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 fidelity0.9999
Error per gate9.999e-5
Depth budget (independent-error proxy)100
0408012016020000.250.50.751Gate time (ns)Average fidelity
Average fidelity versus gate time
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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.

What Pro produces

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/mcp

Connector tool: qubit_coherence

Example: For T1 = T2 = 100 microseconds and a 20 ns gate, what is the decoherence-limited average fidelity?

About the connector

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 fidelityDepth budget (independent-error proxy)
100100200.9999100
100200200.999933150

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