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.
Highlights
According to state of the art resource estimates, accurate fault-tolerant quantum computations, of even the simplest non-trivial problems, will require millions of qubits and days of compute time[1]
We have introduced a new topological-longitudinal transmon (TLT) hybrid qubit which consists of a Majorana-based topological qubit interacting with an longitudinally-coupled transmon qubit
Our TLT qubit architecture paves the way for coherently controlling and manipulating quantum information between topological degrees of freedom and the recently developed longitudinallyinteracting transmon qubit that is crucially equipped with a non-demolition readout mechanism[14]
Summary
According to state of the art resource estimates, accurate fault-tolerant quantum computations, of even the simplest non-trivial problems, will require millions of qubits and days of compute time[1]. Coupling topological with unprotected superconducting qubits is an attractive methodology for scaling up error correcting systems[4]. Improvements in readout fidelity, due to the longitudinal interaction, are important since assignment errors in measurement readout are the dominant error sources, with errors being three to four orders of magnitude larger than that of single qubit gates[15], which hamper fault tolerance. We address the open question of combining these two important qubit platforms by developing a theory for the hybrid topological-longitudinal transmon (TLT) qubit. To do so we derive topological-transmon and topological-resonator couplings and discuss the use of the resulting interactions for quantum gates and readout. We introduce Majorana excitations, supported by a network of one-dimensional (1D) heterostructures, and derive their couplings to both the resonator and transmon. We conclude by discussing potential applications and open questions
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