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PRX Quantum

Protected Hybrid Superconducting Qubit in an Array of Gate-Tunable Josephson Interferometers

Constantin Schrade, Charles M. Marcus, András Gyenis

Published Jul 6, 2022• 0 citations
Publisher

Abstract

We propose a protected qubit based on a modular array of superconducting islands connected by semiconductor Josephson interferometers.The individual interferometers realize effective cos 2φ elements that exchange "pairs of Cooper pairs" between the superconducting islands when gate tuned into balance and frustrated by a half-flux quantum.If a large capacitor shunts the ends of the array, the circuit forms a protected qubit because its degenerate ground states are robust to offset-charge and magnetic field fluctuations for a sizable window around zero offset charge and half-flux quantum.This protection window broadens upon increasing the number of interferometers if the individual elements are balanced.We use an effective spin model to describe the system and show that a quantum phase transition sets the critical flux value at which protection is destroyed.

DOI
10.1103/prxquantum.3.030303

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We propose a protected qubit based on a modular array of superconducting islands connected by semiconductor Josephson interferometers.The individual interferometers realize effective cos 2φ elements that exchange "pairs of Cooper pairs" between the superconducting islands when gate tuned into balance and frustrated by a half-flux quantum.If a large capacitor shunts the ends of the array, the circuit forms a protected qubit because its degenerate ground states are robust to offset-charge and magnetic field fluctuations for a sizable window around zero offset charge and half-flux quantum.This protection window broadens upon increasing the number of interferometers if the individual elements are balanced.We use an effective spin model to describe the system and show that a quantum phase transition sets the critical flux value at which protection is destroyed.
We propose a protected qubit based on a modular array of superconducting islands connected by semiconductor Josephson interferometers. The individual interferometers realize effective cos⁡2ϕ\cos2ϕcos2ϕ elements that exchange `pairs of Cooper pairs' between the superconducting islands when gate-tuned into balance and frustrated by a half flux quantum. If a large capacitor shunts the ends of the array, the circuit forms a protected qubit because its degenerate ground states are robust to offset charge and magnetic field fluctuations for a sizable window around zero offset charge and half flux quantum. This protection window broadens upon increasing the number of interferometers if the individual elements are balanced. We use an effective spin model to describe the system and show that a quantum phase transition point sets the critical flux value at which protection is destroyed.
We propose a protected qubit based on a modular array of superconducting islands connected by semiconductor Josephson interferometers. The individual interferometers realize effective cos2ϕ elements that exchange “pairs of Cooper pairs” between the superconducting islands when gate tuned into balance and frustrated by a half-flux quantum. If a large capacitor shunts the ends of the array, the circuit forms a protected qubit because its degenerate ground states are robust to offset-charge and magnetic field fluctuations for a sizable window around zero offset charge and half-flux quantum. This protection window broadens upon increasing the number of interferometers if the individual elements are balanced. We use an effective spin model to describe the system and show that a quantum phase transition sets the critical flux value at which protection is destroyed.
Coherence of superconducting qubits can be improved by implementing designs that protect the parity of Cooper pairs on superconducting islands. Here, we introduce a parity-protected qubit based on voltage-controlled semiconductor nanowire Josephson junctions, taking advantage of the higher harmonic content in the energy-phase relation of few-channel junctions. A symmetric interferometer formed by two such junctions, gate-tuned into balance and frustrated by a half-quantum of applied flux, yields a cos(2φ) Josephson element, reflecting coherent transport of pairs of Cooper pairs. We demonstrate that relaxation of the qubit can be suppressed tenfold by tuning into the protected regime.
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.
Parity-protected superconducting qubits offer intrinsically long coherence, but many current implementations require magnetic-flux biasing, which introduces flux noise, control overhead, and limited scalability. Here we propose a parity-protected qubit based on a gate-tunable superconductor-altermagnet-superconductor Josephson junction. Altermagnets are compensated magnets with momentum-dependent spin splitting and zero net magnetization, providing spin-dependent functionality without external magnetic fields. In the proposed junction, the two spin sectors acquire opposite phase shifts, generating two Josephson channels whose interference is controlled electrically by the chemical potential. At the tuned 000-πππ transition, the first Josephson harmonic is strongly suppressed while the second harmonic dominates, yielding a double-well potential with two nearly degenerate states of opposite Cooper-pair parity. For realistic gatemon-compatible parameters, we estimate coherence times of up to tens of milliseconds while maintaining fully gate-controlled qubit operations. These results establish altermagnetic Josephson junctions as a promising route toward protected superconducting qubits with local, scalable, and all-electrical control.
Controlling the current-phase relation (CPR) of Josephson elements is essential for tailoring the eigenstates of superconducting qubits, tuning the properties of parametric amplifiers, and designing nonreciprocal superconducting devices. Here, we introduce the hybrid Josephson rhombus, a highly tunable superconducting circuit containing four semiconductor-superconductor hybrid Josephson junctions embedded in a loop. Combining magnetic frustration with gate-voltage-controlled tuning of individual Josephson couplings provides deterministic control of the harmonic content of the rhombus CPR. We show that, for balanced Josephson couplings at full frustration, the hybrid rhombus displays a π -periodic cos ( 2 φ ) potential, indicating coherent charge- 4 e transport. Tuning away from the balanced configuration, we observe a superconducting diode effect with efficiency exceeding 25%. These results showcase the potential of hybrid Josephson rhombi as fundamental building blocks for noise-resilient qubits and quantum devices with custom transport properties.