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 design keeps only EJ/EC=3, much closer to the original 1999 device's ratio than to a transmon's ≈50, with EC/h=0.800GHz fixed.
((a)) The two-state splitting ε2+EJ2, with ε=8EC(ng−21), is stationary in ng at ng=21 for any value of EJ. Say whether this design can still be run at its sweet spot, and to what order in a small drift of ng it is protected there.
((b)) Using that same two-state Hamiltonian, find the splitting at ng=1/2 and at ng=0, and hence the charge dispersion (their difference), for this design.
((c)) Apply the transmon relation ℏω01≈8EJEC−EC to estimate f01 for the same design, and compare it with the exact two-state splitting at ng=1/2 found in (b). What does the size of the disagreement say about trusting this formula at EJ/EC=3?
((d)) Taking the two-state splitting of (b) as the reliable transition frequency and the anharmonicity as of order EC, estimate ∣α∣/f01 and compare it with the transmon reference of the last section (EJ/EC=50, ∣α∣/f01≈5%). In one or two sentences, explain why this design, although protected at its sweet spot exactly as a transmon is, is still a worse qubit: name what happens once it drifts off ng=1/2, and what its anharmonicity signals about which regime it is really in.