A transmon has and pure dephasing time

PHYSICS · Multi-part · Fermi University Physics · Quantum Information & Technology · Physical realizations and quantum technologies · Physical realizations and quantum technologies

Quantum Information and Technology, Ch Superconducting qubits and circuit QED

Problem

A transmon has

T_1 = 70\,\mu\mathrm{s}

and pure dephasing time

T_\phi = 40\,\mu\mathrm{s}

. A single-qubit gate is implemented with a Gaussian pulse of duration

t = 30\,\mathrm{ns}

. Model the coherence-limited average gate infidelity as

r_{\rm coh} = \frac{t}{3}\left(\frac{1}{T_1} + \frac{1}{T_\phi}\right),

the same relation that gives a coherence limit of

1.3\times10^{-4}

for a

20\,\mathrm{ns}

gate at

T_1=T_\phi=100\,\mu\mathrm{s}

. Randomised benchmarking on this qubit, run in isolation, reports an average gate error of

r_{\rm meas} = 5.0\times10^{-4}

. ((a)) Compute

r_{\rm coh}

for this gate. ((b)) Assuming the decoherence contribution and any other error sources combine additively at this level of error (an independent-channel approximation, as for the depolarising channel), find the size of the error not accounted for by coherence alone. ((c)) Name one physical process, other than

T_1

T_\phi

decay, identified as a plausible source of that residual error.

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