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arXiv:1710.04590 · Quantum Science and Technology

Mitigating leakage errors due to cavity modes in a superconducting quantum computer

Thomas McConkey, J. H. Béjanin, C. T. Earnest, Corey Rae McRae, Zachary Pagel, J. R. Rinehart, M. Mariantoni

Published Apr 11, 2018• 10 citations
arXivHTMLPDF

Abstract

Abstract A practical quantum computer requires quantum bit (qubit) operations with low error probabilities in extensible architectures. We study a packaging method that makes it possible to address hundreds of superconducting qubits by means of coaxial Pogo pins. A qubit chip is housed in a superconducting box, where both box and chip dimensions lead to unwanted modes that can interfere with qubit operations. We analyze these interference effects in the context of qubit coherent leakage and qubit decoherence induced by damped modes. We propose two methods, half-wave fencing and antinode pinning , to mitigate the resulting errors by detuning the resonance frequency of the modes from the qubit frequency. We perform electromagnetic field simulations indicating that the resonance frequency of the modes increases with the number of installed pins and can be engineered to be significantly higher than the highest qubit frequency. We estimate that the error probabilities and decoherence rates due to suitably shifted modes in realistic scenarios can be up to two orders of magnitude lower than the state-of-the-art superconducting qubit error and decoherence rates. Our methods can be extended to different types of packages that do not rely on Pogo pins. Conductive bump bonds, for example, can serve the same purpose in qubit architectures based on flip chip technology. Metalized vias, instead, can be used to mitigate modes due to the increasing size of the dielectric substrate on which qubit arrays are patterned.

DOI
10.1088/2058-9565/aabd41

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Abstract A practical quantum computer requires quantum bit (qubit) operations with low error probabilities in extensible architectures. We study a packaging method that makes it possible to address hundreds of superconducting qubits by means of coaxial Pogo pins. A qubit chip is housed in a superconducting box, where both box and chip dimensions lead to unwanted modes that can interfere with qubit operations. We analyze these interference effects in the context of qubit coherent leakage and qubit decoherence induced by damped modes. We propose two methods, half-wave fencing and antinode pinning , to mitigate the resulting errors by detuning the resonance frequency of the modes from the qubit frequency. We perform electromagnetic field simulations indicating that the resonance frequency of the modes increases with the number of installed pins and can be engineered to be significantly higher than the highest qubit frequency. We estimate that the error probabilities and decoherence rates due to suitably shifted modes in realistic scenarios can be up to two orders of magnitude lower than the state-of-the-art superconducting qubit error and decoherence rates. Our methods can be extended to different types of packages that do not rely on Pogo pins. Conductive bump bonds, for example, can serve the same purpose in qubit architectures based on flip chip technology. Metalized vias, instead, can be used to mitigate modes due to the increasing size of the dielectric substrate on which qubit arrays are patterned.
We demonstrate a pogo pin package for a superconducting quantum processor specifically designed with a nontrivial layout topology (e.g., a center qubit that cannot be accessed from the sides of the chip). Two experiments on two nominally identical superconducting quantum processors in pogo packages, which use commercially available parts and require modest machining tolerances, are performed at low temperature (10 mK) in a dilution refrigerator and both found to behave comparably to processors in standard planar packages with wirebonds where control and readout signals come in from the edges. Single- and two-qubit gate errors are also characterized via randomized benchmarking, exhibiting similar error rates as in standard packages, opening the possibility of integrating pogo pin packaging with extensible qubit architectures.
Quantum computing architectures with ten or more quantum bits (qubits) have been implemented using trapped ions and superconducting devices. The next milestone in the quest for a quantum computer is the realization of quantum error correction codes. Such codes will require a large number of qubits that must be controlled and measured by means of classical electronics. This scaling up leads to a number of problems and sources of error that must be accounted for in order to have an operational system. \n \nOne architectural aspect requiring immediate attention is the realization of a suitable interconnect between the quantum and classical hardware. Our proposed solution to this wiring problem is the quantum socket, a three-dimensional wiring method for qubits with superior performance as compared to two-dimensional methods based on wire bonding. The quantum socket also provides a means to counteract another scaling problem, the coupling of qubits to unwanted cavity modes resulting in coherent leakage error. By following our proposed wiring methodologies, half-wave fencing or antinode pinning, we show how the error due to leakage can be mitigated to orders of magnitude below current state-of-the-art error probabilities.
A quantum computer will use the properties of quantum physics to solve certain computational problems much faster than otherwise possible. One promising potential implementation is to use superconducting quantum bits in the circuit quantum electrodynamics (cQED) architecture. There, the low energy states of a nonlinear electronic oscillator are isolated and addressed as a qubit. These qubits are capacitively coupled to the modes of a microwave-frequency transmission line resonator which serves as a quantum communication bus. Microwave electrical pulses are applied to the resonator to manipulate or measure the qubit state. State control is calibrated using diagnostic sequences that expose systematic errors. Hybridization of the resonator with the qubit gives it a nonlinear response when driven strongly, useful for amplifying the measurement signal to enhance accuracy. Qubits coupled to the same bus may coherently interact with one another via the exchange of virtual photons. A two-qubit conditional phase gate mediated by this interaction can deterministically entangle its targets, and is used to generate two-qubit Bell states and three-qubit GHZ states. These three-qubit states are of particular interest because they redundantly encode quantum information. They are the basis of the quantum repetition code prototypical of more sophisticated schemes required for quantum computation. Using a three-qubit Toffoli gate, this code is demonstrated to autonomously correct either bit- or phase-flip errors. Despite observing the expected behavior, the overall fidelity is low because of decoherence. A superior implementation of cQED replaces the transmission-line resonator with a three-dimensional box mode, increasing lifetimes by an order of magnitude. In-situ qubit frequency control is enabled with control lines, which are used to fully characterize and control the system Hamiltonian.
This study primarily investigates variations in the radio-frequency (RF) performance characteristics of components within flip-chip packaged superconducting qubit chips. By comparing changes in the lumped-element parameters of identical qubit chip physical structures across different packaging architectures, we analyze the evolving trends in the qubits' energy dissipation models and nonlinear parameters. Simulation and numerical computation results reveal that the metal layers proximal to the chip surface and the microbumps within the flip-chip architecture significantly impact structural parameters such as the resonant frequency and self-capacitance of resonant elements (including the qubits and readout cavities). This influence manifests as an increase in self-capacitance, consequently leading to an overall decrease in resonant frequency. Furthermore, structures such as the XY/Z control lines and the qubit-readout cavity coupling elements exhibit coupling strength of different change trends due to the altered electromagnetic field distribution within the packaging structure. Additionally, the direction of electromagnetic field leakage during coupling undergoes a change.
Superconducting quantum circuits are typically housed in conducting enclosures in order to control their electromagnetic environment. As devices grow in physical size, the electromagnetic modes of the enclosure come down in frequency and can introduce unwanted long-range cross-talk between distant elements of the enclosed circuit. Incorporating arrays of inductive shunts such as through-substrate vias or machined pillars can suppress these effects by raising these mode frequencies. Here, we derive simple, accurate models for the modes of enclosures that incorporate such inductive-shunt arrays. We use these models to predict that cavity-mediated interqubit couplings and drive-line cross-talk are exponentially suppressed with distance for arbitrarily large quantum circuits housed in such enclosures, indicating the promise of this approach for quantum computing. We find good agreement with a finite-element simulation of an example device containing more than 400 qubits.
Amplitude damping is a dominant source of error in high performance quantum processors. A promising approach in quantum error correction is erasure error conversion, where errors are converted into detectable leakage states. Dual-rail encoding has been shown as a candidate for the conversion of amplitude-damping errors; with unique sensitivities to noise and decoherence sources. Here we present a dual-rail encoding within a single fixed-frequency superconducting multimode transmon qubit. The three island, two junction device comprises two transmonlike modes with a detuning of 0.75-1 GHz, in a coaxial circuit QED architecture. We show the logical bit-flip and phase-flip error rates are more than one order of magnitude lower than the physical error rates, and demonstrate stability and repeatability of the architecture through an extended measurement of three such devices. Finally, we discuss how the error-detected subspace can be used for investigations into the fundamentals of noise and decoherence in fixed-frequency transmon qubits.