Scalable Multi-QPU Circuit Design for Dicke State Preparation: Optimizing Communication Complexity and Local Circuit Costs
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| Format: | Preprint |
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2026
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| _version_ | 1866915758766817280 |
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| author | Chen, Ziheng Nie, Junhong Sun, Xiaoming Zhang, Jialin Zhu, Jiadong |
| author_facet | Chen, Ziheng Nie, Junhong Sun, Xiaoming Zhang, Jialin Zhu, Jiadong |
| contents | Preparing large-qubit Dicke states is of broad interest in quantum computing and quantum metrology. However, the number of qubits available on a single quantum processing unit (QPU) is limited -- motivating the distributed preparation of such states across multiple QPUs as a practical approach to scalability. In this article, we investigate the distributed preparation of $n$-qubit $k$-excitation Dicke states $D(n,k)$ across a general number $p$ of QPUs, presenting a distributed quantum circuit (each QPU hosting approximately $\lceil n/p \rceil$ qubits) that prepares the state with communication complexity $O(p \log k)$, circuit size $O(nk)$, and circuit depth $O\left(p^2 k + \log k \log (n/k)\right)$. To the best of our knowledge, this is the first construction to simultaneously achieve logarithmic communication complexity and polynomial circuit size and depth. We also establish a lower bound on the communication complexity of $p$-QPU distributed state preparation for a general target state. This lower bound is formulated in terms of the canonical polyadic rank (CP-rank) of a tensor associated with the target state. For the special case $p = 2$, we explicitly compute the CP-rank corresponding to the Dicke state $D(n,k)$ and derive a lower bound of $\lceil\log (k + 1)\rceil$, which shows that the communication complexity of our construction matches this fundamental limit. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_20393 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Scalable Multi-QPU Circuit Design for Dicke State Preparation: Optimizing Communication Complexity and Local Circuit Costs Chen, Ziheng Nie, Junhong Sun, Xiaoming Zhang, Jialin Zhu, Jiadong Quantum Physics Preparing large-qubit Dicke states is of broad interest in quantum computing and quantum metrology. However, the number of qubits available on a single quantum processing unit (QPU) is limited -- motivating the distributed preparation of such states across multiple QPUs as a practical approach to scalability. In this article, we investigate the distributed preparation of $n$-qubit $k$-excitation Dicke states $D(n,k)$ across a general number $p$ of QPUs, presenting a distributed quantum circuit (each QPU hosting approximately $\lceil n/p \rceil$ qubits) that prepares the state with communication complexity $O(p \log k)$, circuit size $O(nk)$, and circuit depth $O\left(p^2 k + \log k \log (n/k)\right)$. To the best of our knowledge, this is the first construction to simultaneously achieve logarithmic communication complexity and polynomial circuit size and depth. We also establish a lower bound on the communication complexity of $p$-QPU distributed state preparation for a general target state. This lower bound is formulated in terms of the canonical polyadic rank (CP-rank) of a tensor associated with the target state. For the special case $p = 2$, we explicitly compute the CP-rank corresponding to the Dicke state $D(n,k)$ and derive a lower bound of $\lceil\log (k + 1)\rceil$, which shows that the communication complexity of our construction matches this fundamental limit. |
| title | Scalable Multi-QPU Circuit Design for Dicke State Preparation: Optimizing Communication Complexity and Local Circuit Costs |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2601.20393 |