T1 and T2 Relaxation Times
T1 measures how long a qubit keeps its energy state; T2 measures how long it keeps phase coherence. Both bound useful computation time.
Two coherence metrics
T1 and T2 are the two numbers that summarise how long a qubit stays quantum. T1 is the energy relaxation time; T2 is the dephasing time. Together they set the window in which gates must be applied before the state degrades beyond use.
T1: energy relaxation
An excited qubit in |1> tends to drop to the lower-energy |0> by giving energy to its environment, like an atom emitting a photon. The excited-state population decays as exp(-t/T1). T1 is measured by preparing |1>, waiting a variable time, then reading out the survival probability and fitting the exponential.
T2: dephasing
T2 captures loss of phase coherence between |0> and |1>. Even without energy loss, fluctuating fields randomise the relative phase, washing out interference. A Ramsey experiment prepares a superposition, lets it evolve, and watches the fringe contrast decay as exp(-t/T2).
The relationship
The two are linked by 1/T2 = 1/(2 T1) + 1/T_phi, where T_phi is the pure dephasing time. This forces T2 <= 2 T1. Energy relaxation necessarily contributes to dephasing, but extra phase noise usually makes T2 shorter than the 2 T1 ceiling. Echo sequences can partly recover coherence, defining an extended T2-echo.
- T1: excited-state lifetime, exp(-t/T1)
- T2: phase coherence, exp(-t/T2), with T2 <= 2 T1
- T_phi: pure dephasing, 1/T2 = 1/(2T1) + 1/T_phi
Why the ratio to gate time matters
What determines computational depth is not T1 or T2 alone but their ratio to the gate time. A qubit with a long coherence time but slow gates may execute no more operations than a fast, short-lived one. The figure of merit is roughly T2 divided by gate duration, and pushing it high enough is the precondition for scalable error correction.