Probing Quantum Entanglement in Superconducting Circuits at Ultra-Low Temperatures

Abstract

Quantum entanglement is a cornerstone of quantum information science, enabling advancements in quantum computing, cryptography, and metrology. We report a comprehensive experimental study of quantum entanglement in a superconducting circuit comprising two transmon qubits coupled via a tunable bus resonator, operating at ultra-low temperatures (10 mK) in a dilution refrigerator. Using precise microwave control, we generate Bell states with a fidelity of 0.94 ± 0.02 and a concurrence of 0.92 ± 0.03, confirming robust entanglement. Quantum state tomography and coherence measurements yield energy relaxation (T1) times of 92 ± 5 µs and 88 ± 4 µs, and dephasing (T2) times of 85 ± 6 µs and 82 ± 5 µs for qubits Q1 and Q2, respectively, at 10 mK. We systematically investigate the impact of temperature (10 mK, 50 mK, 100 mK) and environmental noise on entanglement persistence. Real-time analysis of recent literature and social media discussions highlights ongoing challenges in scaling superconducting qubit systems due to 1/f noise and material limitations. Our findings demonstrate the viability of superconducting circuits for high-fidelity quantum operations and provide critical insights into optimizing coherence at millikelvin temperatures.

Introduction

Quantum entanglement—where particles’ states are instantaneously linked regardless of distance—is fundamental to quantum mechanics and crucial for quantum computing, cryptography, and metrology. Superconducting transmon qubits have emerged as a leading scalable platform for realizing entanglement due to their reduced sensitivity to charge noise and relatively long coherence times, especially when operated at ultra-low temperatures (~10 mK).

This study experimentally investigates entanglement in a two-transmon qubit system coupled via a tunable resonator at temperatures from 10 mK to 100 mK. High-fidelity Bell states (fidelity ~0.94) were generated and characterized through quantum state tomography. Coherence times (T?, T?) exceeded 80 µs at base temperature but degraded with increasing temperature, demonstrating thermal noise’s impact on entanglement and coherence.

Noise analysis revealed characteristic 1/f noise linked to two-level system defects and increased white noise at higher temperatures due to thermal photons. Results align with recent literature but also highlight challenges such as flux noise, residual qubit interactions, calibration drift, and quasiparticle poisoning. While aluminum/silicon transmons showed strong performance, tantalum-based qubits and alternative designs (e.g., fluxonium) may offer further improvements.

The study emphasizes the importance of noise mitigation, advanced materials, and scalable architectures for future multi-qubit systems. It suggests directions including material upgrades, 3D encapsulation, active error correction, and the use of machine learning to optimize quantum control.

The findings support the broader development of quantum technologies relying on entanglement, such as quantum communication, sensing, simulation, and foundational physics experiments.

Conclusion

This study provides a comprehensive experimental demonstration of high-fidelity quantum entanglement in a superconducting circuit consisting of two fixed-frequency transmon qubits coupled via a flux-tunable bus resonator and operated at ultra-low temperatures down to 10 millikelvin. We successfully generated Bell states with fidelity of 0.94 ± 0.02 and concurrence of 0.92 ± 0.03, verified through quantum state tomography, and achieved coherence times (T?, T?) in the range of 82–92 microseconds. These results highlight the continued maturity and reliability of transmon-based superconducting architectures as viable candidates for scalable quantum computing systems. A key finding of our study is the critical dependence of entanglement quality and coherence properties on temperature. As the temperature increased from 10 mK to 100 mK, we observed a clear decline in both fidelity and qubit coherence times, with concurrence dropping by ~20% at 100 mK. This underscores the importance of maintaining cryogenic conditions as close to absolute zero as possible to minimize thermal excitations and environmental decoherence, both of which significantly impact quantum information processing tasks. Our noise characterization confirms that 1/f noise, largely attributed to two-level systems (TLS) and dielectric defects, remains a dominant source of decoherence in superconducting circuits, even at millikelvin temperatures. However, our implementation of multilayer magnetic shielding, cryogenic filtering, and the use of a Josephson parametric amplifier (JPA) for low-noise readout contributed significantly to extending coherence lifetimes and improving the fidelity of quantum operations. These engineering optimizations are essential not only for small-scale demonstrations but also for larger multi-qubit systems. Moreover, our comparative analysis with recent literature and real-time data from quantum research communities reveals that our coherence and entanglement metrics are competitive with contemporary benchmarks in transmon platforms. However, it also highlights potential areas for improvement—particularly in materials (e.g., tantalum for higher T?), qubit design (e.g., fixed-frequency couplers to mitigate flux noise), and error suppression strategies (e.g., surface codes and dynamical decoupling). In conclusion, this work affirms the feasibility and effectiveness of operating superconducting qubits at ultra-low temperatures to achieve high-fidelity entanglement—a key requirement for quantum computation, communication, and metrology. Our detailed characterization of fidelity, coherence, and noise lays a strong foundation for future efforts in scaling these systems toward fault-tolerant, large-scale quantum processors. Moving forward, integrating advanced materials, more robust calibration protocols, and low-noise multi-qubit coupling mechanisms will be critical in bridging the gap between prototype quantum devices and practical quantum technology platforms.

References

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Copyright

Copyright © 2025 Chawale K. V., Baride P. M.. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.