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<p>We propose a quantum circuit design for implementing coined quantum walks on complex networks. In complex networks, the coin and shift operators depend on the varying degrees of the nodes, which makes circuit construction more challenging than for regular networks. To address this issue, we use a dual-register encoding to enable a simplified shift operator and reduces the resource overhead. We implement the circuit using Qmod, a high-level quantum programming language, and evaluated the performance through numerical simulations on Erdős–Rényi, Watts–Strogatz, and Barabási–Albert models. The results show that the circuit depth scales as approximately <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(N^{1.9}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>N</mi> <mrow> <mn>1.9</mn> </mrow> </msup> </math></EquationSource> </InlineEquation> regardless of the network topology. Furthermore, we execute the proposed circuits on the <Emphasis FontCategory="NonProportional">ibm_torino</Emphasis> superconducting quantum processor for Watts–Strogatz models with <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(N=4\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>N</mi> <mo>=</mo> <mn>4</mn> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(N=8\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>N</mi> <mo>=</mo> <mn>8</mn> </mrow> </math></EquationSource> </InlineEquation>. The experiments show that hardware-aware optimization slightly improved the variation distance and Hellinger fidelity for the larger network, whereas connectivity constraints imposed overhead for the smaller one. These results indicate that while current NISQ devices are limited to small-scale validations, the polynomial scaling of our framework makes it suitable for larger-scale implementations in the fault-tolerant quantum computing era.</p>

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Coined quantum walks on complex networks for quantum computers

  • 期刊论文

  • 发表日期：

    2026年5月18日

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  • Rei Sato

摘要

We propose a quantum circuit design for implementing coined quantum walks on complex networks. In complex networks, the coin and shift operators depend on the varying degrees of the nodes, which makes circuit construction more challenging than for regular networks. To address this issue, we use a dual-register encoding to enable a simplified shift operator and reduces the resource overhead. We implement the circuit using Qmod, a high-level quantum programming language, and evaluated the performance through numerical simulations on Erdős–Rényi, Watts–Strogatz, and Barabási–Albert models. The results show that the circuit depth scales as approximately \(N^{1.9}\) N 1.9 regardless of the network topology. Furthermore, we execute the proposed circuits on the ibm_torino superconducting quantum processor for Watts–Strogatz models with \(N=4\) N = 4 and \(N=8\) N = 8 . The experiments show that hardware-aware optimization slightly improved the variation distance and Hellinger fidelity for the larger network, whereas connectivity constraints imposed overhead for the smaller one. These results indicate that while current NISQ devices are limited to small-scale validations, the polynomial scaling of our framework makes it suitable for larger-scale implementations in the fault-tolerant quantum computing era.