The Impact of Qubit Connectivity on Quantum Advantage in Noisy IQP Circuits
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914471331495936 |
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| author | Placidi, Leonardo Rinaldi, Enrico Fujii, Keisuke Liu, Chen-Yu |
| author_facet | Placidi, Leonardo Rinaldi, Enrico Fujii, Keisuke Liu, Chen-Yu |
| contents | Instantaneous Quantum Polynomial-time (IQP) circuits are a candidate for demonstrating near-term quantum advantage, as their sampling task is believed to be classically hard in the ideal theoretical setting under standard complexity-theoretic assumptions. In noisy implementations, however, this hardness can disappear once circuit depth exceeds a noise-dependent critical threshold. We show that qubit connectivity is a key parameter in this transition, since sparse architectures require additional routing to implement long-range interactions, thereby increasing compiled circuit depth. To make this explicit, we present a connectivity-aware analysis of compiled IQP circuits. For a fixed abstract IQP instance, different hardware connectivity graphs yield different compiled depths and thus different effective positions relative to the noisy-IQP simulatability boundary. We quantify this architecture-dependent shift using the compiled depth overhead and the corresponding simulatability margin. We combine analytic depth estimates for sparse geometries, including the two-dimensional grid, with native-gateset-aware compilation experiments across seven hardware-grounded experimental device models derived from publicly available topologies. To compare these device models under a unified empirical framework, we approximate the effective noise level primarily through reported two-qubit gate error rates. This lets us compare how much effective noise sparse and fully connected architectures can tolerate for the same position relative to the noisy-IQP simulatability boundary. Our results show that sparse connectivity requires a lower effective noise level to sustain the same margin relative to the noisy-IQP simulatability boundary, and they provide a quantitative framework for determining when compiled IQP experiments are likely to remain outside, or instead enter, the classically simulatable regime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_12635 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Impact of Qubit Connectivity on Quantum Advantage in Noisy IQP Circuits Placidi, Leonardo Rinaldi, Enrico Fujii, Keisuke Liu, Chen-Yu Quantum Physics Instantaneous Quantum Polynomial-time (IQP) circuits are a candidate for demonstrating near-term quantum advantage, as their sampling task is believed to be classically hard in the ideal theoretical setting under standard complexity-theoretic assumptions. In noisy implementations, however, this hardness can disappear once circuit depth exceeds a noise-dependent critical threshold. We show that qubit connectivity is a key parameter in this transition, since sparse architectures require additional routing to implement long-range interactions, thereby increasing compiled circuit depth. To make this explicit, we present a connectivity-aware analysis of compiled IQP circuits. For a fixed abstract IQP instance, different hardware connectivity graphs yield different compiled depths and thus different effective positions relative to the noisy-IQP simulatability boundary. We quantify this architecture-dependent shift using the compiled depth overhead and the corresponding simulatability margin. We combine analytic depth estimates for sparse geometries, including the two-dimensional grid, with native-gateset-aware compilation experiments across seven hardware-grounded experimental device models derived from publicly available topologies. To compare these device models under a unified empirical framework, we approximate the effective noise level primarily through reported two-qubit gate error rates. This lets us compare how much effective noise sparse and fully connected architectures can tolerate for the same position relative to the noisy-IQP simulatability boundary. Our results show that sparse connectivity requires a lower effective noise level to sustain the same margin relative to the noisy-IQP simulatability boundary, and they provide a quantitative framework for determining when compiled IQP experiments are likely to remain outside, or instead enter, the classically simulatable regime. |
| title | The Impact of Qubit Connectivity on Quantum Advantage in Noisy IQP Circuits |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2604.12635 |