The field of superconducting quantum computing, based on Josephson junctions, has recently seen remarkable strides in scaling the number of logical qubits. In particular, the fidelitiesof one- and two-qubit gates have reached the breakeven point with the novel error mitigation and correction methods. Parallel to these advances is the effort to expand the Hilbert space within a single junction or device by employing high-dimensional qubits, otherwise known as qudits. Research has demonstrated the possibility of driving higher-order transitions in a transmon or designing innovative multimode superconducting circuits, termed multimons. These advances can significantly expand the computational basis while simplifying the interconnects in a large-scale quantum processor. In this work we extend the measurement theory of a conventional superconducting qubit to that of a qudit, focusing on modeling the dispersive quadrature measurement in an open quantum system. Under the Markov assumption, the qudit Lindblad and stochastic master equations are formulated and analyzed; in addition, both the ensemble-averaged and the quantum-jump approach of decoherence analysis are detailed with analytical and numerical comparisons. We verify our stochastic model with a series of experimental results on a transmon-type qutrit, verifying the validity of our high-dimensional formalism.
Advanced simulations and calculations on quantum computers require high fidelity implementations of quantum circuits. The universal gateset approach builds complex unitaries from manygates drawn from a small set of calibrated high-fidelity primitive gates, which results in a lower combined fidelity. Compiling a complex unitary for processors with higher-dimensional logical elements, such as qutrits, exacerbates the accumulated error per unitary because a longer gate sequence is needed. Optimal control methods promise time and resource efficient compact gate sequences and, therefore, higher fidelity. These methods generate pulses that can, in principle, directly implement any complex unitary on a quantum device. In this work, we demonstrate that any arbitrary qutrit gate can be realized with high fidelity. We generated and tested pulses for a large set of randomly selected arbitrary unitaries on two separate qutrit compatible processors, LLNL Quantum Device and Integration Testbed (QuDIT) standard QPU and Rigetti Aspen-11, achieving an average fidelity around 99 %. We show that the optimal control gates do not require recalibration for at least three days and the same calibration parameters can be used for all implemented gates. Our work shows that the calibration overheads for optimal control gates can be made small enough to enable efficient quantum circuits based on this technique.
The single flux quantum (SFQ) digital superconducting logic family has been proposed for the scalable control of next-generation superconducting qubit arrays. In the initial implementation,SFQ-based gate fidelity was limited by quasiparticle (QP) poisoning induced by the dissipative on-chip SFQ driver circuit. In this work, we introduce a multi-chip module architecture to suppress phonon-mediated QP poisoning. Here, the SFQ elements and qubits are fabricated on separate chips that are joined with In bump bonds. We use interleaved randomized benchmarking to characterize the fidelity of SFQ-based gates, and we demonstrate an error per Clifford gate of 1.2(1)%, an order-of-magnitude reduction over the gate error achieved in the initial realization of SFQ-based qubit control. We use purity benchmarking to quantify the contribution of incoherent error at 0.96(2)%; we attribute this error to photon-mediated QP poisoning mediated by the resonant mm-wave antenna modes of the qubit and SFQ-qubit coupler. We anticipate that a straightforward redesign of the SFQ driver circuit to limit the bandwidth of the SFQ pulses will eliminate this source of infidelity, allowing SFQ-based gates with fidelity approaching theoretical limits, namely 99.9% for resonant sequences and 99.99% for more complex pulse sequences involving variable pulse-to-pulse separation.
Material defects fundamentally limit the coherence times of superconducting qubits, and manufacturing completely defect-free devices is not yet possible. Therefore, understanding theinteractions between defects and a qubit in a real quantum processor design is essential. We build a model that incorporates the standard tunneling model, the electric field distributions in the qubit, and open quantum system dynamics and draw from the current understanding of two-level system (TLS) theory. Specifically, we start with one million TLSs distributed on the surface of a qubit and pick the 200 highest coupling systems. We then perform a full Lindbladian simulation that explicitly includes the coherent coupling between the qubit and the TLS bath to model the time dependent density matrix of resonant TLS defects and the qubit. We find that the 200 most strongly coupled TLSs can accurately describe the qubit energy relaxation time. This work confirms that resonant TLSs located in areas where the electric field is strong can significantly affect the qubit relaxation time, even if they are located far from the Josephson junction. Similarly, a strongly-coupled resonant TLS located in the Josephson junction does not guarantee a reduced qubit relaxation time if a more strongly coupled TLS is far from the Josephson junction. In addition to the coupling strengths between TLSs and the qubit, the model predicts that the geometry of the device and the TLS relaxation time play a significant role in qubit dynamics. Our work can provide guidance for future quantum processor designs with improved qubit coherence times.
Transmon qubits fabricated with tantalum metal have been shown to possess energy relaxation times greater than 300 μs and, as such, present an attractive platform for high precision,correlated noise studies across multiple higher energy transitions. Tracking the multi-level fluctuating qudit frequencies over the course of hours and even days, with a precision enabled by the high coherence of the device, allows us to extract the underlying charge offset and quasi-particle dynamics. We observe qualitatively different charge offset dynamics in the tantalum device than those measured in previous low frequency charge noise studies. In particular, we find the charge offset dynamics dominated by rare, discrete charge offset jumps between a finite number of quasi-stationary charge configurations, a previously unobserved charge noise process in superconducting qubits.
Nearly all modern solid-state quantum processors approach quantum computation with a set of discrete qubit operations (gates) that can achieve universal quantum control with only ahandful of primitive gates. In principle, this approach is highly flexible, allowing full control over the qubits‘ Hilbert space without necessitating the development of specific control protocols for each application. However, current error rates on quantum hardware place harsh limits on the number of primitive gates that can be concatenated together (with compounding error rates) and remain viable. Here, we report our efforts at implementing a software-defined 0↔2 SWAP gate that does not rely on a primitive gate set and achieves an average gate fidelity of 99.4%. Our work represents an alternative, fully generalizable route towards achieving nontrivial quantum control through the use of optimal control techniques. We describe our procedure for computing optimal control solutions, calibrating the quantum and classical hardware chain, and characterizing the fidelity of the optimal control gate.
Investigations into the microwave surface impedance of superconducting resonators have led to the development of single photon counters that rely on kinetic inductance for their operation.While concurrent progress in additive manufacturing, `3D printing‘, opens up a previously inaccessible design space for waveguide resonators. In this manuscript, we present results from the first synthesis of these two technologies in a titanium, aluminum, vanadium (Ti-6Al-4V) superconducting radio frequency resonator which exploits a design unattainable through conventional fabrication means. We find that Ti-6Al-4V has two distinct superconducting transition temperatures observable in heat capacity measurements. The higher transition temperature is in agreement with DC resistance measurements. While the lower transition temperature, not previously known in literature, is consistent with the observed temperature dependence of the superconducting microwave surface impedance. From the surface reactance, we extract a London penetration depth of 8±3μm – roughly an order of magnitude larger than other titanium alloys and several orders of magnitude larger than other conventional elemental superconductors. This large London penetration depth suggests that Ti-6Al-4V may be a suitable material for high kinetic inductance applications such as single photon counting or parametric amplification used in quantum computing.