Session L39: Characterizing and Controlling Superconducting Circuits II

Measurement and Control of Superconducting Qubits Using Single Flux Quantum Digital Logic

While remarkable progress has been made in the realization of small scale superconducting quantum circuits comprised of order 10 qubits, it is unclear how to scale existing control and readout methods to the millions of qubits required for full implementation of a surface code that can outperform the best available classical computers. In this talk, I describe the development of high-fidelity qubit control and measurement based on the superconducting Single Flux Quantum (SFQ) digital logic family. I present data on SFQ-driven Rabi oscillations of a superconducting qubit and discuss limits to SFQ-based gate fidelity. Additionally, I present a qubit measurement approach based on microwave photon counting. Qubit states are mapped to bright and dark pointer states of a linear resonator followed by subsequent photodetection. Combined, these approaches allow for qubit measurement and control at the millikelvin stage of the cryostat, without the need for microwave pulse shaping, heterodyning, or thresholding at room temperature. These experiments represent a first step toward the integration of a large-scale superconducting quantum processor with proximal logic and control, with the potential for significant reductions in latency, wiring heat load and system footprint.   

Qubit Feedback on a Five-Qubit Transmon Device

Feedback-based dynamic control of quantum processors is a key component for many medium-to-large-scale quantum information processing routines. Several groups have begun addressing this need, often using in-house, custom-built hardware. We have implemented real-time feedback for superconducting qubits using scalable, programmable and commercially available hardware from Keysight Technologies. We will use this hardware to implement a multi-qubit reset protocol and to demonstrate a three-qubit bit-flip error detection code on a five-qubit transmon device. I will present our latest experimental progress towards this goal.   

Mitigating Superconducting Qubit Crosstalk via Optimal Control

Current superconducting quantum computing experiments have reached a level of complexity where two-dimensional lattices of quantum bits (qubits) comprising on the order of 50 qubits can be fabricated and operated. Such architectures are necessary to both implement quantum error correcting codes as well as to perform quantum simulations and machine learning experiments. However, a rectangular qubit arrangement necessarily requires each individual qubit to be coupled to 4 neighbors (qubits or resonators), leading to unwanted interactions or crosstalk. In fact, this frequency crowding often results in qubits idling within 200 MHz of each other, causing conventional single qubit gates to incur errors as large as 2%. By means of numerical simulations, we systematically analyze crosstalk in various physical configurations, and show that pulses generated via GRAPE can eliminate it.   

Superconducting Qubit Control with Single Flux Quantum Pulses: Part I - Fabrication

A large-scale superconducting quantum computer will require significant classical resources for operation, including elements for control, measurement, and feedback. A promising candidate technology to reduce both the wiring heat load and overall system footprint of a future control system is the Single Flux Quantum (SFQ) digital logic family. Here we describe the design and fabrication of an on-chip SFQ pulse driver for control of a superconducting transmon qubit. We discuss optimization of the process flow to preserve the coherence properties of the qubit. Finally, we describe preliminary steps toward the development of a quantum/classical multichip module (MCM) involving a transmon qubit array on one chip and a classical SFQ pattern generator on a second chip, with the two chips coupled in a flip-chip arrangement.   

Coherent Control of a Superconducting Transmon with Single Flux Quantum Pulses: Part II - Experimental

We demonstrate control of a superconducting qubit enacted by a Single Flux Quantum (SFQ) driver. An integrated on-chip DC-SFQ driver emits quantized pulses allowing subharmonic driving of qubit rotations. We compare gate operations between the DC-SFQ driver and microwave pulses through the superconducting resonator. Operation of SFQ driven qubit as a function of control parameters will also be presented.   

Non-Gaussian Noise Spectroscopy With Superconducting Qubits. Part 1: Theory.

Non-Gaussian noise can play an important role in qubit decoherence, for example in the presence of two-level fluctuators or in environments far from thermal equilibrium. While there has been substantial experimental progress in characterizing Gaussian noise, non-Gaussian noise spectroscopy has yet to be experimentally implemented. This task is essential for designing robust control and error correction for realistic noisy environments. To accomplish this, a non-Gaussian noise characterization method based on dynamical decoupling was introduced in Ref. [1]. Before using these protocols on native noise, it is important to assess them with engineered non-Gaussian noise. In this talk, we theoretically describe how to benchmark this method in realistic superconducting qubit systems like the transmon. We also report on progress toward characterizing native non-Gaussian sources of noise in these systems.
[1] Norris et al. Phys. Rev. Lett. 116, 150503 (2016)   

Non-Gaussian Noise Spectroscopy With Superconducting Qubits. Part 2: Experiment

Most quantum control and quantum error-correction protocols assume that the noise causing decoherence is described by Gaussian statistics. However, the Gaussianity assumption breaks down when the system is strongly coupled to a sparse environment, such as those consisting of a few two-state fluctuators. Here, we implement open-loop quantum control protocols to characterize both Gaussian and non-Gaussian dephasing processes in superconducting qubits.   

Gate set tomography on more than two qubits

Quantum tomography is often deemed impractical for “large” quantum information processors of more than 2 qubits. Quantum process tomography and gate set tomography (GST) can be, and have been, used to probe the behavior of gates on 1-2 qubits, but are rarely applied to 3 or more qubits. This stems in large part from the sheer number of parameters that need to be probed in standard gate tomography: O(16^N) for N qubits. We present a framework for intelligently reducing this parameter explosion to poly(N) parameters. Using reduced models that capture physically plausible errors (e.g., few-qubit interactions and Pauli stochastic noise), we show how to perform gate set tomography effectively on larger systems. We present results from applying these methods to processors with 3+ qubits.   

Spectroscopic Measurements on Error Protected Superconducting Qubit Design Based on Josephson Junction Arrays

Since the first demonstration of quantum coherence in superconducting qubits, the coherence times of the various designs have undergone a significant improvement. This remarkable evolution is mainly the result of the combination of new qubit designs with reduced sensitivity to external noise, engineered qubit environments, advances in materials and fabrication techniques. An alternative approach to further increase qubit coherence times is to harness potential intrinsic protections of certain superconducting circuits. This is the case in the recently proposed zero-pi qubit [PRA 87, 052306 (2013)]. In this talk we present a qubit design which is based on the zero-pi circuit in a parameter regime which is experimentally achievable by using long Josephson junction arrays. The circuit offers protection against both energy relaxation, due to disjoint support of the qubit subspace and dephasing, due to diminishing flux sensitivity at the sweet points. We describe the symmetric coupling scheme of the qubit used for dispersive read-out and demonstrate the rich energy level spectrum of the device.   

Strongly driven Josephson circuits for engineering parametric interactions

An outstanding roadblock towards the emergence of large scale quantum devices is the finite lifetime of the underlying qubits. One possible solution is to use a subtle interplay between coherent drives and nonlinear dissipation to protect and manipulate quantum information. This nonlinear dissipation is engineered through parametric methods where a strong off-resonant pump mediates a nonlinear interaction between the system of interest and its bath. The efficiency of this protection scales with the drive strength. In real Josephson circuits, this favorable scaling collapses for a critical drive strength. The purpose of this work is to understand this limitation, and design circuits which circumvent this breakdown. We experimentally investigate the behaviour of two circuit topologies in the presence of strong drives, and discuss the implications for strong qubit readout, and engineered parametric interactions.   

Inductively-shunted transmon for driven-dissipative operations with superconducting circuits

The transmon, a remarkably versatile superconducting qubit, consists of a small Josephson junction shunted by a large capacitance. This capacitance reduces the susceptibility of the qubit to offset charge fluctuations by localizing the superconducting phase across the junction near zero. However, the finite-height potential well of the transmon Hamiltonian renders higher excited states unstable due to their non-negligible running-state component. The effect associated with the non-fully-confining nature of the transmon potential may include the experimentally observed limitations on the transmon ac Stark shift, which limits the efficacy of pumping schemes for driven-dissipative operation such as error correction. We propose modifying the transmon by additionally shunting the junction with a linear inductance approximated by multiple larger junctions. The loop that is formed is maintained at zero flux. In this circuit, the Josephson energy is comparable to the inductive energy of the shunt inductance. Progress on circuit design and experimental results testing these ideas will be reported.   

Coherent control of two qubits in coaxial circuit QED

We demonstrate the extension of a coaxial circuit QED architecture [1] to two qubits, including tune up of two-qubit quantum logic gates based on the cross-resonance interaction [2].

A major obstacle in scaling up monolithic superconducting-circuit quantum computing architectures is the circuit complexity that results from integration of the required control and measurement lines with the qubits. We address this obstacle by adopting a circuit architecture with entirely off-chip out-of-plane wiring; coaxial qubits ("coaxmons") and lumped element LC resonators are fabricated on opposing sides of a single chip, and control and readout are provided by coaxial cables running perpendicular to the chip plane.

We present the first measurements of pairs of detuned, weakly capacitively coupled, static frequency coaxmon qubits. The cross-resonance interaction between the qubits is characterised using process tomography, and the results are used to tune the microwave drives applied to the two qubits to optimise gate fidelities.   

Control of Superconducting Qubits: Merging Pulse Calibration and System Characterization using Optimal Control

The current methodology for designing control pulses for superconducting circuits often results in a somewhat absurd situation: pulses are designed using simplified models, resulting in initially poor fidelities. The pulses are then calibrated in-situ, achieving high-fidelities, but without a corresponding model. We are therefore left with a model we know is inaccurate, working pulses for which we do not have a matching model, and a calibration process from which we learned nothing about the system. We propose a novel procedure to rectify the situation, by merging pulse design, calibration and system characterization: Calibration is recast as a closed-loop search for the best-fit model parameters, starting with a detailed, but only partially characterized model of the system. Fit is evaluated by fidelity of a complete set of gates, which are optimized to fit the current system characterization. The end result is a best-fit characterization of the system model, and a full set of high-fidelity gates for that model. We believe the new approach will greatly improve both gate fidelities and our understanding of the systems they drive.