Mitigating crosstalk errors, whether classical or quantum mechanical, is critically important for achieving high-fidelity entangling gates in multi-qubit circuits. For weakly anharmonicsuperconducting qubits, unwanted ZZ interactions can be suppressed by combining qubits with opposite anharmonicity. We present experimental measurements and theoretical modeling of two-qubit gate error for gates based on the cross resonance interaction between a capacitively shunted flux qubit and a transmon and demonstrate the elimination of the ZZ interaction.
Superconducting circuits consisting of a few low-anharmonic transmons coupled to readout and bus resonators can perform basic quantum computations. Since the number of qubits in suchcircuits is limited to not more than a few tens, the qubits can be designed to operate within the dispersive regime, where frequency detuning are much stronger than coupling strengths. However, scaling up the number of qubits will bring the circuit out of this regime and invalidates current theories. We develop a formalism that allows to consistently diagonalize superconducting circuit hamiltonian beyond dispersive regime. This will allow to study qubit-qubit interaction unperturbatively, therefore our formalism remains valid and accurate at small or even negligible frequency detuning; thus our formalism serves as a theoretical ground for designing qubit characteristics for scaling up the number of qubits in superconducting circuits. We study the most important circuits with single- and two-qubit gates, i.e. a single transmon coupled to a resonator and two transmons sharing a bus resonator. Surprisingly our formalism allows to determine the circuit characteristics, such as dressed frequencies and Kerr couplings, in closed-form formulas that not only reproduce perturbative results but also extrapolate beyond the dispersive regime and can ultimately reproduce (and even modify) the Jaynes-Cumming results at resonant frequencies.
We present a theoretical description for circuits consisting of weak anharmonic qubits coupled to cavity multimodes. We obtain a unitary transformation that diagonalizes harmonic sectorof the circuit. Weak anharmonicity does not alter the normal mode basis, however it can modify energy levels. We study two examples of a transmon and two transmons coupled to bus resonator, and we determine dressed frequencies and Kerr nonlinearities in closed form formulas. Our results are valid for arbitrary frequency detuning and coupling within and beyond dispersive regime.
In a superconducting qubit the lifetime of qubit state is restricted by nonequilibrium quasiparticle tunneling. We calculate the rate of these tunnelings using the nonequilibrium effectsthey induce on the condensate chemical potential of leads and islands. We show that by decreasing temperature below a crossover, the quasiparticle relaxation rate changes from exponential to much slower suppression and saturates to a finite value at zero temperature. This prediction is consistent with recent experiments. Our model also indicates a striking modification to qubit transitions: the matrix element of an energy transition in qubit strongly depends on coupling between tunneling quasiparticles and the environment. This features important fabrication hints to improve quantum state efficiency.