Session Y46: Fluxonium-Based Superconducting Qubits

A noise protected superconducting Fluxonium qubit

Since the early 2000s, there has been a significant improvement in the coherence time of superconducting qubits by five orders of magnitude. Despite this progress, current qubit performances are still a major limitation to the development of a universal quantum processor. Currently, the fluxonium qubit stands as the circuit with the longest observed coherence [1], with recent experiments showing it can achieve milliseconds of coherence.  It is composed of a superconducting loop made of a Josephson junction shunted by a large inductance (often called a super-inductance). An external magnetic field threading the loop can be used to tune the circuit parameters.

Several groups have created Fluxonium devices with a very low frequency of 1-10 MHz. This approach results in a reduced relaxation rate due to the decrease in the charge matrix element at lower frequencies. This is a simple way to enhance the performances of this qubit. Alternatively, a protected qubit can be encoded in multimodal circuit that generalizes the fluxonium to a larger parameter space. In these more complex circuits, protected information can be encoded at the cost of stringent requirements on the circuit parameters [2,3].

In this work, we use the single-loop fluxonium circuit in a new regime. We engineer the circuit parameters so that the qubit wave functions are de-localized over several potential wells to minimize their overlap, hence guaranteeing an extremely small matrix element or equivalently a very long relaxation time. Additionally, the qubit transitions offer a very low sensitivity to flux noise thanks to the very large inductance. We will discuss the depolarization and coherence times, as well as their limitations, for this new type of Fluxonium qubit.

1 Somoroff, Aaron, et al. "Millisecond coherence in a superconducting qubit." Physical Review Letters 130.26 (2023): 267001.

2 Kalashnikov, Konstantin, et al. "Bifluxon: Fluxon-parity-protected superconducting qubit." PRX Quantum 1.1 (2020): 010307.

3 Gyenis, András, et al. "Experimental realization of a protected superconducting circuit derived from the 0–π qubit." PRX Quantum 2.1 (2021): 010339.   

Crossing over from electromagnetic induced transparency (EIT) to Autler-Townes splitting (ATS) in a single superconducting fluxonium artificial atom.

  Electromagnetically induced transparency (EIT) has been demonstrated in the atomic system, artificial atoms, and meta-structures. Previous demonstrations of EIT in superconducting artificial atoms involve coupling to other degrees of freedom such as resonators or other superconducting atoms. Here we report our design and experiment of the EIT with a single Fluxonium qubit inside a microwave waveguide. Because of large anharmonicity and tunability of the Fluxonium qubit, we designed a Lambda-type system with the controlling and probing transitions are strongly coupled to the transmission line while the transition between |0> and |1> states are protected while the fluxonium qubit close to the sweet spot. We observed a cross over from EIT to Autler-Townes splitting (ATS) regimes by tuning the controlling drive power. We further use Akaike information criterion (AIC) to identify the transition from EIT to ATS regime. The experimental results also agree with prediction of a three-level system’s model. This hardware efficient device can be used for slow light and quantum memory in microwave regime.   

Novel charging effects in the fluxonium qubit

The fluxonium circuit has recently emerged as an attractive qubit modality for building a fault-tolerant quantum computer. Because of the presence of an inductive shunt, the fluxonium qubit is insensitive to the dc value of the offset-charge bias, n_g. However, the impact of nonzero-frequency fluctuations of n_g is not fully charted in the literature. In this talk, we derive a convenient form of the fluxonium Hamiltonian that makes it easier to characterize the effects of a time-dependent offset-charge bias. Our fluxonium model reveals a new noise channel for fluxonium related to quasiparticles, and has implications for high-fidelity qubit control.   

Investigating the loss mechanisms of driven fluxonium circuits

The fluxonium qubit has garnered significant interest recently due to its high gate fidelities and strongly anharmonic spectrum. These valuable features have resulted in the fluxonium being proposed as the basis for a quantum processor, for use in transducing between microwave and optical signals, and as a nonlinear element for manipulating long-lifetime linear cavities. A necessary requirement for using the fluxonium in such schemes is a better understanding of the behavior of the fluxonium under the application of microwave drives at different frequencies. Here we review previous work on fluxonium circuits and report on our efforts, both in experiment and theory, to map out the dynamics and loss mechanisms of a driven fluxonium-based circuit. We first focus on the driven behavior of single-fluxonium circuits before moving on to the benefits that are offered in driven multiple-fluxonium devices.   

Optimal fluxonium parameters for capacitive cross-resonance gate

Fluxonium qubits have recently demonstrated millisecond long coherence times enabled by their reduced susceptibility to dielectric losses. This resilience comes from its low qubit frequencies and suppressed charge matrix elements. However, this characteristic also reduces the qubit-qubit coupling between capacitively coupled fluxoniums, which poses a challenge for entangling gates. In this work, we study an architecture for cross-resonance gates with fluxonium qubits. We aim to obtain the fastest gate speed given a low target residual ZZ rate. Using a semi-analytic approach, we find energy design parameters for control and target qubits which generally allows for CNOT gate durations around 150 ns with a 50 kHz residual ZZ under strong charge driving. We further provide estimates of frequency collision windows around harmful control-target and control-spectator transitions.   

Compact 2D Fluxonium Qubits Design with Inductive Coupling for Measurement and Control

The fluxonium, a novel superconducting qubit shunted by a large inductance, has recently exhibited milliseconds coherence times and high-fidelity single/two-qubit gates. A significant advantage of fluxonium lies in its richer matrix elements. At the half- flux point, the phase matrix element of computational states is not only stronger than its charge counterpart but also surpasses the phase matrix elements of non-computational states. It is natural to leverage this inherent strong 0-1 phase coupling to manipulate fluxonium. In this work, we propose a 2D fluxonium architecture with inductive coupling to achieve measurement and control. With all inductive coupling, we achieve a more compact geometric design—reducing the footprint of the resonator-qubit system by a factor 30. The diminished explicit capacitive coupling also holds promise for suppressing sensitivity to external decoherence sources, effectively mitigating dielectric losses between the substrate-metal and metal-air interfaces. We systematically explore various fluxonium designs to study decoherence mechanisms from dielectric loss and photon noise. Finally, we discuss the feasibility of fluxonium-based quantum processing units with the all-inductive coupling architecture.   

Dephasing in fluxonium qubits from coherent quantum phase slips

Phase slips occur at all Josephson junctions (JJs) at a rate dependent on the junction impedance. In superconducting qubits comprised of JJ array superinductors, such as fluxonium, phase slips in the array can lead to decoherence. In particular, phase slip processes at the individual array junctions can coherently interfere, each with an Aharonov-Casher phase dependent on the offset charges of the array islands. These coherent quantum phase slips (CQPS) perturbatively modify the qubit frequency, therefore charge noise on the array islands will lead to dephasing. By varying the impedance of the array junctions, we specifically engineer a set of fluxonium qubits to be sensitive to CQPS-induced dephasing over three orders of magnitude. We characterize the coherence times of these qubits in regimes dominated by CQPS or flux noise and show agreement with theoretical models. A detailed understanding of this dephasing mechanism has implications for improvements to coherence in fluxonium and is relevant for the many novel qubit designs involving JJ arrays. 

 This material is based upon work supported under Air Force Contract No. FA8702-15-D-0001. Any opinions, findings, conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the U.S. government or the U.S. Air Force.    

Overcoming the Rotating-Wave Approximation in Fluxonium with Circularly Polarized Driving (Part 1)

Fluxonium qubits are an attractive candidate for gate-based quantum computing due in part to their long coherence times. Two general features of a typical fluxonium are its low qubit frequency (less than 1 gigahertz) and its high anharmonicity (several gigahertz). One consequence, however, is related to the single-qubit gate speed: as the qubit drive power is increased, the rotating wave approximation breaks down before the leakage into non-computational states dominates the gate error. This is notably different with transmon qubits, which have a high qubit frequency but low anharmonicity.

 

In this work, we circumvent the aforementioned limitation by simultaneously performing linear charge and flux drives on a fluxonium superconducting qubit to create the circuit-quantum-electrodynamics analogue of circularly-polarized light. With this, we show both theoretically and experimentally that the rotating-wave approximation can be completely bypassed and use this technique to calibrate single-qubit gates as short as 10 ns with above 99.99% fidelity. In the first part of this talk, we discuss the theory and realization of a circularly-polarized drive on a fluxonium qubit   

Overcoming the Rotating-Wave Approximation in Fluxonium with Circularly Polarized Driving (Part 2)

Fluxonium qubits are an attractive candidate for gate-based quantum computing due in part to their long coherence times. Two general features of a typical fluxonium are its low qubit frequency (less than 1 gigahertz) and its high anharmonicity (several gigahertz). One consequence, however, is related to the single-qubit gate speed: as the qubit drive power is increased, the rotating wave approximation breaks down before the leakage into non-computational states dominates the gate error. This is notably different with transmon qubits, which have a high qubit frequency but low anharmonicity.

 

In this work, we circumvent the aforementioned limitation by simultaneously performing linear charge and flux drives on a fluxonium superconducting qubit to create the circuit-quantum-electrodynamics analogue of circularly-polarized light. With this, we show both theoretically and experimentally that the rotating-wave approximation can be completely bypassed and use this technique to calibrate single-qubit gates as short as 10 ns with above 99.99% fidelity. In this second part of the talk, we detail gate calibration procedures and discuss current factors limiting gate fidelities.   

Strong coupling between a 2D fluxonium and Tantalum resonators

The state-of-the-art superconducting device has a physical error rate that approaches the error-correction threshold but still stands in a crossover regime in which the logical error initially decreases with more physical qubits and later increases back. Further going beyond this break-even point calls for higher coherence physical system which can ensure higher fidelity limit. Fluxonium has been demonstrated to be a potentially better qubit candidate than the traditional transmon design due to its higher coherence and larger anharmonicity. By coupling two fluxoniums with long lifetime tantalum based resonators, we can perform resonator-induced-phase gate or geometric phase gate that is possible to reach lower error rate. In this talk, I will present our preliminary data on fabricating a 2D fluxonium and achieving strong coupling to a tantalum resonator. The tantalum film is cleaned with piranha solution and BOE to etch the oxide and remove hydrocarbons. The results demonstrate that combining 2D fluxonium and resonator-based two-qubit gates is a practical architecture for fault-tolerant quantum computing.   

Engineering Spectral Properties of Fluxonium through Josephson Plasma Frequency Optimization

The spectral properties of fluxonium exhibit significant variations depending on the circuit parameters E_J, E_C, and E_L. Exploring the large parameter space and the resulting properties that depend on the different combinations allows for the customizability of transition frequencies, matrix elements, and dispersive shifts. In this talk, we emphasize the ability to precisely design and fabricate desired fluxonium properties by optimization of the Josephson plasma frequency; which is tunable within the range of 10-100 GHz. This fabrication methodology paves the way for the exploration of new fluxonium parameter regimes with favorable properties.