Digital-Analog-Digital Quantum Supremacy
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914186157621248 |
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| author | Lidar, Daniel |
| author_facet | Lidar, Daniel |
| contents | Quantum supremacy has been explored extensively in gate-model settings. Here, we introduce a quantum-supremacy framework for a hybrid digital-analog-digital quantum computing (DADQC) model. We consider a device that applies an initial layer of single-qubit gates, a single transverse-field Ising analog block, and a final single-qubit layer before $Z$-basis readout. The analog block approximates $Z$-diagonal Ising evolution, and we prove that the resulting output distribution is within constant total-variation (TV) distance of an Instantaneous Quantum Polynomial-time (IQP) circuit. Our bounds and constructions are established for fully connected as well as bounded-degree hardware graphs, matching a variety of architectures, including trapped-ion, neutral atom, and superconducting platforms. Assuming anticoncentration (which we prove for all-to-all hardware graphs and conjecture for bounded-degree hardware graphs) and an average-case hardness conjecture for the associated complex-temperature Ising partition functions, standard reductions imply that any efficient classical sampler achieving constant TV error collapses the polynomial hierarchy. Our results imply that quantum-supremacy tests are possible on today's quantum annealers, as well as other devices capable of hybrid digital-analog quantum evolution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07127 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Digital-Analog-Digital Quantum Supremacy Lidar, Daniel Quantum Physics Quantum supremacy has been explored extensively in gate-model settings. Here, we introduce a quantum-supremacy framework for a hybrid digital-analog-digital quantum computing (DADQC) model. We consider a device that applies an initial layer of single-qubit gates, a single transverse-field Ising analog block, and a final single-qubit layer before $Z$-basis readout. The analog block approximates $Z$-diagonal Ising evolution, and we prove that the resulting output distribution is within constant total-variation (TV) distance of an Instantaneous Quantum Polynomial-time (IQP) circuit. Our bounds and constructions are established for fully connected as well as bounded-degree hardware graphs, matching a variety of architectures, including trapped-ion, neutral atom, and superconducting platforms. Assuming anticoncentration (which we prove for all-to-all hardware graphs and conjecture for bounded-degree hardware graphs) and an average-case hardness conjecture for the associated complex-temperature Ising partition functions, standard reductions imply that any efficient classical sampler achieving constant TV error collapses the polynomial hierarchy. Our results imply that quantum-supremacy tests are possible on today's quantum annealers, as well as other devices capable of hybrid digital-analog quantum evolution. |
| title | Digital-Analog-Digital Quantum Supremacy |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2512.07127 |