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Bulletin of the American Physical Society

Practical elimination of leakage in superconducting qubits by pulse shaping

Felix Motzoi, Jay Gambetta, Patrick Rebentrost, Frank K. Wilhelm

Published Mar 18, 2009• 0 citations
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Accurate microwave waveform delivery is a critical requirement for superconducting-qubit control.Although pulse-shaping methods are often discussed from a quantumcontrol perspective, their practical performance also depends on electrical-engineering constraints such as baseband-equivalent control-envelope bandwidth, waveform distortion, carrier detuning, and IQ quadrature accuracy.This paper presents a compact RF-control-chain-aware simulation study of microwave pulse shaping for a nominal single-qubit Xπ operation in a three-level superconducting-qubit load model.Square, Gaussian, and derivative-removal-by-adiabatic-gate (DRAG)-style pulse envelopes are compared.As a simplified approximation of bandwidth-limited waveform delivery, a causal low-pass transfer function is applied to padded in-phase and quadrature pulse envelopes before the qubit-load simulation.The results show that shaped pulses reduce leakage relative to abrupt rectangular excitation, but finite bandwidth modifies the delivered waveform and changes the leakage response in a pulse-shape-dependent manner.For the simulated 20 ns case, low-bandwidth filtering smooths and temporally extends the delivered envelopes, while sufficiently large bandwidths approach the ideal-waveform response.The study highlights the importance of joint pulse-shape design, envelope bandwidth budgeting, detuning control, and calibration in microwave control systems for scalable quantum hardware.
Simple analytic pulse-shaping techniques are of great practical utility in quantum control, with prime examples being the DRAG method for suppressing leakage in superconducting microwave gates and the transitionless-driving approach to shortcuts-to-adiabaticity. Standard versions of these methods require two orthogonal control channels, with the second channel effectively breaking time-reversal symmetry. This appears to rule out their use in settings with only a single real-valued control field, such as the kind of baseband flux control that is common in many superconducting circuit architectures. We show here that a simple analytic pulse-shaping technique derived via a Magnus expansion is effective even with just a single baseband control channel. We demonstrate its efficacy by simulating a two-qubit gate between transmons realized with a tunable coupler and baseband flux pulses. Our corrections dramatically reduce non-adiabatic leakage caused by ramping the coupler: for realistic device parameters, leakage in a fast iSWAP gate is suppressed by up to three orders of magnitude. Our approach is general, goes beyond simply suppressing unwanted spectral weight at leakage transitions, and can be applied to a variety of platforms.
In realizations of quantum computing, a two-level system (qubit) is often singled out from the many levels of an anharmonic oscillator. In these cases, simple qubit control fails on short time scales because of coupling to leakage levels. We provide an easy to implement analytic formula that inhibits this leakage from any single-control analog or pixelated pulse. It is based on adding a second control that is proportional to the time derivative of the first. For realistic parameters of superconducting qubits, this strategy reduces the error by an order of magnitude relative to the state of the art, all based on smooth and feasible pulse shapes. These results show that even weak anharmonicity is sufficient and in general not a limiting factor for implementing quantum gates.