A two-qubit gate on a trapped-ion qubit takes

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

t_g = 20\,\mu\mathrm{s}

. The qubit's coherence has been measured as

T_1 = 1.0\,\mathrm{s}

and

T_2 = 0.50\,\mathrm{s}

. Assume the only source of error is coherence-limited noise, with per-gate error

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)) Find the pure dephasing time

T_\phi

implied by the measured

T_1

and

T_2

. ((b)) Estimate

r

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

G

that can be applied in sequence while keeping

F^2 \ge 0.5

Browse the problem library