Two coupled transmons

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

Two coupled transmons, each with

T_1 = T_\phi = 90\,\mu\mathrm{s}

, are joined by a tunable coupler with

J/2\pi = 8.0\,\mathrm{MHz}

. A controlled-phase gate is run for the crossing time

t_{\rm CZ} = \pi/(\sqrt{2}J)

. ((a)) Compute

t_{\rm CZ}

. ((b)) Using the single-qubit coherence-limited infidelity

r_{\rm coh}^{(1)} = \dfrac{2t}{3T}

(valid when

T_1=T_\phi=T

) for each qubit over the duration

t_{\rm CZ}

, and treating the two qubits' decoherence as independent, so that their Pauli errors

e_P=\tfrac32 r_{\rm coh}^{(1)}

add and

r=\tfrac45 e_P

converts the sum back, estimate the coherence-limited infidelity of the two-qubit gate. ((c)) Cross-entropy benchmarking, run with all qubits operating, reports a two-qubit Pauli error of

e_P = 0.50\%

. Using

r = \tfrac{4}{5}e_P

, convert this to an average gate infidelity and compare it with the coherence limit from part (b): give the size of the error left unexplained by decoherence.

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