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arXiv:2009.00027 · PRX Quantum

Dispersive Readout of Majorana Qubits

Thomas B. Smith, Maja C. Cassidy, D. J. Reilly, Stephen D. Bartlett, Arne L. Grimsmo

Published Nov 10, 2020• 32 citations
arXivHTMLPDF

Abstract

We analyze a readout scheme for Majorana qubits based on dispersive coupling to a resonator.We consider two variants of Majorana qubits: the Majorana transmon and the Majorana box qubit.In both cases, the qubit-resonator interaction can produce sizeable dispersive shifts in the megahertz range for reasonable system parameters, allowing for submicrosecond readout with high fidelity.For Majorana transmons, the light-matter interaction used for readout manifestly conserves Majorana parity, which leads to a notion of quantum nondemolition (QND) readout that is stronger than for conventional charge qubits.In contrast, Majorana box qubits only recover an approximately QND readout mechanism in the dispersive limit where the resonator detuning is large.We also compare dispersive readout to longitudinal readout for the Majorana box qubit.We show that the latter gives faster and higher fidelity readout for reasonable parameters, while having the additional advantage of being manifestly QND, and so may prove to be a better readout mechanism for these systems.

DOI
10.1103/prxquantum.1.020313

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We analyze a readout scheme for Majorana qubits based on dispersive coupling to a resonator.We consider two variants of Majorana qubits: the Majorana transmon and the Majorana box qubit.In both cases, the qubit-resonator interaction can produce sizeable dispersive shifts in the megahertz range for reasonable system parameters, allowing for submicrosecond readout with high fidelity.For Majorana transmons, the light-matter interaction used for readout manifestly conserves Majorana parity, which leads to a notion of quantum nondemolition (QND) readout that is stronger than for conventional charge qubits.In contrast, Majorana box qubits only recover an approximately QND readout mechanism in the dispersive limit where the resonator detuning is large.We also compare dispersive readout to longitudinal readout for the Majorana box qubit.We show that the latter gives faster and higher fidelity readout for reasonable parameters, while having the additional advantage of being manifestly QND, and so may prove to be a better readout mechanism for these systems.
Fast, high-fidelity, and quantum nondemolition (QND) qubit readout is an essential element of quantum information processing. For superconducting qubits, state-of-the-art readout is based on a dispersive cross-Kerr coupling between a qubit and its readout resonator. The resulting readout can be high fidelity and QND, but readout times are currently limited to the order of 50 nanoseconds due to the dispersive cross-Kerr of magnitude 10 megahertz. Here, we present a readout scheme that uses the quarton coupler to facilitate a large (greater than 200 megahertz) cross-Kerr between a transmon qubit and its readout resonator. Full master equation simulations of the coupled system show a 5-nanosecond readout time with greater than 99% readout fidelity and greater than 99.9% QND fidelity. The quartonic readout circuit is experimentally feasible and preserves the coherence properties of the qubit. Our work reveals a path for order of magnitude improvements of superconducting qubit readout by engineering nonlinear light-matter couplings in parameter regimes unreachable by existing designs.
We propose a quantum nondemolition Majorana qubit readout protocol based on parametric modulation of a longitudinal interaction between a pair of Majorana bound states and a resonator. The interaction can be modulated through microwave-frequency gate voltage or flux control of a tunable tunnel barrier. The qubit-resonator coupling is quantum nondemolition to exponential accuracy, a property inherited from the topological nature of the Majorana zero modes. The same mechanism as used for single-qubit readout can also be extended to perform multiqubit measurements and be used to enact long-range entangling gates.
We study theoretical models for charge reflectometry and capacitive readout of the Majorana parity degree of freedom in Majorana box qubits, considering decoherence channels within the framework of the Lindblad master equation. Noting that a parity-dependent dynamical susceptibility χ z ( ω ) governs both readout schemes, we provide a general expression for χ z ( ω ) which covers the full crossover from the resonant regime to the off-resonant dispersive regime. In addition, we reexamine previous results which were obtained under a semiclassical factorization assumption. Using three different error measures, we show that this approximation is quantitatively justified in the dispersive regime. In the resonant regime, however, we find deviations from exact reference data, obtained by numerical solution for the steady state of the full Lindblad equation. These deviations are typically of the order of a few percent in the considered error measures.
Multiphoton processes deteriorate the quantum nondemolition (QND) character of the dispersive readout in circuit QED, causing the readout to lag behind single- and two-qubit gates in both speed and fidelity. Alternative methods such as longitudinal readout have been proposed; however, it is unknown to what extent multiphoton processes hinder this approach. Here, we investigate the QND character of the longitudinal readout of the transmon qubit. We show that the deleterious effects that arise due to multiphoton transitions can be heavily suppressed with detuning because the longitudinal interaction strength is independent of the transmon-resonator detuning. We consider the effect of circuit disorder, the selection rules that act on the transmon, and the description of longitudinal readout in the classical limit of the transmon to qualitatively demonstrate that longitudinal readout is robust. We show that fast, high-fidelity QND readout of transmon qubits is possible with longitudinal coupling.
Dispersive readout of superconducting qubits relies on a transverse capacitive coupling that hybridizes the qubit with the readout resonator, subjecting the qubit to Purcell decay and measurement-induced state transitions (MIST). Despite the widespread use of Purcell filters to suppress qubit decay and near-quantum-limited amplifiers, dispersive readout often lags behind single- and two-qubit gates in both speed and fidelity. Here, we experimentally demonstrate junction readout, a simple readout architecture that realizes a strong qubit-resonator cross-Kerr interaction without relying on a transverse coupling. This interaction is achieved by coupling a transmon qubit to its readout resonator through both a capacitance and a Josephson junction. By varying the qubit frequency, we show that this hybrid coupling provides intrinsic Purcell protection and enhanced resilience to MIST, enabling readout at high photon numbers. While junction readout is compatible with conventional linear measurement, in this work we exploit the nonlinear coupling to intentionally engineer a large Kerr nonlinearity in the resonator, enabling bifurcation-based readout. Using this approach, we achieve a 99.4 % assignment fidelity with a 68 ns integration time and a 98.4 % QND fidelity without an external Purcell filter or a near-quantum-limited amplifier. These results establish the junction readout architecture with bifurcation-based readout as a scalable and practical alternative to dispersive readout, enabling fast, high-fidelity qubit measurement with reduced hardware overhead.
Abstract We introduce a new hybrid qubit consisting of a Majorana qubit interacting with a transmon longitudinally coupled to a resonator. To do so, we equip the longitudinal transmon qubit with topological quasiparticles, supported by an array of heterostructure nanowires, and derive charge- and phase-based interactions between the Majorana qubit and the resonator and transmon degrees of freedom. Inspecting the charge coupling, we demonstrate that the Majorana self-charging can be eliminated by a judicious choice of charge offset, thereby maintaining the Majorana degeneracy regardless of the quasiparticles spatial arrangement and parity configuration. We perform analytic and numerical calculations to derive the effective qubit–qubit interaction elements and discuss their potential utility for state readout and quantum error correction. Further, we find that select interactions depend strongly on the overall superconducting parity, which may provide a direct mechanism to characterize deleterious quasiparticle poisoning processes.