⚛️ quantum physics

Measurement-Induced State transitions in Inductively-Shunted Transmons

This paper demonstrates that adding an inductive shunt to transmon qubits eliminates offset charge dependence and stabilizes measurement-induced state transitions (MIST), thereby enabling faster and more reliable qubit measurements for quantum error correction.

Original authors: Nicholas Zobrist, John Mark Kreikebaum, Mostafa Khezri, Sergei V. Isakov, Brian J. Lester, Yaxing Zhang, Agustin Di Paolo, Daniel Sank, W. Clarke Smith

Published 2026-03-13

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CC BY 4.0

Original authors: Nicholas Zobrist, John Mark Kreikebaum, Mostafa Khezri, Sergei V. Isakov, Brian J. Lester, Yaxing Zhang, Agustin Di Paolo, Daniel Sank, W. Clarke Smith

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

The Big Picture: The "Too Loud" Microphone Problem

Imagine you are trying to listen to a very quiet whisper (a quantum bit, or qubit) in a noisy room. To hear it clearly, you need a microphone (the readout resonator).

In the world of quantum computers, the faster and more accurately you want to hear that whisper, the louder you have to turn up the microphone's gain. You pump more energy (photons) into the microphone to get a clear signal.

The Problem:
If you turn the microphone up too loud, the sound waves become so intense that they start shaking the person whispering. Suddenly, the whisperer gets startled, jumps up, and starts shouting nonsense. In quantum terms, this is called Measurement-Induced State Transitions (MIST). The act of measuring the qubit accidentally kicks it out of its calm state and into a chaotic, high-energy state. This ruins the calculation.

The Complication:
In the standard type of quantum bit (called a Transmon), this "shaking" happens at very specific settings. But here's the kicker: these settings are like a wobbly table. As tiny electrical charges drift around inside the chip (like dust motes dancing in a sunbeam), the "wobbly table" moves. The point where the qubit gets kicked changes constantly. This makes it a nightmare for engineers trying to build a stable computer because they have to constantly re-calibrate to avoid the kick zones.

The Solution: The "Inductive Shunt" (The Shock Absorber)

The researchers at Google Quantum AI decided to fix this by changing the design of the qubit. They added a special component called an Inductive Shunt.

The Analogy:
Think of the standard Transmon qubit as a tightrope walker balancing on a wire. If a gust of wind (the measurement energy) hits them, they wobble, and their balance depends heavily on exactly where their feet are placed (the offset charge). If their feet shift slightly, they fall.

The new design, the Inductively-Shunted Transmon (IST), is like putting that tightrope walker inside a giant, heavy shock absorber or a safety net.

The "shock absorber" is a loop of superconducting wire (an inductor) that shorts out the electrical noise.
Because of this safety net, the tightrope walker no longer cares exactly where their feet are placed. The "wobbly table" is now a solid, unshakeable floor.

What They Did in the Lab

Built Two Types of Qubits: They built two groups of these new "shock-absorber" qubits. One group was tuned to be slightly "heavier" (lower frequency) than the microphone, and the other "lighter" (higher frequency). This was to test if the new design worked in different scenarios.
The "Kick" Test: They turned up the volume on the microphone (pumped in photons) and watched what happened.
- Standard Qubits: The "kick" zones were all over the place, shifting as time went on.
- New IST Qubits: The "kick" zones were rock-solid. They stayed in the exact same spot for 24 hours straight, regardless of the drifting electrical charges.
The Simulation Challenge: They tried to use a standard computer model to predict these kicks.
- The Old Model: Imagine trying to predict how a trampoline bounces by treating the trampoline as a solid, rigid board. It works okay for a light bounce, but fails when the trampoline stretches.
- The New Model: They realized that because the new qubit is so "stretchy" (due to the inductive shunt), they had to treat the microphone's energy as actual particles (photons) rather than just a smooth wave. They created a new, more complex math model that accounts for these particles. This model finally matched their real-world data perfectly.

Why This Matters

This paper is a major step forward for building a useful quantum computer.

Stability: By eliminating the "wobbly table," the new qubits make the measurement process much more reliable. You don't have to constantly re-tune the machine to avoid errors.
Speed: Because the system is stable, engineers can push the measurement speed higher without fear of accidentally breaking the qubit.
The Future: This proves that adding an inductive shunt is a winning strategy. It combines the best of two worlds: the easy-to-build nature of standard qubits and the stability of more exotic, hard-to-build qubits.

In a nutshell: The researchers built a new type of quantum bit that acts like a heavy-duty shock absorber. This stops the measurement process from accidentally knocking the bit out of place, and it stays stable even when the environment gets messy. This makes the path to a working quantum computer much smoother.

1. Problem Statement

In superconducting quantum computing, fast and high-fidelity qubit measurement is critical for Quantum Error Correction (QEC). Measurement is typically performed via dispersive coupling to a readout resonator. To achieve speed, the resonator must be populated with a large number of photons. However, high photon numbers induce Measurement-Induced State Transitions (MIST), where the qubit is excited out of its computational subspace (e.g., $|0\rangle$ or $|1\rangle$ ) into higher energy states.

The Specific Challenge with Transmons: In standard transmon qubits, the specific locations in readout parameter space (frequency vs. photon number) where MIST occurs are highly sensitive to offset charge. This sensitivity causes MIST features to drift over time, degrading QEC performance.
Current Mitigation Strategies: Existing solutions involve using very large qubit-resonator detunings (which limits speed) or stabilizing offset charge (which is difficult).
The Gap: While MIST is well-understood in transmons, it has not been fully characterized or modeled for Inductively-Shunted Transmons (ISTs), a qubit architecture designed to eliminate offset charge dependence.

2. Methodology

The authors investigated MIST in IST qubits, which sit between transmons and fluxoniums in terms of design. They utilized a device with two groups of six flux-tunable qubits: one group operating above the resonator frequency ( $\omega_q > \omega_r$ ) and one below ( $\omega_q < \omega_r$ ).

Experimental Approach:

Device Fabrication: The ISTs feature a shunt inductance formed by a linear array of 9 Josephson junctions, eliminating offset charge dependence. The qubits and resonators are fabricated on separate chips and bump-bonded.
Measurement Protocol:
1. Prepare the qubit in $|0\rangle$ or $|1\rangle$ .
2. Flux-bias the qubit to a target frequency.
3. Drive the readout resonator with a microwave tone to populate it with a steady-state number of photons ( $\bar{n}$ ).
4. Turn off the drive and allow the resonator to decay.
5. Measure the final qubit population to determine leakage probability (MIST).
Stability Test: Leakage was measured continuously over 24 hours to observe temporal drift.

Modeling Approach:

Full Quantum Simulation: Used the Jaynes-Tavis-Cummings (JTC) model with the full circuit Hamiltonian. This is computationally expensive but serves as the ground truth.
Effective Kerr Model: Derived an analytical model (Eq. 2) to predict frequencies and anharmonicity efficiently for device calibration.
Modified Semiclassical Model: Standard semiclassical approximations (treating the resonator as a classical drive) fail for ISTs because IST energy levels are unbounded, leading to strong coupling between all levels. The authors introduced a renormalized semiclassical model that adjusts coupling matrix elements to account for the finite photon number and the specific energy structure of the IST.

3. Key Contributions

Experimental Characterization of IST MIST: Provided the first comprehensive experimental data on MIST in inductively-shunted transmons across a broad flux range, covering both $\omega_q > \omega_r$ and $\omega_q < \omega_r$ regimes.
Demonstration of Stability: Showed that MIST features in ISTs are stable over time, confirming that the inductive shunt successfully eliminates offset charge dependence.
Novel Modeling Framework:
- Developed an effective Kerr Hamiltonian for ISTs to simplify parameter extraction.
- Proved that standard semiclassical models fail for ISTs and introduced a renormalized semiclassical model that accurately captures the physics without the computational cost of full quantum simulations.
Comparative Analysis: Directly compared IST stability against standard transmons (Willow processor), highlighting the superior stability of the IST architecture.

4. Key Results

Spectral Agreement: The measured spectra of the ISTs matched the full quantum simulation and the effective Kerr model across most of the flux tuning range.
MIST Behavior:
- The onset of MIST (leakage probability) was observed at specific photon numbers and frequencies.
- Quantum vs. Semiclassical: The full quantum simulation matched experimental data well. The unmodified semiclassical model failed to predict IST MIST accurately due to incorrect coupling assumptions. However, the renormalized semiclassical model successfully reproduced the essential features and onset of MIST, offering a much faster tool for design and calibration.
Stability Confirmation:
- Transmon: Showed significant variability in MIST leakage curves over 24 hours due to offset charge drift.
- IST: Showed negligible drift; the leakage curves remained stable, confirming the theoretical advantage of the inductive shunt.
Coherence: The devices achieved $T_1$ times up to $\sim 100$ $\mu$ s, though some qubits were limited by strongly coupled resonant defects.

5. Significance and Implications

QEC Viability: The stability of MIST in ISTs is a crucial step toward robust Quantum Error Correction. It removes the need for complex charge stabilization or large detunings, allowing for faster, more reliable readout.
Design Tooling: The renormalized semiclassical model provides a computationally efficient method for designing readout circuits for ISTs and similar qubits (like fluxonium), reducing the need for time-consuming full quantum simulations during the calibration phase.
Architecture Evolution: The results validate the IST as a promising platform for superconducting quantum processors, offering the large capacitance and integration ease of transmons combined with the charge-noise insensitivity of fluxoniums.

In conclusion, this work establishes that inductively-shunted transmons offer a stable alternative to standard transmons for high-fidelity measurement, solving a critical drift problem in QEC while providing new theoretical tools to model their complex dynamics.