Hardware & Errors
T1 and T2 Times
The two main coherence timescales of a qubit: T1 for losing energy and T2 for losing phase.
Definition
T1 and T2 are the two clocks that tell you how long a qubit stays useful. T1 is the time it takes a qubit in the excited state to fall back to the ground state by losing energy. T2 is the time over which the delicate phase relationship in a superposition survives. Together with the time a gate takes, they set how many operations a quantum computer can perform before noise takes over.
In depth
The two times measure different failures. Energy relaxation flips a 1 into a 0, through interaction with defects, photons, or phonons. Dephasing leaves the populations alone but scrambles the relative phase of the 0 and 1 components, so a superposition turns into a classical mixture. Dephasing is usually faster than relaxation, caused by slowly fluctuating fields that shift the qubit frequency, and that is why T2 is often much shorter than T1.
Typical values vary by platform by many orders of magnitude. Superconducting transmons have T1 of about 100 to 300 microseconds in processors and above a millisecond in the best devices. Trapped-ion hyperfine qubits have coherence times of seconds to many minutes, and neutral atoms reach seconds. Silicon spin qubits have T2 from microseconds to seconds depending on purification and dynamical decoupling, and NV centers reach milliseconds. These numbers must be compared with gate times, which are tens of nanoseconds for superconductors and tens of microseconds for ions.
A useful rule is to divide coherence time by gate time to estimate how many gates fit in one coherence window. A transmon with a 100-microsecond T2 and 50-nanosecond gates gives about 2,000 gates, and an ion with a 1-second T2 and 100-microsecond gates gives about 10,000. Real error rates are also affected by control imperfections, so the actual figure is smaller. Dynamical decoupling, which applies refocusing pulses, can extend T2 toward the limit of 2 T1.
Technical Definition
T1 is the energy relaxation time, the exponential decay constant of the excited-state population. T2 is the dephasing time, the decay constant of the off-diagonal coherence of the density matrix. They are related by one over T2 equals one over twice T1 plus one over T phi, where T phi is the pure dephasing time, so T2 is at most 2 times T1. T2 star is the free-induction decay time, and T2 echo, measured with a refocusing pulse, is longer.
Visual Explanation: An Analogy
Think of a spinning top. T1 is how long until it falls over and lies flat, losing its energy. T2 is how long until it wobbles so that you can no longer tell which way it was pointing. A top can wobble out of sync long before it falls.
Key facts
| Item | Detail |
|---|---|
| T1 | Energy relaxation: the time for an excited qubit to decay to the ground state |
| T2 | Dephasing: the time for superposition phase coherence to decay; at most 2 times T1 |
| Superconducting qubits | T1 about 100 to 300 microseconds in processors, above 1 ms in lab devices |
| Trapped ions | Coherence from seconds to minutes in hyperfine states |
| Gate budget | Roughly T2 divided by gate time gives the number of gates that fit |
Where the idea comes from
The terms come from nuclear magnetic resonance, where Felix Bloch introduced the longitudinal and transverse relaxation times in 1946. Quantum computing adopted them as the standard characterization of a qubit, and measuring T1 and T2 is the first calibration experiment on any new device.
Real-World Use Cases
- Characterizing and comparing qubit technologies and fabrication improvements.
- Estimating how deep a circuit can be before errors dominate.
- Choosing which qubits on a chip to use based on current calibrations.
- Designing dynamical decoupling and error mitigation strategies.
How it differs from related ideas
- T1 describes loss of energy and flips, while T2 describes loss of phase, which is the more fragile property.
- T2 star measures free decay with slow noise included, and T2 echo removes slow noise with a refocusing pulse.
- A long T1 does not guarantee a long T2.
Common Misconceptions
- A long coherence time does not mean a good quantum computer. Gate speed, fidelity, and connectivity also matter.
- T2 can never exceed 2 T1. If a measurement suggests otherwise, it is an error or a different quantity.
- Coherence times can fluctuate over hours, so single numbers are snapshots.
Frequently asked questions
What is the difference between T1 and T2?
T1 is how long a qubit holds its energy state, and T2 is how long it keeps the phase of a superposition. T2 is at most twice T1.
What are good T1 and T2 values?
It depends on the platform. For superconducting qubits, a few hundred microseconds is good, and for ions, seconds or more.
How are they measured?
T1 by exciting the qubit and measuring decay over time, and T2 by Ramsey or echo experiments that track phase decay.
Related Terms
Keep exploring
- Algorithm: Quantum Error Mitigation Techniques
- Hardware: IBM Heron (r1, r2, and r3)
- Hardware: Quantinuum H2