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Bulletin of the American Physical Society

Quantum measurement in action with the transmon qubit

Michael Hatridge, Shyam Shankar, Flavius Schackert, K. Geerlings, T. Brecht, Katrina Sliwa, Baleegh Abdo, Luigi Frunzio, Robert J. Schoelkopf, Michel Devoret

Published Feb 28, 2012• 0 citations
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Accurately controlling the state of a transmon qubit via applied microwave pulses is essential in successfully running quantum computers that use these qubits. Currently, control pulses are designed using classical simulations of time-dependent quantum systems that neglect any back-action of the transmon on the transmission lines that deliver the microwaves. In this work, we develop a semiclassical model for a transmon capacitively coupled to a transmission line that treats the transmon quantum mechanically and the transmission line classically. This model can be used in the future to study the detailed interactions of microwave control pulses with transmon qubits to better optimize the control pulses. We show results from a classical model of this system to highlight that the back-action of the transmon may not be negligible for common experimental parameters, emphasizing the need for more rigorous models as experimental parameters are changed to accommodate scaling in device density.
This thesis mainly summarizes two experiments that relate to building a quantum computer out of superconducting transmon qubits. Transmon qubits have emerged as one of the foremost solid state qubits, realizing processors with more than ten qubits and demonstrating small scale quantum algorithms as well as quantum error correction schemes. Right now, there is a race between different academic and industry research groups to scale up transmon qubit processors. The first experiment was a demonstration of qubit control by selective broadcasting in order to reduce the scaling of expensive electronics with the number of qubits for individual single-qubit control. We demonstrated that we can bring two transmon qubits to the same frequency (combining fabrication accuracy and in-situ fine tuning) and use the same hardware to control both, routing the pulses with a nanosecond-timescale vector switch matrix. Despite the compromises required by this technique, we show a scalable path to single qubit control beyond the threshold required for quantum error correction. In benchmarking, we take into account gate leakage due to the fact that transmons are fundamentally multi-level systems. In the second experiment we establish entanglement between two transmon qubits on different chips. We use an entanglement by measurement scheme and demonstrate that we can overcome minor fabrication imperfections by shaping our measurement pulses. Ultimately, performance is mainly limited by photon loss between the chips and up to the amplification chain. This entanglement mediated by traveling photons could be used to make a distributed transmon processor where computations are spread across several chip modules. This modularity could enable connectivities that cannot be realized on chip and ease fabrication requirements, as modules could be individually fabricated and selected. Thus, both of these experiments fit into the larger effort to converge on the hardware, control equipment and architecture of a future large-scale transmon quantum computer. Other experiments I contributed to are summarized in the conclusion chapter to show the diverse physics that can be studied in cQED experiments.