Qubit coherence and gate fidelity calculator
Estimate decoherence-limited single-qubit gate fidelity from T1, T2 and gate time.
Average gate fidelity: 0.9999
| Coherence T2 (microseconds) | 100 |
|---|---|
| Pure dephasing Tphi (microseconds) | 200 |
| Pure dephasing rate (1/s) | 5000 |
| Average gate fidelity | 0.9999 |
| Error per gate | 9.999e-5 |
| Depth budget (independent-error proxy) | 100 |
For T1 = T2 = 100 microseconds and a 20 ns gate, the Markovian amplitude/phase damping model gives an average fidelity of about 99.9900%. Enter T1 and T2 (or Tphi) to calculate pure dephasing, error per gate and an illustrative depth budget.
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Batch runs over a table of inputs, a PDF report with inputs, method and citations, CSV export and saved cases. Join the waiting list and we will write once, when it opens.
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https://scienceshot.com/mcpConnector tool: qubit_coherence
Example: For T1 = T2 = 100 microseconds and a 20 ns gate, what is the decoherence-limited average fidelity?
Gamma_phi = 1/T2 – 1/(2T1); Favg = (3 + 2 exp(-tg/T2) + exp(-tg/T1))/6 (Nielsen, 2002). Error per gate = 1 – Favg. Depth budget = floor(log(P)/log(Favg)).
Worked examples with user inputs
Target success proxy P = 0.99, one serial gate per layer.
| Relaxation T1 (microseconds) | T2 or Tphi (microseconds) | Gate time (ns) | Average gate fidelity | Depth budget (independent-error proxy) |
|---|---|---|---|---|
| 100 | 100 | 20 | 0.9999 | 100 |
| 100 | 200 | 20 | 0.999933 | 150 |
Cite this
ScienceShot. Qubit coherence and gate fidelity calculator. https://scienceshot.com/qubit-coherence-calculator.
More formats
ScienceShot. (2026). Qubit coherence and gate fidelity calculator [Online calculator]. https://scienceshot.com/qubit-coherence-calculator
@misc{scienceshot-qubit-coherence-calculator-2026,
author = {{ScienceShot}},
title = {{Qubit coherence and gate fidelity calculator}},
year = {2026},
note = {Online calculator},
url = {https://scienceshot.com/qubit-coherence-calculator}
}Sources: Nielsen (2002), Physics Letters A 303, 249-252; Nielsen and Chuang (2010), amplitude and phase damping.
Reviewed by a physicist with CERN experience