Physical implementations of qubits can be extremely sensitive to environmental coupling, which can result in decoherence. While efforts are made for protection, coupling to the environmentis necessary to measure and manipulate the state of the qubit. As such, the goal of having long qubit energy relaxation times is in competition with that of achieving high-fidelity qubit control and measurement. Here we propose a method that integrates filtering techniques for preserving superconducting qubit lifetimes together with the dispersive coupling of the qubit to a microwave resonator for control and measurement. The result is a compact circuit that protects qubits from spontaneous loss to the environment, while also retaining the ability to perform fast, high-fidelity readout. Importantly, we show the device operates in a regime that is attainable with current experimental parameters and provide a specific example for superconducting qubits in circuit quantum electrodynamics.
Quantum error correction (QEC) is an essential step towards realising scalable quantum computers. Theoretically, it is possible to achieve arbitrarily long protection of quantum informationfrom corruption due to decoherence or imperfect controls, so long as the error rate is below a threshold value. The two-dimensional surface code (SC) is a fault-tolerant error correction protocol} that has garnered considerable attention for actual physical implementations, due to relatively high error thresholds ~1%, and restriction to planar lattices with nearest-neighbour interactions. Here we show a necessary element for SC error correction: high-fidelity parity detection of two code qubits via measurement of a third syndrome qubit. The experiment is performed on a sub-section of the SC lattice with three superconducting transmon qubits, in which two independent outer code qubits are joined to a central syndrome qubit via two linking bus resonators. With all-microwave high-fidelity single- and two-qubit nearest-neighbour entangling gates, we demonstrate entanglement distributed across the entire sub-section by generating a three-qubit Greenberger-Horne-Zeilinger (GHZ) state with fidelity ~94%. Then, via high-fidelity measurement of the syndrome qubit, we deterministically entangle the otherwise un-coupled outer code qubits, in either an even or odd parity Bell state, conditioned on the syndrome state. Finally, to fully characterize this parity readout, we develop a new measurement tomography protocol to obtain a fidelity metric (90% and 91%). Our results reveal a straightforward path for expanding superconducting circuits towards larger networks for the SC and eventually a primitive logical qubit implementation.
The simultaneous suppression of charge fluctuations and offsets is crucial
for preserving quantum coherence in devices exploiting large quantum
fluctuations of the superconducting phase.This requires an environment with
both extremely low DC and high RF impedance. Such an environment is provided by
a superinductance, defined as a zero DC resistance inductance whose impedance
exceeds the resistance quantum $R_Q = h/(2e)^2 simeq 6.5 mathrm{kOmega}$ at
frequencies of interest (1 – 10 GHz). In addition, the superinductance must
have as little dissipation as possible, and possess a self-resonant frequency
well above frequencies of interest. The kinetic inductance of an array of
Josephson junctions is an ideal candidate to implement the superinductance
provided its phase slip rate is sufficiently low. We successfully implemented
such an array using large Josephson junctions ($E_J >> E_C$), and measured
internal losses less than 20 ppm, self-resonant frequencies greater than 10
GHz, and phase slip rates less than 1 mHz.