Coherence Time

Coherence time is the clock that every quantum computation races against. Quantum information is fragile; the environment constantly tries to destroy it through decoherence. Coherence time quantifies how long a qubit can hold useful quantum state before the noise wins. Every gate you apply must finish before the coherence expires.

Longer coherence times mean deeper circuits, which means more complex algorithms. This is why coherence time is one of the most closely watched figures of merit across all qubit platforms.

The details

Two distinct timescales characterize qubit coherence:

$T_1$ (relaxation time, or longitudinal coherence time): The time it takes for a qubit in the excited state $|1\rangle$ to spontaneously decay back to the ground state $|0\rangle$. This is energy dissipation. A qubit initialized to $|1\rangle$ will, on average, return to $|0\rangle$ after time $T_1$. Physically, this corresponds to emitting a photon or phonon to the environment.

$T_2$ (dephasing time, or transverse coherence time): The time over which the relative phase between the $|0\rangle$ and $|1\rangle$ components of a superposition remains stable. Dephasing does not flip the qubit; it randomizes the phase angle $\phi$ in $|\psi\rangle = \alpha|0\rangle + e^{i\phi}\beta|1\rangle$. Once that phase is randomized, quantum interference is destroyed and the computation fails.

The bound $T_2 \leq 2T_1$ always holds. In practice, $T_2$ is often much shorter than $2T_1$ because many environmental perturbations (charge noise, magnetic field fluctuations) cause dephasing without causing energy relaxation.

An extended dephasing time is also characterized by $T_2^*$, which accounts for inhomogeneous broadening across an ensemble of qubits. Spin-echo techniques can recover part of the dephasing, giving the longer $T_2$ value.

Gate budget: The maximum useful circuit depth is roughly:

$\text{gate budget} \approx \frac{T_2}{t_{\text{gate}}}$

For superconducting qubits with $T_2 \approx 100\,\mu\text{s}$ and gate times $t_{\text{gate}} \approx 50\,\text{ns}$:

$\text{gate budget} \approx \frac{100\,\mu\text{s}}{50\,\text{ns}} = 2{,}000 \text{ gates}$

Platform comparison (approximate, as of 2025):

Platform	$T_1$	$T_2$	Gate time	Gate budget
Superconducting	100-500 us	10-500 us	10-100 ns	~2,000-5,000
Trapped ion	10-1,000 s	0.1-1,000 s	1-100 us	~100,000+
Spin qubit	10 ms - 1 s	1 ms - 1 s	0.1-10 us	~10,000+

Why it matters for learners

Coherence time directly limits which algorithms are executable on current hardware. The circuits needed for fault-tolerant algorithms like Shor’s algorithm require millions of gates, far beyond the gate budget of any current system without quantum error correction.

This explains the appeal of trapped ions: their coherence times measured in seconds give them a massive gate budget advantage, even though their gates are much slower. Superconducting qubits trade coherence for speed and scalability.

When comparing hardware platforms, always look at gate budget (coherence time divided by gate time), not raw qubit count.

Common misconceptions

Misconception 1: $T_1$ and $T_2$ are the same thing. They measure different physical processes. $T_1$ is energy relaxation (the qubit falls from $|1\rangle$ to $|0\rangle$). $T_2$ is phase randomization (the superposition loses its interference structure). A qubit can have long $T_1$ but short $T_2$ if its phase is disturbed by low-energy noise that does not flip the state.

Misconception 2: Longer coherence time means better qubit quality overall. Coherence time is one figure of merit, not the whole picture. Gate fidelity, connectivity, readout fidelity, and gate speed all matter. A qubit with excellent $T_2$ but poor gate fidelity may still produce worse results than a qubit with shorter $T_2$ and high-fidelity gates.

Misconception 3: Coherence times cannot be extended. Dynamical decoupling applies carefully timed pulse sequences that periodically refocus dephasing errors, effectively extending $T_2$. Cryogenic environments, electromagnetic shielding, and material improvements all contribute to pushing $T_1$ higher. These are active research areas across all platforms.

See also

• Decoherence
• Superconducting Qubit
• Trapped Ion
• Quantum Error Correction
• NISQ