⚛️ quantum physics

Localized Thermometry via Dayem Bridges Integrated on Superconducting Qubit Chips

This paper presents a simple, non-invasive, and scalable method for accurate on-chip thermometry in superconducting quantum circuits by integrating Dayem bridges alongside transmon qubits to directly measure local temperature and correlate it with qubit decoherence without requiring complex microwave calibration.

Original authors: Ella O. Lachman, Dave P. Pappas, Jayss Marshall, Josh Y. Mutus

Published 2026-07-09

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CC BY 4.0

Original authors: Ella O. Lachman, Dave P. Pappas, Jayss Marshall, Josh Y. Mutus

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 bake the perfect cake, but your oven's thermostat is broken. You know the kitchen is cold, but you don't know if the inside of the oven is actually at the right temperature. If the oven is too hot or too cold, your cake (in this case, a super-sensitive computer chip) won't work right.

This is the problem scientists at Rigetti Computing faced with superconducting qubits. These are the tiny brains of quantum computers. They need to be incredibly cold (colder than outer space) to function. Usually, scientists check the temperature of the giant refrigerator (the "cryostat") holding the chip. But, just like a house can have cold drafts even if the thermostat says it's warm, the chip itself might be warmer than the fridge thinks.

The Problem: Blindfolded Thermometers

Traditionally, to check the chip's temperature, scientists had to use the qubits themselves as thermometers. This is like trying to check the oven temperature by tasting the cake while it's still baking. It's messy, complicated, and requires special recipes (complex measurement protocols) that slow everything down. Plus, if the cake is burnt for another reason (like a draft), you might think it's just the oven temperature, leading to wrong conclusions.

The Solution: The "Dayem Bridge" Thermometer

The researchers developed a new, simpler tool: a Dayem bridge.

Think of a Dayem bridge as a tiny, super-thin "choke point" made of metal on the chip.

How it works: Imagine a river flowing through a narrow canyon. When it's very cold, the water flows smoothly (superconducting). As it gets warmer, the water gets turbulent and starts to splash (resistive).
The Trick: The scientists found that the exact moment the water starts to splash depends only on the temperature. By measuring how much "push" (current) it takes to make the water splash, they can calculate the exact temperature of the bridge.

Why This is a Big Deal

It's Built-In: They didn't have to build a separate thermometer. They stamped these tiny bridges right next to the qubits during the same manufacturing process. It's like having a built-in thermometer on every single cake pan.
It's Simple: You don't need complex microwave signals or special computer code to read it. You just run a tiny electric current through it and see when it changes state. It's like checking a light switch instead of performing a full medical exam.
It's Honest: The researchers tested this new thermometer against the old "tasting the cake" method (using the qubits). They matched perfectly. This proves the new tool is accurate and can be trusted.

What They Found

The "Sweet Spot": They tuned the material of the bridge (a mix of Titanium and Palladium) so it is most sensitive at the exact temperatures where quantum computers operate (between 10 and 150 millikelvin).
The Connection: They showed that when the bridge gets warmer, the qubits get "confused" and lose their memory (a process called decoherence) faster. This confirms that heat is a major enemy of quantum computers.
No Disturbance: They checked if measuring the bridge's temperature would accidentally heat up the qubits next to it. The answer was no; the bridge is quiet and doesn't disturb its neighbors.

The Catch (Limitations)

The paper notes two small hiccups:

The "Floor" Effect: Below a certain temperature (around 50 millikelvin), the thermometer stops working as well. It's like a thermometer that gets stuck at the bottom of the scale because the electrons inside it get "stuck" and can't cool down fast enough to match the fridge.
Slight Variations: No two bridges are exactly identical, so they sometimes give slightly different readings, but they are close enough to be useful.

The Bottom Line

This paper introduces a simple, cheap, and reliable way to check the temperature of quantum computer chips directly where it matters. Instead of guessing based on the fridge or using the complex computer brain to check itself, scientists can now use these tiny, built-in "choke points" to see exactly how hot the chip is. This helps them build better, faster, and more reliable quantum computers by diagnosing temperature problems quickly and easily.

Technical Summary: Localized Thermometry via Dayem Bridges Integrated on Superconducting Qubit Chips

Problem Statement
Accurate knowledge of on-chip temperature is critical for characterizing superconducting quantum circuits and optimizing high-fidelity operations, particularly for transmon qubits. These devices are sensitive to superconducting quasiparticle generation and operate at low frequencies, making their excited-state populations, quasiparticle densities, and coherence times highly dependent on local temperature. However, standard cryostat thermometry (e.g., RuOx resistive thermometers in the mixing chamber) often fails to reflect the actual local temperature experienced by the qubit chip due to imperfect thermalization, residual infrared radiation, and dissipation from control wiring.

Existing methods to measure local temperature directly face significant limitations:

Qubit-based thermometry: Using the qubit's excited-state population to infer temperature requires complex calibration, specialized control sequences, and assumes temperature is the sole cause of excitations. It is limited by qubit coherence and quasiparticle-induced relaxation, adding substantial operational overhead.
Mesoscopic transport thermometry (e.g., Coulomb Blockade): While accurate, these techniques typically require dedicated device structures and measurement schemes that are not naturally integrated into standard superconducting qubit fabrication workflows.

There is a need for a simple, robust, and integrated thermometry method that is compatible with superconducting qubit platforms and does not require microwave calibration or qubit-specific protocols.

Methodology
The authors demonstrate a complementary on-chip thermometry method using superconducting Dayem bridges (DBs) integrated directly onto the same chip as transmon qubits.

Device Design: The DBs are lithographically defined superconducting weak links (constrictions) that do not require insulating tunnel barriers, distinguishing them from Josephson junctions. They are fabricated using a single electron-beam lithography step and a single superconducting thin-film deposition.
Material Engineering: To achieve sensitivity in the sub-100 mK regime relevant for transmon qubits (10–150 mK), the authors utilized a Palladium/Titanium (Pd/Ti) bilayer. The Pd layer suppresses the critical temperature ( $T_c$ ) of the Ti layer via the inverse proximity effect. A specific composition with a 1/10 thickness ratio yielded a $T_c$ of 166 mK, placing the maximum sensitivity range ( $\approx 0.707 \times T_c$ ) within the desired operating window.
Measurement Protocol: The local temperature is determined by extracting the critical current ( $I_c$ ) of the DB through current-voltage (I-V) measurements. The bridge is embedded in a shunted measurement circuit and read out using a Superconducting Series Array Amplifier (SSAA). The critical current is identified as the switching current where the device transitions from the superconducting to the resistive state.
Calibration: The temperature is derived from the measured $I_c$ using the Bardeen relation: $I_c(T) = I_c(0) [1 - (T/T_c)^2]^{3/2}$ . The parameters $T_c$ and $I_c(0)$ were determined via independent measurements on similar devices in an Adiabatic Demagnetization Refrigeration (ADR) system and by fitting data from devices mounted directly to the mixing chamber.
Experimental Setup: Experiments were conducted on a 16-qubit chip containing fixed-frequency and tunable transmons. Three DB thermometers were fabricated in close proximity to the qubits. Measurements were performed within the same cooldown cycle, correlating DB readings with qubit energy relaxation ( $T_1$ ), dephasing ( $T_2$ Ramsey), and excited-state population.

Key Results

Temperature Correlation: The DB critical current showed a monotonic decrease with increasing temperature, following the Bardeen relation. Above 50 mK, the DB-inferred temperatures agreed well with both the mixing chamber temperature and the effective temperature derived from qubit excited-state populations.
Stability: Continuous measurements over 30 minutes demonstrated remarkable stability in the critical current with minimal deviation, confirming the reliability of the sensor under steady-state conditions.
Coherence Tracking: The study established a correlation between the DB-measured temperature and qubit coherence. As the inferred temperature increased (from 15 mK to 150 mK), the median $T_2$ Ramsey time decreased significantly (from 11.5 $\mu$ s to 1.8 $\mu$ s). This inverse correlation validates the DBs as a proxy for temperature-dependent decoherence mechanisms.
Operational Compatibility: Preliminary cross-validation measurements showed that concurrent thermometry (active DB sweeps) did not introduce immediate, severe thermal or electronic penalties to adjacent qubit coherence. Statistical analysis (Welch's t-test and Mann-Whitney U test) yielded p-values well above 0.05, indicating no significant degradation in $T_2$ Ramsey distributions.
Limitations Observed:
- Saturation below 50 mK: The critical current saturated below approximately 50 mK, indicating the electrons in the weak link were decoupled from the mixing chamber stage. The authors attribute this to insufficient thermalization volume (small thermal pads) and potential measurement-induced heating.
- Device Variability: Nominally identical thermometers showed deviations of $\sim$ 10 mK, likely due to variations in $I_c(0)$ or $T_c$ between devices.

Significance and Claims
The paper establishes integrated Dayem bridges as a practical, scalable, and non-invasive tool for cryogenic hardware development. The authors claim that this method offers several distinct advantages over existing thermometry:

Simplicity and Integration: DBs require minimal fabrication steps (single layer, single lithography) and can be co-fabricated with qubits without disrupting the standard process flow.
Low Overhead: The measurement requires only DC current bias and voltage monitoring, eliminating the need for microwave calibration or complex qubit control sequences.
Diagnostic Utility: By providing an independent, local temperature measurement, DBs allow researchers to decouple physical temperature from other decoherence mechanisms (e.g., quasiparticles, flux noise), aiding in the root-cause analysis of qubit performance degradation.
Scalability: The small footprint and simple design suggest the potential for integrating thermometers next to every qubit to map local thermal gradients across a chip.

The authors conclude that while the current implementation has limitations regarding low-temperature saturation and device-to-device variability, the Dayem bridge thermometer represents a significant step toward routine, on-chip diagnostics for superconducting quantum circuits. Future work will focus on optimizing thermalization geometries and implementing pulsed measurement schemes to mitigate self-heating and enable transient "pump-probe" experiments.