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arXiv:2603.13114

Experimental realization of a $\cos(2\varphi)$ transmon qubit

Erwan Roverc'h, Alvise Borgognoni, Marius Villiers, Kyrylo Gerashchenko, W. Clarke Smith, Christopher Wilson, Benoit Douçot, Alexandru Petrescu, Philippe Campagne-Ibarcq, Zaki Leghtas

quant-phcond-mat.supr-conSubmitted Mar 13, 2026• Announced Mar 16, 2026• 0 citations
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Abstract

Superconducting circuits with embedded symmetries are good candidates to robustly protect quantum information from dominant error channels. The $\cos(2\varphi)$ qubit, consisting of an island shunted to ground through a tunneling element that selectively transmits pairs of Cooper pairs, leverages charge-parity symmetry to protect from charge-induced errors. In this experiment, we observe a doublet of states of opposite Cooper-pair parity split by $13.6~\mathrm{MHz}$. Operating in a soft-transmon regime, this splitting is two orders of magnitude smaller than in previous implementations, pushing charge-induced losses well beyond the measured coherence times. Despite the low transition frequency, we demonstrate coherent qubit control, single-shot readout, and resolve quantum jumps. Charge protection of the qubit is evidenced by a $100-$fold suppression of the island charge matrix element compared to the unprotected plasmon transition, placing dielectric loss limits above $10~\mathrm{ms}$. The measured $T_1 = 70~μ\mathrm{s}$ and $T_2^\mathrm{echo}= 2.5~μ\mathrm{s}$ are instead limited by $1/f$ flux noise in the tunnelling element's loop. This experiment shows that pushing Cooper-pair pairing in the transmon regime sets high limits on charge-induced losses while preserving coherent control and single-shot readout of the low-frequency qubit. We identify flux noise as the dominant remaining limitation, calling for gradiometric designs or novel $4e$-tunneling elements.

Related papers

Coherence limitations of a Fourier-engineered $\cos(2\varphi)$ transmon qubit

Nataliia K. Zhurbina, Siddharth Singh, Lukas J. Splitthoff +4 more

Intrinsically protected superconducting qubits are a promising route toward enhancing coherence times and advancing hardware towards applications in quantum computing. The $\cos(2\varphi)$ qubit achieves protection against qubit relaxation by allowing only the coherent tunneling of pairs of Cooper pairs, resulting in Cooper-pair parity symmetry and thereby suppressing charge-induced errors. In this work, we experimentally realize a $\cos(2\varphi)$ qubit by Fourier engineering the energy-phase relation in a multi-junction superconducting circuit. Using an interference-based architecture, we are able to suppress the odd harmonics of an effective qubit potential and we observe good agreement between the measured transition spectrum and the effective theoretical model. We further investigate the energy relaxation time as a function of external flux and find that the qubit lifetime at the flux symmetry point is limited by $1/f$ flux noise. This strong sensitivity arises from residual fluctuations in the first harmonic, which possesses a large prefactor despite being nominally canceled. In contrast, a fluxonium qubit with a similar energy spectrum and noise amplitude is less affected by flux noise, highlighting a key challenge for interference-based protection schemes.

quant-pharXiv:2605.06372•May 8, 2026•0 citations

Symmetries and model reduction in a $\cos 2\varphi$ transmon qubit

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Engineered symmetries in superconducting circuits can protect quantum information; much like selection rules in atomic physics, they forbid transitions between the qubit states. Protected circuits, however, combine several loops and islands and host multiple nonlinearly coupled modes, calling for reduced low-energy models that inherit the circuit symmetries and make the protection manifest. We develop such a reduction for the $\cos 2\varphi$ transmon qubit, recently realized experimentally with a two-Cooper-pair interferometer, whose circuit hosts three coupled modes. Exploiting the separation of energy scales between the heavy transmon mode and the light internal modes of the interferometer, we derive an effective single-band Born-Oppenheimer model, including its geometric correction, and extend it to several bands. We identify the symmetries of the full and reduced Hamiltonians and derive exact selection rules. Finally, we identify a parameter regime beyond the single-band description that suppresses flux-noise dephasing without degrading charge-noise protection.

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We investigate the coherence properties of parity-protected $\cos(2\varphi)$ qubits based on interferences between two Josephson elements in a superconducting loop. We show that qubit implementations of a $\cos(2\varphi)$ potential using a single loop, such as those employing semiconducting junctions, rhombus circuits, flowermon and KITE structures, can be described by the same Hamiltonian as two multi-harmonic Josephson junctions in a SQUID geometry. We find that, despite the parity protection arising from the suppression of single Cooper pair tunneling, there exists a fundamental trade-off between charge and flux noise dephasing channels. Using numerical simulations, we examine how relaxation and dephasing rates depend on external flux and circuit parameters, and we identify the best compromise for maximum coherence. With currently existing circuit parameters, the qubit lifetime $T_1$ can exceed milliseconds while the dephasing time $T_\varphi$ remains limited to only a few microseconds due to either flux or charge noise. Our findings establish practical limits on the coherence of this class of qubits and raise questions about the long-term potential of this approach.

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Novel qubits with intrinsic noise protection constitute a promising route for improving the coherence of quantum information in superconducting circuits.However, many protected superconducting qubits exhibit relatively low transition frequencies, which could make their integration with conventional transmon circuits challenging.In this work, we propose and study a scheme for entangling a tunable transmon with a Cooper-pair parity-protected qubit, a paradigmatic example of a low-frequency protected qubit that stores quantum information in opposite Cooper-pair parity states on a superconducting island.By tuning the external flux on the transmon, we show that noncomputational states can mediate a two-qubit entangling gate that preserves the Cooper-pair parity independent of the detailed pulse sequence.Interestingly, the entangling gate bears similarities to a controlled-phase gate in conventional transmon devices.Hence, our results suggest that standard high-precision gate calibration protocols could be repurposed for operating heterogeneous quantum processors.

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We develop and characterize a symmetry-protected superconducting qubit that offers simultaneous exponential suppression of energy decay from charge and flux noises, and dephasing from flux noise.The qubit consists of a Cooper-pair box (CPB) shunted by a superinductor, forming a superconducting loop.Provided the offset charge on the CPB island is an odd number of electrons, the qubit potential corresponds to that of a cos (φ/2) Josephson element, preserving the parity of fluxons in the loop via Aharonov-Casher interference.In this regime, the logical-state wavefunctions reside in disjoint regions of Hilbert space, thereby ensuring protection against energy decay.By switching the protection on, we observe a tenfold increase of the decay time, reaching up to 100 μs.Though the qubit is sensitive to charge noise, the sensitivity is much reduced in comparison with the charge qubit, and the charge-noise-induced dephasing time of the current device exceeds 1 μs.Implementation of full dephasing protection can be achieved in the next-generation devices by combining several cos(φ/2) Josephson elements in a small array.

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Inductively shunted transmons exhibit noise insensitive plasmon states and a fluxon decay exceeding 3 hours

Farid Hassani, Matilda Peruzzo, Lucky N. Kapoor +3 more

Currently available quantum processors are dominated by noise, which severely limits their applicability and motivates the search for new physical qubit encodings. In this work, we introduce the inductively shunted transmon, a weakly flux-tunable superconducting qubit that offers charge offset protection for all levels and a 20-fold reduction in flux dispersion compared to the state-of-the-art resulting in a constant coherence over a full flux quantum. The parabolic confinement provided by the inductive shunt as well as the linearity of the geometric superinductor facilitates a high-power readout that resolves quantum jumps with a fidelity and QND-ness of >90% and without the need for a Josephson parametric amplifier. Moreover, the device reveals quantum tunneling physics between the two prepared fluxon ground states with a measured average decay time of up to 3.5 h. In the future, fast time-domain control of the transition matrix elements could offer a new path forward to also achieve full qubit control in the decay-protected fluxon basis.

Nature Communications•Jul 5, 2023•23 citations
Experimental realization of a cos⁡(2φ)\cos(2\varphi)cos(2φ) transmon qubit
Superconducting circuits with embedded symmetries are good candidates to robustly protect quantum information from dominant error channels. The cos⁡(2φ)\cos(2\varphi)cos(2φ) qubit, consisting of an island shunted to ground through a tunneling element that selectively transmits pairs of Cooper pairs, leverages charge-parity symmetry to protect from charge-induced errors. In this experiment, we observe a doublet of states of opposite Cooper-pair parity split by 13.6 MHz13.6~\mathrm{MHz}13.6 MHz. Operating in a soft-transmon regime, this splitting is two orders of magnitude smaller than in previous implementations, pushing charge-induced losses well beyond the measured coherence times. Despite the low transition frequency, we demonstrate coherent qubit control, single-shot readout, and resolve quantum jumps. Charge protection of the qubit is evidenced by a 100−100-100−fold suppression of the island charge matrix element compared to the unprotected plasmon transition, placing dielectric loss limits above 10 ms10~\mathrm{ms}10 ms. The measured T1=70 μsT_1 = 70~μ\mathrm{s}T1​=70 μs and T2echo=2.5 μsT_2^\mathrm{echo}= 2.5~μ\mathrm{s}T2echo​=2.5 μs are instead limited by 1/f1/f1/f flux noise in the tunnelling element's loop. This experiment shows that pushing Cooper-pair pairing in the transmon regime sets high limits on charge-induced losses while preserving coherent control and single-shot readout of the low-frequency qubit. We identify flux noise as the dominant remaining limitation, calling for gradiometric designs or novel 4e4e4e-tunneling elements.
Coherence limitations of a Fourier-engineered cos⁡(2φ)\cos(2\varphi)cos(2φ) transmon qubit
Intrinsically protected superconducting qubits are a promising route toward enhancing coherence times and advancing hardware towards applications in quantum computing. The cos⁡(2φ)\cos(2\varphi)cos(2φ) qubit achieves protection against qubit relaxation by allowing only the coherent tunneling of pairs of Cooper pairs, resulting in Cooper-pair parity symmetry and thereby suppressing charge-induced errors. In this work, we experimentally realize a cos⁡(2φ)\cos(2\varphi)cos(2φ) qubit by Fourier engineering the energy-phase relation in a multi-junction superconducting circuit. Using an interference-based architecture, we are able to suppress the odd harmonics of an effective qubit potential and we observe good agreement between the measured transition spectrum and the effective theoretical model. We further investigate the energy relaxation time as a function of external flux and find that the qubit lifetime at the flux symmetry point is limited by 1/f1/f1/f flux noise. This strong sensitivity arises from residual fluctuations in the first harmonic, which possesses a large prefactor despite being nominally canceled. In contrast, a fluxonium qubit with a similar energy spectrum and noise amplitude is less affected by flux noise, highlighting a key challenge for interference-based protection schemes.
Symmetries and model reduction in a cos⁡2φ\cos 2\varphicos2φ transmon qubit
Engineered symmetries in superconducting circuits can protect quantum information; much like selection rules in atomic physics, they forbid transitions between the qubit states. Protected circuits, however, combine several loops and islands and host multiple nonlinearly coupled modes, calling for reduced low-energy models that inherit the circuit symmetries and make the protection manifest. We develop such a reduction for the cos⁡2φ\cos 2\varphicos2φ transmon qubit, recently realized experimentally with a two-Cooper-pair interferometer, whose circuit hosts three coupled modes. Exploiting the separation of energy scales between the heavy transmon mode and the light internal modes of the interferometer, we derive an effective single-band Born-Oppenheimer model, including its geometric correction, and extend it to several bands. We identify the symmetries of the full and reduced Hamiltonians and derive exact selection rules. Finally, we identify a parameter regime beyond the single-band description that suppresses flux-noise dephasing without degrading charge-noise protection.
We investigate the coherence properties of parity-protected cos⁡(2φ)\cos(2\varphi)cos(2φ) qubits based on interferences between two Josephson elements in a superconducting loop. We show that qubit implementations of a cos⁡(2φ)\cos(2\varphi)cos(2φ) potential using a single loop, such as those employing semiconducting junctions, rhombus circuits, flowermon and KITE structures, can be described by the same Hamiltonian as two multi-harmonic Josephson junctions in a SQUID geometry. We find that, despite the parity protection arising from the suppression of single Cooper pair tunneling, there exists a fundamental trade-off between charge and flux noise dephasing channels. Using numerical simulations, we examine how relaxation and dephasing rates depend on external flux and circuit parameters, and we identify the best compromise for maximum coherence. With currently existing circuit parameters, the qubit lifetime T1T_1T1​ can exceed milliseconds while the dephasing time TφT_\varphiTφ​ remains limited to only a few microseconds due to either flux or charge noise. Our findings establish practical limits on the coherence of this class of qubits and raise questions about the long-term potential of this approach.
Novel qubits with intrinsic noise protection constitute a promising route for improving the coherence of quantum information in superconducting circuits.However, many protected superconducting qubits exhibit relatively low transition frequencies, which could make their integration with conventional transmon circuits challenging.In this work, we propose and study a scheme for entangling a tunable transmon with a Cooper-pair parity-protected qubit, a paradigmatic example of a low-frequency protected qubit that stores quantum information in opposite Cooper-pair parity states on a superconducting island.By tuning the external flux on the transmon, we show that noncomputational states can mediate a two-qubit entangling gate that preserves the Cooper-pair parity independent of the detailed pulse sequence.Interestingly, the entangling gate bears similarities to a controlled-phase gate in conventional transmon devices.Hence, our results suggest that standard high-precision gate calibration protocols could be repurposed for operating heterogeneous quantum processors.
We develop and characterize a symmetry-protected superconducting qubit that offers simultaneous exponential suppression of energy decay from charge and flux noises, and dephasing from flux noise.The qubit consists of a Cooper-pair box (CPB) shunted by a superinductor, forming a superconducting loop.Provided the offset charge on the CPB island is an odd number of electrons, the qubit potential corresponds to that of a cos (φ/2) Josephson element, preserving the parity of fluxons in the loop via Aharonov-Casher interference.In this regime, the logical-state wavefunctions reside in disjoint regions of Hilbert space, thereby ensuring protection against energy decay.By switching the protection on, we observe a tenfold increase of the decay time, reaching up to 100 μs.Though the qubit is sensitive to charge noise, the sensitivity is much reduced in comparison with the charge qubit, and the charge-noise-induced dephasing time of the current device exceeds 1 μs.Implementation of full dephasing protection can be achieved in the next-generation devices by combining several cos(φ/2) Josephson elements in a small array.
Currently available quantum processors are dominated by noise, which severely limits their applicability and motivates the search for new physical qubit encodings. In this work, we introduce the inductively shunted transmon, a weakly flux-tunable superconducting qubit that offers charge offset protection for all levels and a 20-fold reduction in flux dispersion compared to the state-of-the-art resulting in a constant coherence over a full flux quantum. The parabolic confinement provided by the inductive shunt as well as the linearity of the geometric superinductor facilitates a high-power readout that resolves quantum jumps with a fidelity and QND-ness of >90% and without the need for a Josephson parametric amplifier. Moreover, the device reveals quantum tunneling physics between the two prepared fluxon ground states with a measured average decay time of up to 3.5 h. In the future, fast time-domain control of the transition matrix elements could offer a new path forward to also achieve full qubit control in the decay-protected fluxon basis.