⚛️ quantum physics

Offset Charge Dependence of Measurement-Induced Transitions in Transmons

This paper experimentally confirms that the photon number triggering measurement-induced transitions in transmons depends on gate charge, a phenomenon that persists even in the deep transmon regime and requires higher-order harmonics in the Hamiltonian for accurate theoretical modeling.

Original authors: Mathieu Féchant, Marie Frédérique Dumas, Denis Bénâtre, Nicolas Gosling, Philipp Lenhard, Martin Spiecker, Simon Geisert, Sören Ihssen, Wolfgang Wernsdorfer, Benjamin D'Anjou, Alexandre Blais, Ioan M.

Published 2026-01-15

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Mathieu Féchant, Marie Frédérique Dumas, Denis Bénâtre, Nicolas Gosling, Philipp Lenhard, Martin Spiecker, Simon Geisert, Sören Ihssen, Wolfgang Wernsdorfer, Benjamin D'Anjou, Alexandre Blais, Ioan M. Pop

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: Reading a Quantum Mind Without Waking It Up

Imagine you have a very delicate, sleeping cat (the qubit) that you need to check on. You want to know if it's sleeping (state 0) or awake (state 1) without making a sound that wakes it up. This is the goal of quantum readout in superconducting computers.

To check the cat, you shine a flashlight (microwaves) into the room where the cat is. The brighter the light, the clearer the picture you get. However, there's a catch: if the light gets too bright, the cat gets startled and jumps out of bed (a measurement-induced transition). In the quantum world, this "jumping out of bed" is called ionization, where the qubit gets knocked into a high-energy state it wasn't supposed to be in, ruining your measurement.

The scientists in this paper discovered a hidden "switch" that controls exactly how bright the flashlight can get before the cat jumps. This switch is called the gate charge.

The Problem: The "Goldilocks" Dilemma

For years, scientists knew that if you shine too much light on a superconducting qubit (specifically a transmon), it would get excited and jump to higher energy levels. This is bad because it destroys the information you are trying to read.

They knew this happened at specific "critical" levels of light (photon numbers). But they didn't know that this critical level wasn't fixed. It was like a speed limit sign that kept changing depending on where you were standing.

The Discovery: The "Tuning Knob"

The researchers found that the qubit has a hidden control knob called gate charge (think of it as a tiny electrical offset).

The Old Belief: Scientists thought that once a transmon was built, its behavior was mostly fixed and didn't care much about this tiny electrical offset, especially when it was in its "sleeping" state.
The New Finding: The paper proves that while the "sleeping" state is stable, the high-energy states (the ones the qubit jumps into when startled) are extremely sensitive to this gate charge.

The Analogy: Imagine a trampoline.

If you are just standing gently in the middle (the normal state), it doesn't matter if the trampoline is slightly tilted; you stay put.
But if you start bouncing high (the high-energy state), that tiny tilt changes exactly how high you can jump before you fly off the edge.
The researchers found that by adjusting the "tilt" (the gate charge), they could change the exact height at which the jumper flies off.

What They Did: The Experiment

The team built two different "trampolines" (transmon devices) with different stiffness levels. They set up a system where they could:

Shine the light: Pump photons into the resonator (the room).
Adjust the tilt: Actively and precisely change the gate charge of the qubit in real-time.
Watch the jump: See exactly when the qubit got knocked out of its state.

They found that by turning the gate charge knob, they could move the "danger zone" (where the qubit jumps) to a higher or lower number of photons.

Bad Spot: At some charge settings, the qubit jumps even with a dim flashlight.
Good Spot: At other charge settings, the qubit can handle a very bright flashlight without jumping.

The Secret Ingredient: The "Hidden Harmonics"

Here is the most technical part made simple. To predict exactly where the "jump" would happen, the scientists had to use a very complex mathematical model.

Usually, scientists model these qubits like a simple swing that goes back and forth. But this paper shows that for high-energy jumps, the swing is actually more like a complex, wobbly swing set with extra springs and weird curves.

The researchers had to include higher-order harmonics (these are the extra wobbles and curves in the math) to get the prediction right.
Without these extra details, their math was like a map that was missing the hills and valleys; it couldn't predict where the jumper would fly off.
With the extra details, their map was perfect. They could predict exactly how much light the qubit could handle based on the gate charge.

The Result: A Path to Better Computers

The main takeaway is that active calibration works.
Instead of just building a qubit and hoping for the best, the researchers showed that you can actively tune the gate charge to find a "safe zone." In this safe zone, you can use a much brighter flashlight (more photons) to read the qubit without waking it up.

This is a big deal because reading qubits faster and more accurately is one of the biggest hurdles in building a large-scale, fault-tolerant quantum computer. By finding these "safe zones" and understanding the hidden "wobbles" (harmonics) in the system, they have provided a recipe for making quantum computers more reliable.

Summary in One Sentence

This paper proves that by carefully adjusting a tiny electrical setting (gate charge) and accounting for complex mathematical details (higher-order harmonics), we can prevent superconducting qubits from getting startled by bright lights, allowing us to read them more clearly and reliably.

Technical Summary: Offset Charge Dependence of Measurement-Induced Transitions in Transmons

Problem Statement
Achieving scalable fault tolerance in superconducting quantum processors is currently hindered by readout fidelity, which lags behind single- and two-qubit gate fidelities. A primary limitation in improving readout is the occurrence of measurement-induced transitions (MIST), also termed qubit ionization. These transitions are caused by multiphoton qubit-resonator excitations that occur at specific intraresonator photon numbers. While increasing the number of probing photons is theoretically expected to improve the signal-to-noise ratio (SNR) while preserving quantum non-demolition (QND) properties, experimental observations show that high photon numbers induce unwanted transitions to highly excited states, negating the benefits of strong readout drives.

Theoretical frameworks predict that because MIST involves highly excited states of the transmon, the critical photon numbers at which these transitions occur should depend on the gate charge ( $n_g$ ). This stands in contrast to the transmon's computational $0$-$1$ transition frequency, where gate-charge dependence is exponentially suppressed in the transmon regime. Furthermore, because these transitions involve high-energy states, the higher-order harmonics of the transmon Hamiltonian are expected to influence the ionization process. However, previous experimental evidence for this charge dependence was indirect, relying on shot-to-shot variations attributed to uncontrolled charge fluctuations.

Methodology
The authors experimentally characterize measurement-induced transitions by actively calibrating the transmon's gate charge while varying the resonator photon population. The study utilizes two distinct transmon devices (Device A and Device B) with different ratios of Josephson energy to charging energy ( $E_J/E_C$ ):

Device A: $E_J/E_C \approx 18.5$ (shallow transmon regime), with a readout resonator frequency of 6.12 GHz.
Device B: $E_J/E_C \approx 40.2$ (deeper transmon regime), with a readout resonator frequency of 7.05 GHz.

The experimental setup involves a flux-tunable transmon capacitively coupled to a readout resonator measured in reflection via a Josephson amplifier. A key methodological advancement is the active calibration of the gate charge offset ( $n_g$ ). For Device A, this is achieved by measuring Ramsey fringes of the $0$-$1$ transition as a function of offset voltage. For Device B, where charge dispersion is too small for Ramsey interferometry, the authors monitor the charge offset imprinted on the resonator's dispersive shift for the $|2\rangle$ state.

The authors map the probability of finding the transmon in an excited state ( $1-P(0)$ ) as a function of external flux ( $\phi_{ext}$ ) and gate charge ( $n_g$ ) for varying photon numbers. To understand the dynamics at high photon numbers, they employ a semiclassical model where the resonator field acts as an effective classical drive on the transmon. The transmon Hamiltonian includes higher-order harmonics ( $m \geq 1$ ) in the Josephson potential. Theoretical predictions are generated using Floquet quasienergy spectrum analysis to identify avoided crossings (multiphoton resonances) and time-domain simulations solving the Schrödinger equation with the driven Hamiltonian.

Key Contributions and Results

Direct Confirmation of Charge Dependence: The study provides direct experimental confirmation that the critical photon numbers for measurement-induced transitions are gate-charge dependent. By actively calibrating $n_g$ , the authors observe distinct features in the transition probability that shift with the gate charge, validating theoretical predictions [20, 22]. This dependence persists even deep in the transmon regime (Device B), where the computational states are nominally charge-insensitive.
Necessity of Higher-Order Harmonics: The authors demonstrate that achieving quantitative agreement between theory and experiment requires accounting for higher-order harmonics in the transmon Hamiltonian. Simulations using a conventional single-harmonic transmon model fail to reproduce the experimental features, particularly the positions of the resonances. In contrast, models including harmonics up to $m=3$ show remarkable agreement with the data without adjustable parameters.
Identification of Robust Readout Regions: The active calibration allows the identification of specific gate charge values where QND behavior persists up to significantly higher photon numbers. This suggests that optimizing the gate charge can mitigate measurement-induced transitions.
Dynamics of Transients: The results highlight that the ring-up and ring-down transients of the resonator population influence the transition probability. The non-monotonic behavior of QNDness with increasing photon number is attributed to Landau-Zener transitions occurring as the system sweeps through multiphoton resonances. The probability of transition depends on the crossing rate and the size of the associated energy gap.
Spurious Mode Scattering: The authors identify leakage features in Device B that do not match direct multiphoton transitions, attributing them to inelastic scattering via a spurious mode at $\omega_s \approx 0.78$ GHz.

Significance
The paper claims that these findings are significant for several reasons:

Calibration Strategy: Active charge calibration can be used to identify "robust regions" for readout, avoiding gate charge values most susceptible to unwanted multiphoton transitions. This offers a pathway to higher fidelity QND readout.
Modeling Accuracy: The work underscores that accurate modeling of the transmon's high-energy sector, including higher-order harmonics, is essential for predicting the onset of measurement-induced state transitions. This is crucial for the design and optimization of future qubits.
Broader Applicability: The insights regarding charge dependence and higher-order harmonics are applicable to other nonlinear driven superconducting circuits, including parametric gates, couplers, qubit reset protocols, and quantum state stabilization schemes.

The authors conclude that while the computational subspace is protected from charge noise, the high-energy states involved in ionization are not, making gate charge a critical parameter for optimizing readout fidelity in superconducting quantum processors.