Layden, Nathanan Tantivasadakarn, Guanyu Zhu, Sarah Sheldon, Ashvin Vishwanath, Simon Trebst, Abhinav Kandala
• Abstract summary: We study the generation of the simplest long-range order on a 127 superconducting qubit device. By experimentally tuning coherent and incoherent error rates, we demonstrate stability of this decoded long-range order in two spatial dimensions. Our study exemplifies how measurement-based state preparation can be meaningfully explored on quantum processors beyond a hundred qubits.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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