Andreev Pair Qubit

Figure

Description

An Andreev pair qubit uses the two even-parity states of one highly transmitting Andreev bound-state doublet in a superconducting weak link. The logical ground state has the negative-energy Andreev level occupied by a Cooper pair; the excited state has the positive-energy partner occupied. Their transition changes the occupancy by two quasiparticles while preserving even parity.

This is not the Andreev spin qubit. The pair qubit uses the even-parity ground/excited pair transition; the spin qubit uses the odd-parity spin degree of freedom of a trapped quasiparticle.

Hamiltonian

For a short, spin-degenerate channel of transmission $\tau$,

$E_A(\phi )=\Delta \sqrt{1-\tau {\sin }^2(\phi /2)},$

and the even-parity transition energy is $2E_A$. The logical states are the even-parity configurations with the negative-energy level pair occupied ($|0⟩$) or the positive-energy level pair occupied ($|1⟩$); singly occupied configurations belong to the odd-parity sector.

A representative transverse two-level model for coupling to a microwave mode is the quantum-Rabi Hamiltonian,

$\frac{H}{\hslash }=\frac{{\omega }_A(\phi )}{2}{\sigma }_z+{\omega }_r{a}^{†}a+g(a+a^{†}){\sigma }_x,{\omega }_A=\frac{2E_A}{\hslash }.$

For $g\ll {\omega }_A,{\omega }_r$, the rotating-wave approximation reduces the interaction to $g(a^{†}{\sigma }_{-}+a{\sigma }_{+})$. That approximation is not valid when the coupling approaches the ultrastrong regime. Flux tunes $\phi$ and therefore the qubit frequency; a resonator provides spectroscopy, control, readout, and remote coupling.

Motivation

• Use the microscopic degrees of freedom that carry supercurrent as a compact qubit.
• Tune frequency with phase bias and couple distant weak links through microwave photons.
• Probe few-channel Josephson physics with coherent-control tools.

Experimental Status

Zazunov et al. proposed the Andreev-level qubit in 2003. Bretheau et al. directly observed excited Andreev pair states by spectroscopy in 2013, and Janvier et al. demonstrated coherent control and single-shot circuit-QED readout in 2015. Cheung et al. demonstrated cavity-mediated coherent coupling between two pair qubits and identified entangled eigenstates across 6 mm in 2024. In 2025, Shvetsov et al. observed a pair-transition coupling of about 490 MHz to a high-impedance resonator and extracted larger phase-dependent couplings, approaching the ultrastrong-coupling regime. No peer-reviewed 2026 experiment found in this audit supersedes those pair-qubit milestones.

Key Metrics

Metric	Value	Notes	Fidelity reference
Remote separation	6 mm	Two pair qubits coupled through a microwave cavity mode	Cheung et al. 2024
Frequency control	Flux/phase tunable	Follows $2E_A(\phi )$	Bretheau et al. 2013
Two-qubit interaction	Photon mediated	Avoided crossings and entangled two-qubit eigenstates	Cheung et al. 2024
Coherent-control times	$T_1\approx 4\mu \text{s}$; $T_2^{\ast }\approx 38\text{ns}$; echo $T_2\approx 565\text{ns}$	Representative atomic-contact result at $\phi =\pi$	Janvier et al. 2015
Pair-transition resonator coupling	$g/2\pi \approx 490\text{MHz}$ observed	High-impedance InAs–Al device; model gives $968\pm 7$ MHz maximum for the fitted transition	Shvetsov et al. 2025

Scaling Considerations

• Quasiparticle poisoning moves the weak link between even and odd parity sectors.
• Atomic contacts and nanowire weak links require reproducible high-transmission channels.
• Flux sensitivity, dielectric loss, and cavity crowding remain system-level constraints.
• Universal calibrated two-qubit gates and processor-scale integration remain to be demonstrated.
• The 2025 high-impedance-resonator result strengthens light–matter coupling, but its largest inferred value lies beyond the perturbative model used to extract it and should not be read as a gate benchmark.

References

• A. Zazunov et al., “Andreev Level Qubit,” Physical Review Letters 90, 087003 (2003); arXiv:cond-mat/0206342.
• L. Bretheau et al., “Exciting Andreev pairs in a superconducting atomic contact,” Nature 499, 312–315 (2013); arXiv:1305.4091.
• C. Janvier et al., “Coherent manipulation of Andreev states in superconducting atomic contacts,” Science 349, 1199–1202 (2015); arXiv:1509.03961.
• L. Y. Cheung et al., “Photon-mediated long-range coupling of two Andreev pair qubits,” Nature Physics 20, 1793–1797 (2024); arXiv:2310.15995.
• O. O. Shvetsov et al., “Approaching the ultrastrong-coupling regime between an Andreev level and a microwave resonator,” Physical Review Applied 24, 044015 (2025); arXiv:2502.09243.

Linked Papers

• zazunov-2003-andreev-level-qubit
• bretheau-2013-andreev-pairs
• janvier-2015-andreev-coherent-control
• cheung-2024-andreev-pair-coupling
• shvetsov-2025-andreev-ultrastrong-coupling

Evergreen context

• josephson-junction-as-nonlinear-element — Andreev levels are the microscopic weak-link spectrum beneath the Josephson effect.
• jaynes-cummings-in-circuits — cavity coupling supplies the control and remote-interaction layer.
• spin-orbit-coupling-for-qubit-control — helps distinguish spin-active odd-parity Andreev devices from this even-parity pair encoding.

Related Entries

• andreev-spin-qubit — odd-parity quasiparticle-spin encoding in a hybrid weak link.
• gatemon — uses the same gate-tunable weak-link family but encodes in a collective circuit mode.
• circuit-qed — shared microwave coupling and readout architecture.