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8-qubit superconducting quantum chip simulation
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About the 8-Qubit Superconducting Quantum Chip Simulation Project
This project presents a finite-element electromagnetic simulation of an ๐ด-๐พ๐๐ฏ๐ถ๐ ๐๐๐ฝ๐ฒ๐ฟ๐ฐ๐ผ๐ป๐ฑ๐๐ฐ๐๐ถ๐ป๐ด ๐พ๐๐ฎ๐ป๐๐๐บ ๐ฐ๐ต๐ถ๐ฝ performed using ๐ก๐๐บ๐ฒ๐ฟ๐ถ๐ฐ๐ฎ๐น๐๐'๐ ๐ฐ๐ผ๐บ๐ฝ๐๐๐ฎ๐๐ถ๐ผ๐ป๐ฎ๐น ๐ฒ๐น๐ฒ๐ฐ๐๐ฟ๐ผ๐บ๐ฎ๐ด๐ป๐ฒ๐๐ถ๐ฐ (๐๐๐ ) ๐๐ผ๐น๐๐ฒ๐ฟ. The model uses an adaptive tetrahedral/triangular finite-element mesh with strong local refinement around the qubit structures, coupling regions, and lumped Josephson-junction ports. The substrate is modeled with a relative permittivity of 11.9, while the surrounding region is treated as vacuum. An eigenmode analysis was performed to identify the electromagnetic and qubit-like modes of the full chip. A total of 20 eigenmodes were solved, with the eight dominant qubit modes appearing between approximately 4.81 and 5.51 GHz. The extracted qubit frequencies are: ย ย โข Q1: 4.808 GHz ย ย โข Q2: 4.892 GHz ย ย โข Q3: 4.976 GHz ย ย โข Q4: 5.075 GHz ย ย โข Q5: 5.172 GHz ย ย โข Q6: 5.281 GHz ย ย โข Q7: 5.392 GHz ย ย โข Q8: 5.512 GHz The Josephson junctions were represented using lumped inductive-capacitive elements. Their inductances range from 14.5 nH to 11.0 nH, with a junction capacitance of 2 fF for each qubit. Energy Participation Ratio (EPR) data from Palace were used to identify the qubit-like modes and estimate the nonlinear properties of the circuit. The calculated qubit anharmonicities are approximately โ221 to โ248 MHz, consistent with transmon-type superconducting qubits. The EPR analysis was also used to construct an 8ร8 cross-Kerr / ZZ interaction matrix, revealing the dominant nonlinear interactions between the qubits. The strongest calculated cross-Kerr couplings include: ย ย โข Q7โQ8: 1.94 MHz ย ย โข Q6โQ7: 1.91 MHz ย ย โข Q5โQ6: 1.42 MHz ย ย โข Q2โQ3: 1.37 MHz ย ย โข Q3โQ4: 0.99 MHz ย ย โข Q1โQ5: 0.70 MHz The results demonstrate how full-wave finite-element eigenmode simulations can be combined with Energy Participation Ratio quantization to characterize multi-qubit superconducting circuits, including mode frequencies, junction participation, anharmonicity, and qubitโqubit nonlinear coupling.
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August 22nd, 2026 Uploaded
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