Experimental realization of a $\cos(2\varphi)$ transmon qubit

This paper reports the experimental realization of a low-frequency $\cos(2\varphi)$ transmon qubit that achieves a 100-fold suppression of charge-induced errors through Cooper-pair parity protection, enabling coherent control and single-shot readout while identifying flux noise as the primary remaining limitation to coherence.

The Gist

The Big Picture: Building a "Ghost" Qubit

Imagine you are trying to build a computer that uses the strange rules of quantum mechanics (a quantum computer). The biggest problem is that these computers are incredibly fragile. A tiny bit of static electricity, a stray vibration, or a fluctuation in temperature can cause the information to scramble and disappear. This is called decoherence.

Most current quantum computers (like the famous "transmons") are like delicate glass houses. They work well, but they need constant, active repair crews (error correction) to fix the cracks as soon as they appear.

This paper introduces a new type of quantum bit (qubit) that is built like a fortress. Instead of trying to fix the cracks, the designers built the house so that the most common types of damage simply cannot get inside. They call this the cos(2φ) qubit.

The Main Character: The "KITE"

To build this fortress, the researchers created a special component they nicknamed the KITE (Kinetic Interference co-Tunneling Element).

• The Analogy: Imagine a playground with a central island (the qubit) and a bridge leading to the ground.
• The Problem: In normal bridges, single people (electrons) can walk across easily. If a gust of wind (noise) blows, a person might fall off, ruining the game.
• The KITE Solution: The KITE is a magical bridge that only lets pairs of people walk across together, holding hands. If a single person tries to cross, the bridge simply doesn't let them.
• Why it matters: In the quantum world, "single people" are single electrons (charge). "Pairs" are Cooper pairs (the stuff superconductors are made of). By forcing electrons to move in pairs, the qubit becomes immune to the most common type of noise: charge noise. It's like building a door that only opens for a specific handshake; a random bump won't open it.

The Experiment: The "Soft" Transmon

The researchers wanted to test this KITE in a regime they call the "Soft Transmon."

• The Analogy: Think of a pendulum.
  • A Hard Pendulum swings wildly and is very sensitive to where you push it.
  • A Soft Pendulum swings very slowly and gently.
• The Trade-off: Usually, if you make a pendulum swing very slowly (low frequency), it becomes hard to control and measure. It's like trying to hear a whisper in a noisy room.
• The Breakthrough: The researchers managed to tune their "Soft Pendulum" to swing at a very low frequency (13.6 MHz) but still managed to hear the whisper clearly. They could control the qubit and read its state without the noise drowning it out.

What They Found

1. The "Doublet" Discovery: They found two distinct states in their qubit that act like a "doublet" (a pair of twins). One twin represents an even number of electron pairs, and the other represents an odd number.

   • The Magic: Because of the KITE's rules, these two twins are separated by a tiny gap (13.6 MHz). Crucially, the "charge" (the single electron noise) cannot easily jump between them. It's like having two rooms separated by a wall that is 100 times thicker than usual.

2. The "Ghost" Protection: They measured how much the qubit's state changed when they tried to shake it with electric noise.

   • Result: The qubit was 100 times more resistant to charge noise than a standard qubit. It's as if they built a shield that blocks 99% of the static electricity that usually kills quantum computers.

3. The New Villain: While they successfully blocked the "Charge Monster," they found a new enemy: Flux Noise.

   • The Analogy: Imagine you built a fortress that is immune to rain (charge noise), but you forgot to waterproof the roof against wind (magnetic flux noise).
   • The qubit's lifespan (how long it remembers information) is currently limited by magnetic fluctuations in the loop of the KITE. It lasts for about 70 microseconds. While this is short, it proves the concept works: the charge protection is real, and the only thing stopping it from being perfect is the magnetic wind.

Why This Matters

This experiment is a major step forward because it proves that symmetry can be used as a shield.

• Old Way: Build a fragile qubit and use software to constantly fix errors (like a car with a mechanic sitting in the back seat fixing the engine while you drive).
• New Way: Build a qubit that is naturally immune to the most common errors (like a car with a self-sealing fuel tank that never leaks).

The researchers showed that even with a very low-frequency, "soft" qubit, you can still control it and read its state. This opens the door to building quantum computers that require much less error correction, potentially making them smaller, cheaper, and more powerful.

The Future

The team says the next step is to fix the "wind" problem (flux noise). They suggest using better designs (like "gradiometric" layouts, which are like noise-canceling headphones for magnets) or finding new materials that can do the "pair-tunneling" trick without needing a magnetic loop at all.

In summary: They built a quantum bit that is naturally immune to electrical noise by forcing electrons to move in pairs. It works beautifully, proving that "protected" qubits are possible, and now they just need to shield it from magnetic wind to make it truly unstoppable.

Technical Summary

1. Problem Statement

Superconducting quantum computing currently relies heavily on active quantum error correction (QEC) to mitigate decoherence, primarily because physical qubits (like the standard transmon) are highly susceptible to charge noise and dielectric loss. This necessitates a large overhead of physical qubits to create a single logical qubit.

• The Goal: To engineer "protected" physical qubits that intrinsically suppress dominant error channels (specifically charge-induced errors) through circuit symmetries, thereby reducing the overhead required for QEC.
• The Challenge: Theoretical proposals for protected qubits, such as the cos(2φ) qubit, require specific circuit elements (Cooper-pair quartet tunneling) and operation in specific regimes (transmon regime) that are difficult to realize experimentally. Previous implementations operated in a "light" regime with high charge dispersion, failing to achieve the necessary protection. Furthermore, pushing these qubits into the deep transmon regime (to eliminate charge sensitivity) often results in vanishingly small qubit frequencies, making control and readout nearly impossible.

2. Methodology

The authors designed and fabricated a superconducting circuit implementing a cos(2φ) qubit operating in a "soft transmon" regime.

• Circuit Design (The KITE): The core component is a Kinetic Interference co-Tunneling Element (KITE). This is a two-identical-arm interferometer composed of Josephson junctions (JJs) and superinductors (arrays of JJs).
  • The KITE is biased at half a flux quantum ($\Phi_0/2$).
  • It selectively transmits pairs of Cooper pairs (charge $4e$) while suppressing single Cooper-pair tunneling ($2e$), creating an effective potential $E_{J2} \cos(2\phi)$.
  • The circuit consists of a large superconducting island (Niobium) shunted to ground by the KITE (Aluminum) and coupled to a readout resonator and bias lines.
• Operating Regime: The device was engineered with a ratio of Josephson energy to charging energy $E_{J2}/E_C \approx 22$. This places the qubit in the "soft transmon" regime:
  • Frequency: The qubit transition frequency is 13.6 MHz, which is 400 times lower than previous implementations.
  • Protection: This low frequency ensures charge noise is non-limiting, while the frequency remains high enough to allow for coherent control and single-shot readout.
• Readout Strategy: Instead of direct dispersive readout of the low-frequency qubit, the authors utilized the plasmonic ladder. The state of the low-frequency doublet (Cooper-pair parity) induces a distinct frequency pull on the higher-frequency plasmonic transitions, which are then coupled to a 4.3 GHz readout resonator. This allows for high-fidelity, single-shot readout.
• Experimental Setup: The device was measured in a dilution refrigerator (10 mK) using standard cQED techniques, including two-tone spectroscopy, Rabi oscillations, Ramsey sequences, and echo measurements.

3. Key Contributions

1. First Realization of a Soft-Transmon cos(2φ) Qubit: Successfully demonstrated a qubit operating at 13.6 MHz with $E_{J2}/E_C = 22$, a regime previously unexplored for this topology.
2. Demonstration of Charge Protection: Provided experimental evidence that the qubit is protected against charge noise by observing a 100-fold suppression of the charge matrix element compared to an unprotected plasmon transition.
3. Coherent Control and Readout at Low Frequency: Overcame the challenge of controlling a 13.6 MHz qubit, achieving:
   • Coherent Control: Rabi oscillations with a rate of 1 MHz.
   • Single-Shot Readout: 83% fidelity in 5 µs integration time, allowing initialization at an effective temperature of 400 µK.
   • Quantum Jumps: Real-time resolution of quantum jumps between the ground state doublet and higher plasmonic states.
4. Identification of Dominant Error Channels: Quantified that while charge-induced losses are suppressed to the millisecond scale, the current coherence is limited by 1/f flux noise in the KITE loop.

4. Key Results

• Energy Spectrum: Observed a doublet of states with opposite Cooper-pair parity split by 13.6 MHz. The splitting is two orders of magnitude smaller than in previous experiments, confirming the deep transmon regime.
• Charge Protection:
  • The charge matrix element for the protected transition ($|0+\rangle \leftrightarrow |0-\rangle$) was measured at $1.3 \times 10^{-2}$, compared to 2.2 for the unprotected transition.
  • This suppression implies a theoretical dielectric loss limit ($T_1$) of >10 ms, far exceeding the measured coherence times.
• Coherence Times:
  • $T_1$ (Relaxation): 70 µs.
  • $T_2^{echo}$ (Dephasing): 2.5 µs.
  • Limiting Factor: Analysis shows these times are limited by 1/f flux noise in the KITE loop (noise amplitude $A_\Phi \approx 5.6 \, \mu\Phi_0/\sqrt{\text{Hz}}$), not by charge noise or dielectric loss.
• Readout Performance:
  • Achieved 83% single-shot fidelity.
  • Successfully resolved quantum jumps and distinguished between even and odd quasiparticle parity on the island.
  • Measured a circuit temperature of 43 mK.
• Spectroscopy: Two-tone spectroscopy confirmed the 3-mode circuit model, accurately capturing the broadband spectrum (up to 4 GHz) and the specific low-energy doublet structure.

5. Significance and Outlook

• Validation of Protected Qubits: This work proves that "soft transmon" regimes are a viable path for protected qubits. It demonstrates that one can achieve strong charge protection (pushing charge-induced errors well beyond coherence times) without sacrificing the ability to control and read out the qubit.
• Roadmap for Improvement: The paper identifies flux noise as the primary bottleneck. Future improvements are proposed, including:
  • Reducing the KITE loop area.
  • Implementing gradiometric designs.
  • Using fluxoid locking techniques.
  • Exploring novel materials (e.g., twisted d-wave superconductors) that could enable quartet tunneling without a flux loop, potentially eliminating flux sensitivity entirely.
• Broader Impact: The device acts as a sensitive detector for quasiparticle dynamics and charge noise, offering a platform to study fundamental decoherence mechanisms in superconducting circuits. It bridges the gap between heavy fluxoniums (high anharmonicity, low transitions) and Cooper-pair boxes (quantized charge), offering a unique hybrid architecture for fault-tolerant quantum computing.