High-fidelity quantum operations on superconducting qubits in the presence of noise

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Note that a deviation δ M i \delta_{M}^{i} from the -0.5:1 ratio in Fig. 1

Cited in the paper.

The same structure could also be obtained by coupling split cooper-pair box qubits with a flux qubit

Cited in the paper.

The level structure in Fig. 2

Cited in the paper.

We simulated the full single-qubit dynamics ( ± \pm 16 charge states) under the action of flux and microwave pulses; pulse parameters were chosen to keep nonadiabatic and off-resonant microwave excitation out of the lowest two states below 10 − 5 10^{-5} . We checked the n p ​ h = 1 n_{ph}=1 truncation of resonator photon states by simulating up to n p ​ h = 3 n_{ph}=3

Cited in the paper.

We assumed the following physical values: Data qubits: E J / h = 175 E_{\textrm{J}}/h=175 GHz, I p = 250 I_{\textrm{p}}=250 nA, E J / E C = 40 , β = 0.925 E_{\textrm{J}}/E_{\textrm{C}}=40,\beta=0.925 , and Φ Δ = 371 ​ m ​ Φ 0 \Phi_{\Delta}=371\;\textrm{m}\Phi_{0} ; Coupler qubit: E J / h = 350 E_{\textrm{J}}/h=350 GHz, I p = 500 I_{\textrm{p}}=500 nA, E J / E C = 160 , β = 0.375 E_{\textrm{J}}/E_{\textrm{C}}=160,\beta=0.375 ; ( OPEN Φ ϵ , Φ Δ ) = ( 0,179 ) \Phi_{\epsilon},\Phi_{\Delta})=(0,179) and ( 5.44 , 0 ) ​ m ​ Φ 0 (5.44,0)\;\textrm{m}\Phi_{0} for the coupled and uncoupled states. Then, M iC = M_{\textrm{iC}}= 10 pH gives J C / h ≈ 0.3 J_{\textrm{C}}/h\approx 0.3 GHz

Cited in the paper.

For each ϵ \epsilon and Δ \Delta we used 40 independent fluctuators, with average switching rates spaced logarithmically from ν ir = 1 \nu_{\textrm{ir}}=1 Hz to ν uv = 0.2 \nu_{\textrm{uv}}=0.2 GHz, and relative amplitudes chosen to maximize convergence to a 1/f spectrum. Net amplitudes are determined by the slopes d ​ ϵ / d ​ Φ ϵ d\epsilon/d\Phi_{\epsilon} and d ​ Δ i / d ​ Φ Δ d\Delta_{i}/d\Phi_{\Delta} . Error rates do depend on ν ir \nu_{\textrm{ir}} as expected [ 21 ] , but are independent of ν uv \nu_{\textrm{uv}} for ν uv ≥ 0.2 \nu_{\textrm{uv}}\geq 0.2 GHz

Cited in the paper.

We explicitly neglect any cooperative effects in decay

Cited in the paper.

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