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Register a new userFlux Qubits with Long Coherence Times for Hybrid Quantum Circuits
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We present measurements of superconducting flux qubits embedded in a three dimensional copper cavity. The qubits are fabricated on a sapphire substrate and are measured by coupling them inductively to an on-chip superconducting resonator located in the middle of the cavity. At their flux-insensitive point, all measured qubits reach an intrinsic energy relaxation time in the 6-20 microseconds range and a pure dephasing time comprised between 3 and 10 microseconds. This significant improvement over previous works opens the way to the coherent coupling of a flux-qubit to individual spins.
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An effective Hamiltonian is derived for two coupled three-Josephson-junction (3JJ) qubits. This is not quite trivial, for the customary free 3JJ Hamiltonian is written in the limit of zero inductance L. Neglecting the self-flux is already dubious for one qubit when it comes to readout, and becomes untenable when discussing inductive coupling. First, inductance effects are analyzed for a single qubit. For small L, the self-flux is a fast variable which can be eliminated adiabatically. However, the commonly used junction phases are_not_ appropriate slow variables, and instead one introduces degrees of freedom which are decoupled from the loop current to leading order. In the quantum case, the zero-point fluctuations (LC oscillations) in the loop current diverge as L->0. Fortunately, they merely renormalize the Josephson couplings of the effective (two-phase) theory. In the coupled case, the strong zero-point fluctuations render the full (six-phase) wave function significantly entangled in leading order. However, in going to the four-phase theory, this uncontrollable entanglement is integrated out completely, leaving a computationally usable mutual-inductance term of the expected form as the effective interaction.
We investigate the waiting time distributions (WTDs) of superconducting hybrid junctions, considering both conventional and topologically nontrivial superconductors hosting Majorana bound states at their edges. To this end, we employ a scattering matrix formalism that allows us to evaluate the waiting times between the transmissions and reflections of electrons or holes. Specifically, we analyze normal-metal-superconductor (NIS) junctions and NISIN junctions, where Cooper pairs are spatially split into different leads. The distribution of waiting times is sensitive to the simultaneous reflection of electrons and holes, which is enhanced by the zero-energy state in topological superconductors. For the NISIN junctions, the WTDs of trivial superconductors feature a sharp dependence on the applied voltage, while for topological ones they are mostly independent of it. This particular voltage dependence is again connected to the presence of topological edge states, showing that WTDs are a promising tool for identifying topological superconductivity.
We have studied the low-frequency magnetic susceptibility of two inductively coupled flux qubits using the impedance measurement technique (IMT), through their influence on the resonant properties of a weakly coupled high-quality tank circuit. In a single qubit, an IMT dip in the tanks current--voltage phase angle at the level anticrossing yields the amplitude of coherent flux tunneling. For two qubits, the difference (IMT deficit) between the sum of single-qubit dips and the dip amplitude when both qubits are at degeneracy shows that the system is in a mixture of entangled states (a necessary condition for entanglement). The dependence on temperature and relative bias between the qubits allows one to determine all the parameters of the effective Hamiltonian and equilibrium density matrix, and confirms the formation of entangled eigenstates.
We have investigated decoherence in Josephson-junction flux qubits. Based on the measurements of decoherence at various bias conditions, we discriminate contributions of different noise sources. In particular, we present a Gaussian decay function of the echo signal as evidence of dephasing due to $1/f$ flux noise whose spectral density is evaluated to be about $(10^{-6} Phi_0)^2$/Hz at 1 Hz. We also demonstrate that at an optimal bias condition where the noise sources are well decoupled the coherence observed in the echo measurement is mainly limited by energy relaxation of the qubit.
We discuss a practical design for tunably coupling a pair of flux qubits via the quantum inductance of a third high-frequency qubit. The design is particularly well suited for realizing a recently proposed microwave-induced parametric coupling scheme. This is attractive because the qubits can always remain at their optimal points. Furthermore, we will show that the resulting coupling also has an optimal point where it is insensitive to low-frequency flux noise. This is an important feature for the coherence of coupled qubits. The presented scheme is an experimentally realistic way of carrying out two-qubit gates and should be easily extended to multiqubit systems.
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