⚛️ quantum physics

Construction of new type of CNOT gate using cross-resonance pulse in the transmon-PPQ system

This paper proposes a high-fidelity CNOT gate implementation with over 0.998 average fidelity in a hybrid superconducting system combining a tunable transmon and a parity-protected qubit by utilizing cross-resonance pulses, thereby offering a promising platform for advancing fault-tolerant quantum computing.

Original authors: Jeongsoo Kang, Younghun Kwon

Published 2026-06-25

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Jeongsoo Kang, Younghun Kwon

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to build a super-fast, super-smart calculator (a quantum computer) using tiny electrical switches called qubits. Currently, the most popular switch is called a Transmon. It's like a reliable, fast-running race car. It's been around for a while, works well, and is easy to drive. However, even the best race cars have a problem: they eventually run out of gas or get tired (they lose their "coherence") before they can finish a very long, complex race.

To fix this, scientists invented a new, special switch called a PPQ (Parity-Protected Qubit). Think of the PPQ as a high-tech, armored tank. It's built with a special shield that protects its energy much better than the race car, allowing it to stay "awake" and working for much longer. This is great for long races, but there's a catch: nobody knew how to make the race car and the armored tank work together in the same team. They speak different "languages" and have different shapes, so connecting them is like trying to hook up a bicycle to a spaceship.

The Big Idea
The authors of this paper, Jeongsoo Kang and Younghun Kwon, figured out how to make these two very different switches work together as a team. They designed a way to connect the "race car" (Transmon) and the "tank" (PPQ) using a shared wire (a resonator) and a specific type of radio signal (microwave pulses).

How They Made Them Talk: The "Cross-Resonance" Trick
Usually, to make two switches interact, you have to tune them to be exactly the same. But since the Transmon and PPQ are so different, they can't be tuned to match perfectly.

The researchers used a clever trick called Cross-Resonance (CR). Imagine two people standing next to each other. One person (the Transmon) is shouting a specific note. Even though the other person (the PPQ) is tuned to a slightly different note, the sound waves from the first person are strong enough to make the second person vibrate only if the first person is shouting in a certain way.

In their system:

The Control (Transmon): This is the "boss." It sends out a microwave pulse (a radio signal).
The Target (PPQ): This is the "worker." It listens to the boss.
The Magic: If the boss is in one state, the signal makes the worker flip its switch. If the boss is in the other state, the worker stays still. This flipping action is the core of a CNOT gate, which is a fundamental logic operation (like an "IF-THEN" statement) needed for any computer to do math.

The Results
The team didn't just guess; they built a detailed mathematical model and ran computer simulations to see if this would work.

They designed the perfect "recipe" for the radio signals (pulses), including exactly how long to send them and how strong they should be.
They found that by using this method, the two different switches could perform a logic gate with an accuracy of 99.89%.

Why This Matters
In the world of quantum computing, 99.89% is a very high score. It's high enough that scientists believe they could use these mixed teams of "race cars" and "tanks" to build machines that can fix their own mistakes (fault-tolerant computing).

In Summary
This paper proves that you don't have to choose between the fast, common Transmon and the long-lasting, protected PPQ. You can actually combine them. By using a specific radio signal trick, they showed that these two different types of quantum switches can work together to perform complex calculations with high accuracy. It's like finally figuring out how to drive a race car and an armored tank in a convoy, giving us a new, powerful way to build the quantum computers of the future.

Technical Summary: A Novel Superconducting Two-Qubit System Based on Transmon and PPQ, and the Design of a CNOT Gate via Cross-Resonance Pulses

Problem Statement
Superconducting quantum processors, predominantly utilizing transmon qubits, face significant hurdles in achieving fault-tolerant quantum computing. While transmons offer fast operation times and microsecond-scale coherence, their gate fidelities are limited by incoherent errors (relaxation and dephasing) and coherent errors stemming from structural constraints. Recently, Parity-Protected Superconducting Qubits (PPQs) have been proposed as a superior alternative, offering significantly longer relaxation times by protecting Cooper pair parity on a superconducting island. However, a critical gap remains in the practical implementation of heterogeneous systems that combine transmons and PPQs. Specifically, the most efficient method for realizing two-qubit gates in such a heterogeneous architecture is unknown. Previous attempts, such as flux-pulse modulated controlled-phase gates via capacitive coupling, face limitations in scalability and spatial layout. Furthermore, it is unclear whether Cross-Resonance (CR) pulses—a standard method for high-fidelity CNOT gates in homogeneous transmon systems—can function effectively in heterogeneous systems where large frequency mismatches and structural differences exist between qubit types.

Methodology
The authors propose a theoretical framework for a heterogeneous system comprising a tunable transmon qubit and a PPQ, coupled indirectly via a coplanar waveguide resonator. The methodology involves:

Hamiltonian Modeling: The system is modeled by deriving effective Hamiltonians for both qubits reduced to two-level systems (TLS). The transmon is treated as a quantum Duffing oscillator, while the PPQ is modeled as a weakly anharmonic oscillator where dynamics are restricted to specific parity states. By applying a Schrieffer-Wolff transformation, the authors derive an effective two-qubit Hamiltonian featuring a transverse interaction term ( $J\hat{\sigma}_{x,T}\hat{\sigma}_{x,P}$ ), demonstrating that the heterogeneous system is equivalent to a homogeneous two-qubit system at the Hamiltonian level.
Hardware Parameter Specification: The authors define specific hardware parameters to facilitate the CR interaction. The transmon frequency ( $\omega_T$ ) is set to 2.8830 GHz, and the PPQ frequency ( $\omega_P$ ) to 2.8470 GHz, with a resonator frequency ( $\omega_R$ ) of 2.4 GHz. The capacitive coupling strength ( $G$ ) between the qubits and the resonator is set to 10 MHz.
Pulse Sequence Design: A CNOT gate (designated $CNOT_{TP}$ $C N O T_{T P}$ ) is designed using a Cross-Resonance pulse applied to the control qubit (transmon) and an auxiliary single-qubit pulse applied to the target qubit (PPQ). The CR pulse frequency is tuned near the target qubit's frequency to induce conditional resonance. The pulse sequence includes:
- A CR pulse on the transmon with a sinusoidal flat-top envelope.
- An auxiliary $R_X$ pulse on the PPQ to complete the rotation.
- Virtual Z (VZ) gates to correct phase accumulation.
- Optimization of pulse parameters (frequencies, durations, amplitudes, and phases) using the Nelder-Mead algorithm to maximize gate fidelity.

Key Contributions

Theoretical Demonstration of CR in Heterogeneous Systems: The paper theoretically establishes that Cross-Resonance pulses can successfully induce conditional rotations in a system combining a transmon and a PPQ, despite their structural and frequency differences.
Effective Hamiltonian Equivalence: The work demonstrates that the transmon-PPQ system, when coupled via a resonator, reduces to an effective Hamiltonian identical to that of homogeneous transmon systems, validating the use of standard CR gate protocols.
Hardware and Pulse Specifications: The authors provide a complete set of theoretical hardware specifications (frequencies, coupling strengths) and optimized pulse parameters required to simulate the gate operation.

Results
Numerical simulations of the proposed $CNOT_{TP}$ gate yield an average gate fidelity of 0.9989. The simulation results include:

State Tomography: High success probabilities for all four computational basis states ( $|00\rangle, |01\rangle, |10\rangle, |11\rangle$ ) with relative phases close to zero.
Bloch Vector Trajectories: The evolution of the Bloch vectors confirms that the control qubit (transmon) undergoes an adiabatic process, while the target qubit (PPQ) experiences the intended X or -X rotations conditional on the control state.
Fidelity Analysis: The achieved fidelity of 0.9989 is presented as being sufficient for error suppression using quantum error-correcting codes.

Significance and Claims
The paper claims that the proposed transmon-PPQ heterogeneous system offers a promising new platform for advancing toward fault-tolerant quantum computing. By leveraging the long coherence times of PPQs while utilizing the mature control infrastructure of transmons (specifically microwave drive lines and CR pulses), this architecture addresses the scalability and fidelity limitations of current processors. The authors assert that their theoretical design proves that high-fidelity two-qubit gates are achievable in such heterogeneous systems, laying a new foundation for integrating parity-protected qubits into scalable superconducting quantum processors. The work suggests that while fixed coupling is used in this specific model, future iterations could incorporate tunable couplers to further suppress crosstalk, though this is presented as a suggestion rather than a result of the current study.

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