We develop a high speed on-chip flux measurement using a capacitively shunted SQUID as an embedded cryogenic transducer and apply this technique to the qualification of a near-termscalable printed circuit board (PCB) package for frequency tunable superconducting qubits. The transducer is a flux tunable LC resonator where applied flux changes the resonant frequency. We apply a microwave tone to probe this frequency and use a time-domain homodyne measurement to extract the reflected phase as a function of flux applied to the SQUID. The transducer response bandwidth is 2.6 GHz with a maximum gain of 1200∘/Φ0 allowing us to study the settling amplitude to better than 0.1%. We use this technique to characterize on-chip bias line routing and a variety of PCB based packages and demonstrate that step response settling can vary by orders of magnitude in both settling time and amplitude depending on if normal or superconducting materials are used. By plating copper PCBs in aluminum we measure a step response consistent with the packaging used for existing high-fidelity qubits.
Complex integrated circuits require multiple wiring layers. In complementary metal-oxide-semiconductor (CMOS) processing, these layers are robustly separated by amorphous dielectrics.These dielectrics would dominate energy loss in superconducting integrated circuits. Here we demonstrate a procedure that capitalizes on the structural benefits of inter-layer dielectrics during fabrication and mitigates the added loss. We separate and support multiple wiring layers throughout fabrication using SiO2 scaffolding, then remove it post-fabrication. This technique is compatible with foundry level processing and the can be generalized to make many different forms of low-loss multi-layer wiring. We use this technique to create freestanding aluminum vacuum gap crossovers (airbridges). We characterize the added capacitive loss of these airbridges by connecting ground planes over microwave frequency λ/4 coplanar waveguide resonators and measuring resonator loss. We measure a low power resonator loss of ∼3.9×10−8 per bridge, which is 100 times lower than dielectric supported bridges. We further characterize these airbridges as crossovers, control line jumpers, and as part of a coupling network in gmon and fuxmon qubits. We measure qubit characteristic lifetimes (T1’s) in excess of 30 μs in gmon devices.
We present a fabrication process for fully superconducting interconnects compatible with superconducting qubit technology. These interconnects allow for the 3D integration of quantumcircuits without introducing lossy amorphous dielectrics. They are composed of indium bumps several microns tall separated from an aluminum base layer by titanium nitride which serves as a diffusion barrier. We measure the whole structure to be superconducting (transition temperature of 1.1K), limited by the aluminum. These interconnects have an average critical current of 26.8mA, and mechanical shear and thermal cycle testing indicate that these devices are mechanically robust. Our process provides a method that reliably yields superconducting interconnects suitable for use with superconducting qubits.
Josephson junctions form the essential non-linearity for almost all superconducting qubits. The junction is formed when two superconducting electrodes come within ∼1 nm of each other.Although the capacitance of these electrodes is a small fraction of the total qubit capacitance, the nearby electric fields are more concentrated in dielectric surfaces and can contribute substantially to the total dissipation. We have developed a technique to experimentally investigate the effect of these electrodes on the quality of superconducting devices. We use λ/4 coplanar waveguide resonators to emulate lumped qubit capacitors. We add a variable number of these electrodes to the capacitive end of these resonators and measure how the additional loss scales with number of electrodes. We then reduce this loss with fabrication techniques that limit the amount of lossy dielectrics. We then apply these techniques to the fabrication of Xmon qubits on a silicon substrate to improve their energy relaxation times by a factor of 5.
An ideal preamplifier for qubit measurement must not only provide high gain and near quantum-limited noise performance, but also isolate the delicate quantum circuit from noisy downstreammeasurement stages while producing negligible backaction. Here we use a Superconducting Low-inductance Undulatory Galvanometer (SLUG) microwave amplifier to read out a superconducting transmon qubit, and we characterize both reverse isolation and measurement backaction of the SLUG. For appropriate dc bias, the SLUG achieves reverse isolation that is better than that of a commercial cryogenic isolator. Moreover, SLUG backaction is dominated by thermal emission from dissipative elements in the device. When the SLUG is operated in pulsed mode, it is possible to characterize the transmon qubit using a measurement chain that is free from cryogenic isolators or circulators with no measurable degradation of qubit performance.
By analyzing the dissipative dynamics of a tunable gap flux qubit, we extract both sides of its two-sided environmental flux noise spectral density over a range of frequencies around2kBT/h≈1GHz, allowing for the observation of a classical-quantum crossover. Below the crossover point, the symmetric noise component follows a 1/f power law that matches the magnitude of the 1/f noise near 1Hz. The antisymmetric component displays a 1/T dependence below 100mK, providing dynamical evidence for a paramagnetic environment. Extrapolating the two-sided spectrum predicts the linewidth and reorganization energy of incoherent resonant tunneling between flux qubit wells.
A critical question for the field of quantum computing in the near future is whether quantum devices without error correction can perform a well-defined computational task beyond thecapabilities of state-of-the-art classical computers, achieving so-called quantum supremacy. We study the task of sampling from the output distributions of (pseudo-)random quantum circuits, a natural task for benchmarking quantum computers. Crucially, sampling this distribution classically requires a direct numerical simulation of the circuit, with computational cost exponential in the number of qubits. This requirement is typical of chaotic systems. We extend previous results in computational complexity to argue more formally that this sampling task must take exponential time in a classical computer. We study the convergence to the chaotic regime using extensive supercomputer simulations, modeling circuits with up to 42 qubits – the largest quantum circuits simulated to date for a computational task that approaches quantum supremacy. We argue that while chaotic states are extremely sensitive to errors, quantum supremacy can be achieved in the near-term with approximately fifty superconducting qubits. We introduce cross entropy as a useful benchmark of quantum circuits which approximates the circuit fidelity. We show that the cross entropy can be efficiently measured when circuit simulations are available. Beyond the classically tractable regime, the cross entropy can be extrapolated and compared with theoretical estimates of circuit fidelity to define a practical quantum supremacy test.
Surface distributions of two level system (TLS) defects and magnetic vortices are limiting dissipation sources in superconducting quantum circuits. Arrays of flux-trapping holes arecommonly used to eliminate loss due to magnetic vortices, but may increase dielectric TLS loss. We find that dielectric TLS loss increases by approximately 25% for resonators with a hole array beginning 2 μm from the resonator edge, while the dielectric loss added by holes further away was below measurement sensitivity. Other forms of loss were not affected by the holes. Additionally, we bound the loss tangent due to residual magnetic effects to <9×10−11/mG for resonators patterned with flux-traps and operated in magnetic fields up to 50mG.[/expand]
For a variety of superconducting qubits, tunable interactions are achieved through mutual inductive coupling to a coupler circuit containing a nonlinear Josephson element. In this paperwe derive the general interaction mediated by such a circuit under the Born-Oppenheimer approximation. This interaction naturally decomposes into a classical part with origin in the classical circuit equations and a quantum part associated with the zero-point energy of the coupler. Our result is non-perturbative in the qubit-coupler coupling strengths and circuit nonlinearities, leading to significant departures from previous treatments in the nonlinear or strong coupling regimes. Specifically, it displays no divergences for large coupler nonlinearities, and it can predict k-body and non-stoquastic interactions that are absent in linear theories. Our analysis provides explicit and efficiently computable series for any term in the interaction Hamiltonian and can be applied to any superconducting qubit type.
Many superconducting qubit systems use the dispersive interaction between the qubit and a coupled harmonic resonator to perform quantum state measurement. Previous works have foundthat such measurements can induce state transitions in the qubit if the number of photons in the resonator is too high. We investigate these transitions and find that they can push the qubit out of the two-level subspace. Furthermore, these transitions show resonant behavior as a function of photon number. We develop a theory for these observations based on level crossings within the Jaynes-Cummings ladder, with transitions mediated by terms in the Hamiltonian which are typically ignored by the rotating wave approximation. We confirm the theory by measuring the photon occupation of the resonator when transitions occur while varying the detuning between the qubit and resonator.