Case Study: Diagnosing a Qubit That Went Bad Overnight

Executive Summary

Qubit 14 worked yesterday. This morning its two-qubit gates with qubit 15 fail at $4.2\times10^{-2}$ — six times worse than the day before — while every other pair on the device is unchanged.

Superconducting processors are physical instruments that drift, and diagnosing a degraded qubit is routine operational work. This case study runs the standard diagnostic sequence in order of cost, identifies the culprit, and along the way surveys the failure modes a superconducting qubit actually exhibits — which are more varied and more mundane than the theory suggests.

Skills applied

• Interpreting $T_1$, $T_2$, and $T_2^*$ measurements (§26.6).
• Distinguishing coherence loss from calibration drift from crosstalk.
• Recognizing two-level-system (TLS) defects (§26.11).
• Choosing between recalibration, remapping, and reporting.

Phase 1: Narrow the fault

First question: is it qubit 14, qubit 15, or the interaction?

Both qubits are individually fine, and each performs normally with a different partner. The fault is specific to the Q14–Q15 interaction.

That eliminates most single-qubit failure modes immediately and is worth doing first because single-qubit RB is fast and cheap.

Phase 2: Coherence

Even so, check coherence — a marginal $T_1$ can show up disproportionately in the slower two-qubit gate.

Q14's $T_1$ fell by 66%. Single-qubit RB missed it because a 35 ns gate is short compared even to 38 μs; the 400 ns two-qubit gate is affected ten times more.

Diagnostic lesson. Single-qubit RB is nearly blind to moderate $T_1$ degradation. Always measure coherence directly rather than inferring it from gate fidelity.

Phase 3: Why did $T_1$ drop?

Four standard causes, distinguished by their signatures:

1. TLS defect coupling. Two-level systems — atomic-scale defects in the junction oxide or substrate — drift in frequency. When one crosses the qubit's frequency, it opens a fast decay channel. Signature: $T_1$ varies sharply with qubit frequency, and the pattern changes over hours to days.

2. Quasiparticle poisoning. Broken Cooper pairs, often from stray infrared radiation or cosmic rays. Signature: $T_1$ drops across many qubits simultaneously, often recovering over minutes.

3. Package or radiation issue. Signature: broad, persistent, affects many qubits.

4. Flux drift (for tunable qubits). Signature: frequency shifted from its calibrated value.

Q15 and the rest of the device are unaffected, which rules out causes 2 and 3. So: a $T_1$-versus-frequency spectroscopy scan on Q14.

Frequency (GHz)   T1 (μs)
4.960             104
4.970              98
4.980              41
4.985              22   ← dip
4.990              37
5.000              95
5.010             101

A sharp $T_1$ dip at 4.985 GHz, and Q14's operating frequency is 4.984 GHz. A TLS defect has drifted onto the qubit.

Phase 4: The fix

Three options, in increasing order of disruption:

1. Retune Q14's frequency. If Q14 is flux-tunable, move it 20–30 MHz away from the defect. Constraints: it must not collide with a neighbour's frequency (crowding), and the two-qubit gate scheme may require a specific detuning from Q15.

Moving Q14 to 5.005 GHz restores $T_1$ to 101 μs. Checking for collisions: nearest neighbour frequencies are 4.930 and 5.070 GHz, so 5.005 is clear. Recalibrate the Q14–Q15 gate at the new frequency — result: $7.0\times10^{-3}$, back to normal.

2. Remap the circuit to avoid Q14 entirely. Always available, costs connectivity and possibly routing overhead.

3. Wait. TLS defects drift on their own; the qubit may recover in hours or days. Not a strategy for a production device, but a real explanation for why a qubit that failed on Tuesday works on Thursday.

Phase 5: What this teaches about the platform

TLS defects are not an occasional nuisance; they are a defining constraint of superconducting qubits.

• They arise from amorphous oxide in and around the Josephson junction — a byproduct of how the junctions are made.
• Their density means every device has qubits sitting near defects, and a device's usable qubit count fluctuates day to day.
• They are the main reason published error rates carry timestamps, and why any experiment spanning days must record calibration data (Chapter 8).
• Materials research — better substrates, cleaner interfaces, tantalum instead of niobium films — targets TLS density directly, and is responsible for much of the coherence improvement of the past several years.

Operationally, this is why: - Backends publish per-qubit properties updated at least daily. - Qubit selection matters as much as it does (Chapter 8's 7-point fidelity gain). - Reproducibility requires recording the calibration snapshot, not just the backend name.

Discussion Questions

1. Single-qubit RB was normal while $T_1$ had fallen 66%. Explain quantitatively, and say what that implies about relying on RB alone.
2. TLS defects drift on hour-to-day timescales. What does that imply for benchmark claims measured on a single day?
3. Retuning Q14 required checking for frequency collisions. How does this constraint scale with qubit count?
4. Materials work targets TLS density. Why is that a more fundamental lever than better control electronics?

Your Turn: Extensions

• Pull a real backend's properties over several days and plot per-qubit $T_1$; look for sudden drops.
• Compute the fidelity impact of $T_1 = 38$ μs versus 112 μs on gates of 35 ns and 400 ns; confirm the 10× sensitivity difference.
• Simulate a $T_1$-versus-frequency scan with an injected TLS and locate the dip.
• Estimate how many qubits collide in frequency on a 100-qubit device given 1% fabrication spread.

Key Takeaways

• Localize the fault first — single-qubit, partner-specific, or device-wide — because it eliminates most causes cheaply.
• Single-qubit RB is nearly blind to moderate $T_1$ loss; measure coherence directly.
• A sharp $T_1$ dip at a specific frequency is the signature of a TLS defect; device-wide drops suggest quasiparticles or radiation.
• Retuning away from a defect is the standard fix, constrained by frequency crowding with neighbours.
• TLS defects make usable qubit counts fluctuate day to day, which is why calibration timestamps and qubit selection matter so much in practice.