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T1 and T2 Coherence Times

T1 (energy relaxation time) and T2 (phase coherence time) are the two time constants that set how long a qubit survives: T1 measures how fast |1⟩ decays back to |0⟩, T2 how long a superposition keeps its phase.

What it means

A real qubit is an open quantum system: it constantly interacts with uncontrolled degrees of freedom in its environment, and the Bloch-Redfield model characterizes the resulting decoherence with two time constants.T1, the longitudinal relaxation time, sets how fast an excited qubit loses energy from |1⟩ back to |0⟩.It is measured by applying an Xπ pulse and sweeping the waiting time τ; the excited-state population traces an exponential decay.T2, the transverse relaxation time, sets how long the phase relationship inside a superposition survives, and is measured with Ramsey interferometry — the energy can remain while the phase information leaks away.During a gate, the coherence-limited error is, to first order, proportional to exposure time: ε_coh ∼ T_gate/T_coh.On deployed transmons T1 is typically in the 100–300 µs range, with 2025 lab records approaching 1 ms — even 100 µs is roughly 2,500 times a 40 ns gate, which sounds generous until a circuit chains thousands of gates.Crucially, T1 and T2 are living quantities: they differ between qubits on the same chip and drift from day to day, which is why devices must be recalibrated continuously.

Everyday analogy

T1 is a balloon slowly deflating: you inflate the qubit up to |1⟩, and over time it goes pfff — the energy leaks back down to |0⟩. T2 is a choir of children clapping 'one, two!' in perfect sync who gradually drift out of rhythm: the sound (the energy) is still all there, but the togetherness (the phase) is gone. The slower your gate, the more the balloon deflates and the more the choir scatters.
The etymology tells the physics: 'relaxation' comes from Latin re- + laxare, 'to loosen' — a sibling of 'release' and 'lax' — which is exactly what T1 does, letting a taut, excited state slacken back to the ground. 'Phase' comes from Greek phasis, 'appearance', originally the phases of the Moon: T2 dephasing is waves losing track of where in their cycle they appear.

Common misconceptions

  • T1 and T2 are NOT fixed constants of a device — qubits on the same chip can differ by factors of several, and even a single qubit's values drift from day to day. Yesterday's optimal pulse may not be optimal today.
  • The simple error formula ε ≈ T_gate/T_coh is NOT always valid — it lies in the leakage-limited (short-gate) regime, because it contains no leakage term at all and badly underestimates the true error of aggressively shortened gates.

Key takeaways

  • T1 (longitudinal relaxation) is the |1⟩→|0⟩ energy decay time, measured by applying an Xπ pulse and sweeping a waiting time τ to trace an exponential decay — a measured example in the Krantz guide is T1 = 85 µs.
  • T2 (transverse relaxation) is the lifetime of phase coherence in a superposition, measured with Ramsey interferometry — the energy can survive while the phase is lost.
  • Modern transmons reach T1 ≈ 100 µs, about 2,500× a 40 ns gate — generous-sounding, but a circuit with thousands of gates burns through it fast.
  • Coherence error grows with exposure time: ε_coh ∼ T_gate/T_coh, valid only in the coherence-limited (slow-gate) regime.

Check your understanding

In the six-year-old version: which pair of one-word analogies matches T1 and T2?

  1. A.T1 = choir, T2 = balloon
  2. B.T1 = balloon, T2 = choir
  3. C.T1 = ladder, T2 = balloon
  4. D.T1 = swing, T2 = ladder
Show the answer

Answer: B. T1 = balloon, T2 = choir

Why: T1 is the deflating balloon: energy pumped into |1⟩ leaks back to |0⟩. T2 is the choir drifting out of rhythm: the energy remains, but the shared phase — the 'togetherness' — is lost.

When does the simple estimate ε ≈ T_gate/T_coh seriously mislead you?

  1. A.When the gate is very slow (coherence-limited regime)
  2. B.When the gate is very fast (leakage-limited regime)
  3. C.Whenever T1 is longer than T2
  4. D.Never — it is always exact
Show the answer

Answer: B. When the gate is very fast (leakage-limited regime)

Why: The formula contains no leakage term, so in the short-gate, leakage-limited regime it badly underestimates the true error. It is a reasonable first-order estimate only in the slow-gate, coherence-limited regime.

Builds on

QubitDecoherence

Primary source: Krantz et al., A Quantum Engineer's Guide to Superconducting Qubits, Appl. Phys. Rev. 6, 021318 (2019), doi:10.1063/1.5089550

T1/T2 definitions and measurement protocols (Xpi + tau sweep, Ramsey) per Krantz SIII. Typical T1 values are explicitly phrased as approximate/era-dependent in the text; drift caveat sourced to arXiv:2606.03815 (verified 2026-07-03). Numbers refreshed 2026-07-10: deployed-transmon T1 typically 100-300 us; ~1 ms lab record per Aalto Univ., Nat. Commun. (2025).

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