A superconducting single-qubit gate takes to apply

PHYSICS · Multi-part · Fermi University Physics · Quantum Information & Technology · Open quantum systems, decoherence and error correction · Physical realizations and quantum technologies

Quantum Information and Technology, Ch Noise as a quantum operation

Problem

A superconducting single-qubit gate takes

t_g = 40\,\mathrm{ns}

to apply. Coherence measurements on the qubit give

T_1 = 150\,\mu\mathrm{s}

and pure dephasing time

T_\phi = 200\,\mu\mathrm{s}

. Assume the only source of error is coherence-limited noise (no control errors), so that each gate's error is

r \approx t_g/(3T_1) + t_g/(3T_\phi)

, and that

G

such gates in sequence give squared-type fidelity

F^2 \approx (1-r)^G

. ((a)) Estimate

r

for one gate. ((b)) Estimate the largest number of gates

G

that can be applied in sequence while keeping

F^2 \ge 0.5

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