Collaborative Research: Non-Ideal Majorana Fermions: A Practical Approach to Topological Quantum Computation

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The main obstacle to quantum computation is the “noise” affecting the basic units of a quantum computer – the so-called qubits – as a result of their weak, but nonzero coupling to the environment. Since this coupling is essentially local, a promising approach to overcoming the noise problem is to encode the information using topological quantum phenomena – robust global properties characterizing certain types of quantum systems that are immune to local perturbations. A promising platform for realizing robust topological qubits is based on a special kind of quantum quasiparticle called a Majorana fermion or Majorana zero mode (MZM). Recent theoretical studies by the PIs and other groups indicate that experiments may have already uncovered non-ideal versions of MZMs, the so-called quasi-Majorana modes. In this project the PIs will examine fundamental aspects of topological protection and practical design questions related to maximizing qubit lifetime and minimizing noise rates in quantum devices with non-ideal Majorana fermions. With most of the ongoing research in the field focusing on ideal Majorana fermions, which in practice may be hard to realize, the present studies will be critical to engineering the first generation of topological qubits using what may be already available, namely, non-ideal Majorana fermions. The project will serve the national interest and promote the NSF mission of progress of science by deepening our understanding of topological quantum matter in condensed matter systems and investigating the feasibility of topological quantum computation based on experimentally available devices. The project will provide excellent education and training opportunities to undergraduate and graduate students at Clemson University, including economically disadvantaged students and underrepresented minorities who constitute a significant percentage of the student population. This project is jointly funded by the Quantum Information Science Program (Physics Division), and the Established Program to Stimulate Competitive Research (EPSCoR). Majorana zero modes (MZMs) in semiconductor-superconductor (SM-SC) nanowire heterostructures are currently being investigated as possible building blocks for topological qubits in a future quantum computer. Theoretical studies by the PIs and others have shown that much of the parameter space of the experimentally investigated SM-SC heterostructures is in fact occupied by so-called quasi-Majorana zero modes, which are separated from each other by a length scale well below the nanowire length. Since the principle of fault tolerance in topological quantum computation (TQC) depends critically on the non-local encoding of quantum information using topological MZMs separated by the length of the nanowire, this situation presents a major problem for the feasibility of TQC, as quasi-Majoranas do not enjoy sufficient topological protection for fault-tolerant qubit operations. Nonetheless, quasi-Majoranas are likely to be present in the first generation of Majorana-based qubit devices either by design, or by accident. This project fills the critical void created by the near absence of studies of topological qubit designs and schemes for braiding and error correction when the constituent building blocks are quasi-Majoranas, rather than ideal topological MZMs. The PIs will perform analytical and numerical research with the following intellectual goals: (1) Designing and modeling SM-SC qubit devices based on controllable quasi-Majorana zero modes, (2) Understanding and characterizing the key physical processes that control the quasi-Majorana qubit lifetimes, and (3) Error analysis in measurement-only TQC schemes with quasi-Majorana zero modes. The overarching goal is to investigate the feasibility of fault tolerant TQC with quasi-Majorana zero modes (rather than ideal MZMs) and to better understand practical aspects of engineering Majorana-based topological qubits.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.