Realizing the Nishimori transition across the error threshold for constant-depth quantum circuits
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arXiv
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| Format: | Preprint |
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2023
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| author | Chen, Edward H. Zhu, Guo-Yi Verresen, Ruben Seif, Alireza Bäumer, Elisa Layden, David Tantivasadakarn, Nathanan Zhu, Guanyu Sheldon, Sarah Vishwanath, Ashvin Trebst, Simon Kandala, Abhinav |
| author_facet | Chen, Edward H. Zhu, Guo-Yi Verresen, Ruben Seif, Alireza Bäumer, Elisa Layden, David Tantivasadakarn, Nathanan Zhu, Guanyu Sheldon, Sarah Vishwanath, Ashvin Trebst, Simon Kandala, Abhinav |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_02863 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Realizing the Nishimori transition across the error threshold for constant-depth quantum circuits Chen, Edward H. Zhu, Guo-Yi Verresen, Ruben Seif, Alireza Bäumer, Elisa Layden, David Tantivasadakarn, Nathanan Zhu, Guanyu Sheldon, Sarah Vishwanath, Ashvin Trebst, Simon Kandala, Abhinav Quantum Physics Disordered Systems and Neural Networks Statistical Mechanics Strongly Correlated Electrons 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. |
| title | Realizing the Nishimori transition across the error threshold for constant-depth quantum circuits |
| topic | Quantum Physics Disordered Systems and Neural Networks Statistical Mechanics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2309.02863 |