Decoherence, T1 and T2: how long a qubit holds its state

Short answer: T1 is the relaxation time, the time scale on which a qubit in its excited state decays to the ground state. T2 is the dephasing (coherence) time, the time after which the qubit's phase information is lost. A 2019 benchmarking study of superconducting transmon qubits found both fluctuate over days, which is why those devices need frequent recalibration. These are measurements from one lab study and do not describe a product.

What T1 and T2 mean

A Quantum Computing Stack Exchange answer gives the standard definitions. T1 is the relaxation time, the time for a qubit to go from the excited state to the ground state. Relaxation is a specific case of decoherence. T2 is the dephasing time. It describes how long it takes for the phase information of a qubit to be lost in its preferred basis, which is typically the computational basis. If a qubit starts in a superposition with some relative phase, T2 is roughly the time after which the state no longer depends on that phase.

The two lose different things. Dephasing destroys the phase relationship that quantum interference depends on. Relaxation changes the energy of the qubit. The same answer notes that when T1 is much larger than T2, the populations of the two states are approximately unaffected over the dephasing time, and the qubit converges towards a mixed state. That is a plain-language reading of the answer's more formal description, which is a community answer rather than a peer-reviewed source.

How stable are they in practice?

A 2019 paper in npj Quantum Information benchmarked the decoherence of superconducting transmon qubits to examine how stable energy relaxation, dephasing and qubit frequency are over time. By collecting statistics across measurements spanning multiple days, the authors found mean values of T1 = 49 microseconds and T2* = 95 microseconds. Both quantities fluctuate, which the authors say explains the need for frequent recalibration in qubit setups.

Those numbers belong to the qubits in that study. Other devices and other years will differ, so they should not be read as typical figures for the field.

What causes the fluctuations?

The authors' main finding is that fluctuations in qubit relaxation are local to the qubit and are caused by instabilities of near-resonant two-level systems (TLS). Through statistical analysis they determined sub-millihertz switching rates for these systems and observed coherent coupling between an individual TLS and a transmon qubit. They also report evidence that the qubit's frequency stability limits pure dephasing to 0.8 milliseconds, which they also observe.

Why it matters

The authors conclude that their findings raise the need for qubit metrology that examines the reproducibility of qubit parameters, because these fluctuations could affect qubit gate fidelity. In other words, a single best-case coherence time does not tell you how a device behaves from day to day.

What this does not tell you

This article summarises one study and one community explanation. It does not describe any commercial machine, and we have not verified the measurements.

FAQ

What is T1?

The relaxation time: how long it takes a qubit to go from the excited state to the ground state. It is a specific case of decoherence.

What is T2?

The dephasing time: how long it takes for a qubit's phase information to be lost in its preferred basis, usually the computational basis.

Are T1 and T2 fixed numbers for a qubit?

No. A 2019 study of transmon qubits found both fluctuate over time, explaining the need for frequent recalibration.

What did that study measure?

Mean values of T1 = 49 microseconds and T2* = 95 microseconds across measurements spanning multiple days, for the qubits studied.

What causes T1 to fluctuate?

According to the study, instabilities of near-resonant two-level systems, with sub-millihertz switching rates.