Operation of a high-frequency, phase-slip qubit

This paper demonstrates the successful operation, readout, and coherent control of a high-frequency (~17 GHz) superconducting qubit based on a titanium nitride phase-slip junction, achieving lifetimes exceeding 60 μs and operation at temperatures above 300 mK, thereby establishing phase-slip junctions as a viable tool for advanced quantum information processing.

The Gist

Imagine you are trying to build a tiny, super-fast computer that uses the laws of quantum physics instead of electricity. To make this computer work, you need a special "switch" that can behave in weird, non-linear ways. For decades, scientists have used a specific type of switch called a Josephson Junction (made of aluminum) to do this. It's like a very special door that only lets certain quantum particles through in a specific way.

This paper introduces a brand-new type of switch called a Phase-Slip Junction. Think of it as the "twin" or "mirror image" of the old switch. While the old switch acts like a special spring (an inductor), this new switch acts like a special capacitor (a bucket that holds charge).

Here is what the researchers achieved with this new switch, explained simply:

1. The New Switch: A Tiny Bottleneck

To make this new switch, the team didn't use the usual aluminum. Instead, they used a thin film of Titanium Nitride (TiN). They carved a microscopic "bottleneck" into this film, only about 18 nanometers wide (that's thinner than a strand of DNA).

• The Analogy: Imagine a river (electricity) flowing through a pipe. The old switches are like a valve that controls the flow. This new switch is like a tiny, narrow crack in the pipe. Because the crack is so small, the water (quantum particles) sometimes "slips" through it in a quantum way, creating a unique effect called a "phase slip."

2. Building a "Qubit" (The Computer Bit)

They used this new switch to build a qubit, which is the basic unit of information in a quantum computer.

• How it works: They connected this switch to a loop of wire. In this loop, magnetic "chunks" (flux quanta) can tunnel through the narrow crack. This creates a state where the qubit is a mix of different magnetic states, similar to a coin spinning in the air being both heads and tails at once.
• The Sweet Spot: They tuned the system so it operates at "zero flux" (no outside magnetic interference). At this spot, the qubit's speed is determined mostly by the size of the loop, which is easy to control, rather than the tiny, tricky details of the crack itself.

3. What They Did (The Experiments)

The team proved this new qubit actually works by doing three main things:

• Reading it: They could check if the qubit was in the "ground" state or "excited" state with 96% accuracy. It's like being able to tell if a spinning coin has landed on heads or tails.
• Controlling it: They could make the qubit switch back and forth between states (Rabi oscillations) by hitting it with microwave pulses. They proved it behaves like a clean, two-state system without leaking into unwanted states.
• Timing it: They measured how long the qubit stays in its state before losing its information. They found it could hold its state for over 60 microseconds (which is a long time in the quantum world).

4. The Superpower: Running Hotter

The biggest surprise and advantage of this new design is that it can run at higher temperatures.

• The Old Way: Most quantum computers using aluminum need to be cooled to near absolute zero (about -273°C or 10 millikelvin) because the aluminum "melts" (loses its superconducting properties) if it gets too warm.
• The New Way: Because they used Titanium Nitride, which has a higher "melting point" for superconductivity, they were able to run the qubit at temperatures above 300 millikelvin (about -272.8°C).
• The Result: Even at this "warm" temperature, the qubit still worked well, keeping its memory for over 10 microseconds. This is like being able to run a delicate ice sculpture in a slightly warmer room without it melting immediately.

5. Why This Matters (According to the Paper)

The authors state that this is a major step forward because:

• It adds a new tool to the quantum toolbox. Instead of just having one type of switch (the Josephson Junction), scientists now have a second type (the Phase-Slip Junction) that acts differently.
• It opens the door to new types of quantum computers that might be more protected from noise or could operate at higher frequencies.
• It suggests that in the future, we might be able to build quantum computers that don't require the most extreme, expensive cooling systems, because they can handle slightly warmer environments.

In Summary:
The researchers built a new kind of quantum bit using a microscopic crack in a Titanium Nitride film. They proved it works, can be controlled, and can survive at temperatures warmer than traditional quantum computers, offering a promising new path for building better quantum machines.

Technical Summary

Technical Summary: Operation of a High-Frequency, Phase-Slip Qubit

Problem Statement
Superconducting quantum information processing currently relies heavily on aluminum-based Josephson junctions (JJs) as the primary source of nonlinearity. The dual of a JJ, the phase-slip junction (PSJ), acts as a nonlinear capacitor and offers a pathway to new classes of protected qubits, high-frequency operation, and operation at elevated temperatures using superconductors with larger energy gaps. However, the practical implementation of PSJ-based qubits has been severely limited by fabrication challenges and the difficulty of controlling junction parameters. Previous attempts have resulted in devices where qubit frequencies could not be reliably determined by design, and coherence times were only inferred indirectly. Furthermore, existing PSJ implementations have often operated at half-flux quantum, a point of extreme sensitivity to geometric variations, or suffered from poor coherence.

Methodology
The authors demonstrate the operation of a superconducting qubit based on a single-phase-slip junction fabricated from a thin (5 nm) film of titanium nitride (TiN). The device consists of a superinductance (150 nm wide) in parallel with a PSJ (an 18 nm wide constriction, narrower than the TiN coherence length), forming a superconducting loop. The device is inductively coupled to a readout resonator for dispersive measurement using standard circuit QED techniques.

The qubit is biased at zero external magnetic flux ($\Phi_{ext} = 0$). This operating point is chosen because the qubit frequency is primarily determined by the inductive energy ($E_L$) rather than the phase-slip rate ($E_{s,i}$), making the device robust against geometric variations of the constriction. The system is modeled using a Hamiltonian in the fluxon basis, accounting for single and double flux quanta tunneling events.

The experimental characterization includes:

• Two-tone spectroscopy to identify transition frequencies and fit Hamiltonian parameters.
• Single-shot readout to distinguish ground and excited states.
• Coherent control via Rabi oscillations to verify two-level system behavior.
• Time-domain measurements (relaxation $T_1$, Ramsey $T_{2R}$, and Hahn-echo $T_{2E}$) to characterize coherence and identify noise sources.
• Temperature-dependent studies up to 385 mK to evaluate the benefits of the larger TiN energy gap.

Key Results

• Device Operation: The team successfully operated a phase-slip qubit at zero flux with a transition frequency of approximately 17 GHz. Spectroscopic data fitted well to the theoretical Hamiltonian, yielding an inductive energy $E_L = 34.4$ GHz, a single phase-slip rate $E_{s,1} = 1.03$ GHz, and a double phase-slip rate $E_{s,2} = 0.05$ GHz.
• Coherent Control: The authors demonstrated high-fidelity single-shot readout (96% assignment fidelity) and coherent manipulation via Rabi oscillations. The system behaved as a well-controlled two-level system with no observed leakage to the second excited state ($|f\rangle$).
• Coherence Times: The qubit exhibited relaxation times ($T_1$) exceeding 60 $\mu$s at zero flux, representing a significant improvement over previous PSJ measurements. However, coherence times were limited, with Ramsey times ($T_{2R}$) of approximately 17 ns. The authors attribute the short $T_{2R}$ to strong dephasing, likely caused by flux noise and Aharonov-Casher (AC) noise arising from charge fluctuations along the wire.
• High-Temperature Operation: Leveraging the higher energy gap of TiN (transition temperature $T_c \approx 2.9$ K), the qubit was operated at temperatures exceeding 300 mK. While $T_1$ began to degrade significantly above 240 mK (attributed to increasing quasiparticle density and inductive loss), the qubit remained functional with $T_1 > 10$ $\mu$s and stable $T_{2R}$ at temperatures where aluminum-based qubits typically fail.

Significance and Claims
The paper claims that the phase-slip junction is a viable alternative source of nonlinearity for superconducting quantum devices. By demonstrating a functional qubit with $T_1$ comparable to standard Josephson junction-based qubits, the work validates the PSJ as a tool for quantum information processing.

The authors highlight three specific advantages of this approach:

1. Nonlinear Capacitance: The PSJ provides a nonlinear capacitor, enabling novel oscillator designs and potential noise-protected qubit architectures when combined with a Josephson junction.
2. Material Flexibility: The use of a single TiN film allows for the construction of the entire qubit-resonator device, potentially offering higher quality factors than evaporated aluminum.
3. High-Temperature Potential: The successful operation above 300 mK demonstrates a pathway toward reducing the cooling requirements for superconducting quantum processors, potentially enabling operation at temperatures significantly higher than those achievable with aluminum-based systems.

The authors conclude modestly that while the relaxation times are competitive, the coherence times are currently short. They suggest that improved device processing (cleaning methods) and geometric optimizations to reduce sensitivity to charge fluctuations are necessary to elucidate decoherence mechanisms and make the phase-slip qubit a competitive platform for scalable quantum information processing.