Superconducting SQUID Qubit Coherence Measurements

The pursuit of stable quantum computation relies heavily on extending the coherence of qubits, and new architectures are constantly being explored. Researchers at Univ. Grenoble Alpes, CNRS, Grenoble INP, and Institut N eel, led by S. Messelot, A. Leblanc, and J.-S. Tettekpoe, have investigated the coherence limits within interference‑based cos(2) qubits. Their work demonstrates that several promising qubit designs, including flower‑mon and KITE structures, share a common underlying Hamiltonian with SQUID geometries featuring multi‑harmonic Josephson junctions. This research is significant because it reveals a fundamental trade‑off between charge and flux noise affecting qubit coherence, establishing practical limitations and prompting further investigation into optimising long‑term stability for this promising quantum technology. Through detailed numerical simulations, the team determined that while lifetimes can exceed milliseconds, dephasing times remain constrained by environmental noise.

The research focuses on qubits constructed from interferences between two Josephson elements within a superconducting loop, revealing a fundamental trade‑off between charge and flux noise that limits performance. The team achieved a detailed understanding of how relaxation and dephasing rates are influenced by external flux and circuit parameters through extensive numerical simulations. This work establishes that, despite inherent parity protection suppressing single Cooper‑pair tunneling, maintaining long coherence times presents significant challenges.

The study unveils that implementations of a cos(2φ) potential using a single loop, including designs employing semiconducting junctions, rhombus circuits, flowmon and KITE structures, can be accurately modelled using the same Hamiltonian as two multi‑harmonic Josephson junctions in a SQUID geometry. Researchers meticulously examined the impact of circuit parameters, imperfections, and finite‑temperature effects on energy‑relaxation protection, demonstrating its robustness under varying conditions. Experiments show that the introduction of a loop into the circuit inevitably creates a balance between protection against charge and flux noise, directly impacting dephasing time. This breakthrough reveals that biasing the circuit loop away from a point of maximum frustration can be strategically advantageous, allowing for a balance between susceptibility to charge and flux noise.

Through optimisation of circuit parameters, the team identifies conditions under which qubit lifetime, T₁, can exceed milliseconds, while simultaneously striving to maintain a dephasing time, T_φ, of several microseconds. The research establishes practical limits on the coherence of this qubit class, raising important questions about its long‑term viability as a scalable quantum computing platform. The work opens new avenues for exploring advanced qubit designs and control strategies, particularly in mitigating the effects of environmental noise. With currently accessible circuit parameters, the study suggests that coherence times approaching those of leading transmon qubits, with state‑of‑the‑art decay and dephasing times reaching T₁, T_φ ≈ 1 ms, are potentially achievable. This detailed analysis of coherence mechanisms provides crucial insights for future development of robust and high‑performance superconducting qubits based on parity protection.

Superconducting SQUID Qubit Coherence Measurements

The study investigates the coherence properties of parity‑protected qubits based on interferences between two Josephson elements within a superconducting loop. Researchers engineered a system comprising two bi‑harmonic Josephson junctions arranged in a SQUID configuration, shunted by a single capacitance, as depicted in their circuit diagram. The Hamiltonian governing this system, derived from circuit quantum electrodynamics, incorporates both first and second harmonic terms for each junction, expressed as

[

\hat H = 4E_C (\hat n - n_g)^2 + E_{J A1}\cos(\hat\varphi_A) + E_{J B1}\cos(\hat\varphi_B) + E_{J A2}\cos(2\hat\varphi_A) + E_{J B2}\cos(2\hat\varphi_B),

]

where (E_C) represents the charging energy and (E_{Jij}) denotes the Josephson energy of each harmonic. Scientists meticulously modelled the circuit’s behaviour, defining the Josephson potential as

[

U(\varphi) = E_{J1}\cos(\varphi) + E_{J2}\cos(2\varphi),

]

typically with negative (E_{J1}) and positive (E_{J2}) values.

Crucially, the quantum phase operators of the two junctions adhere to flux quantisation, described by

[

\varphi_A - \varphi_B = 2\pi n + 2\pi \frac{\Phi}{\Phi_0},

]

where (\Phi) is the externally controlled flux offset and (\Phi_0) is the flux quantum. This configuration allows for the creation of a π‑periodic potential, suppressing single Cooper‑pair tunnelling and providing parity protection. To explore the system’s dynamics, the team employed numerical simulations to examine the dependence of relaxation and dephasing rates on external flux and circuit parameters. These simulations revealed a fundamental trade‑off between charge‑ and flux‑noise dephasing channels, a critical consideration for coherence optimisation.

The work demonstrates that with currently achievable circuit parameters, qubit lifetimes can exceed milliseconds, although dephasing times remain limited to a few microseconds due to noise. By biasing the circuit away from the frustration point, the study identifies a pathway to balance susceptibility to charge and flux noise, potentially extending coherence times to several microseconds. This detailed analysis establishes practical limits on coherence and raises important questions regarding the long‑term viability of this qubit approach.