Scalable Multi-QPU Circuit Design for Dicke State Preparation: Optimizing Communication Complexity and Local Circuit Costs

• URL: http://arxiv.org/abs/2601.20393v1
• Date: Wed, 28 Jan 2026 09:00:38 GMT
• Title: Scalable Multi-QPU Circuit Design for Dicke State Preparation: Optimizing Communication Complexity and Local Circuit Costs
• Authors: Ziheng Chen, Junhong Nie, Xiaoming Sun, Jialin Zhang, Jiadong Zhu,
• Abstract summary: The number of qubits available on a single quantum processing unit (QPU) is limited.<n>We investigate the distributed preparation of large-qubit Dicke states $D(n,k)$ across a general number $p$ of QPUs.<n>To the best of our knowledge, this is the first construction to simultaneously achieve logarithmic communication complexity and circuit size and depth.
• Score: 13.575071625377097
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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