Recent experiments have measured flux dependent capacitance at radio frequencies leading to the potential for a fast parity read-out of a Majorana qubit. In this work we argue that the quantum dot used in the capacitance measurement can be reasonably approximated by a non-interacting weakly coupled orbital. We then predict the measured flux and parity dependent capacitance for several parameter regimes of the disordered Majorana nanowire model that are both topological and trivial. Following this we study how such a fast capacitance read-out can be used to characterize the quantum coherence of a Majorana nanowire-based qubit using Rabi oscillations. We additionally show that such measurements, if made possible by coherent inter-wire tunneling, would provide a valuable way of characterizing the low energy states in the frequency domain.
Recent experiments have measured flux dependent capacitance at radio frequencies leading to the potential for a fast parity read-out of a Majorana qubit. In this work we argue that the quantum dot used in the capacitance measurement can be reasonably approximated by a non-interacting weakly coupled orbital. We then predict the measured flux and parity dependent capacitance for several parameter regimes of the disordered Majorana nanowire model that are both topological and trivial. Following this we study how such a fast capacitance read-out can be used to characterize the quantum coherence of a Majorana nanowire-based qubit using Rabi oscillations. We additionally show that such measurements, if made possible by coherent inter-wire tunneling, would provide a valuable way of characterizing the low energy states in the frequency domain.
We theoretically examine a scheme for projectively reading out the parity state of a pair of Majorana bound states (MBSs) using a tunnel-coupled quantum dot. The dot is coupled to one end of the topological wire but isolated from any reservoir and is capacitively coupled to a charge sensor for measurement. The combined parity of the MBS-dot system is conserved, and charge transfer between the MBS and dot only occurs through resonant tunneling. Resonance is controlled by the dot potential through a local gate and by the MBS energy splitting due to the overlap of the MBS pair wave functions. The latter splitting can be tuned from zero (topologically protected regime) to a finite value by gate-driven shortening of the topological wire. Simulations show that the oscillatory nature of the MBS splitting is not a fundamental obstacle to readout but requires precise gate control of the MBS spatial position and dot potential. With experimentally realistic parameters, we find that high-fidelity parity readout is achievable given nanometer-scale spatial control of the MBS and that there is a trade-off between required precisions of temporal and spatial control. Use of the scheme to measure the MBS splitting versus separation would present a clear signature of topological order and could be used to test the robustness of this order to spatial motion, a key requirement in certain schemes for scalable topological qubits. We show how the scheme can be extended to distinguish valid parity measurements from invalid ones due to gate calibration errors.
Measurement-induced enhancement of the X-parity lifetime in a Majorana tetron
A recent experiment [arXiv:2507.08795] has reported measurements of the interwire X-parity lifetime in a Majorana tetron device via the quantum capacitance of an auxiliary readout dot. Motivated by these measurements, we theoretically study the interwire parity lifetime in a minimal model of the coupled dot-tetron system subject to electrostatic noise. We show that coupling to the measurement dot can itself strongly modify the parity dynamics by generating an energy splitting that shifts noise-induced transitions to finite frequency and thereby stabilizes the measured states against low-frequency fluctuations. For representative noise strengths motivated by disordered nanowire devices, we find X-parity switching lifetimes of order microseconds in the measurement configuration even when the corresponding bare-tetron coherence time is only tens of nanoseconds long. We analyze both the dispersive regime, where the dot can be integrated out and the dynamics reduces to an effective two-level system, and the near-resonant regime, where all four low-energy states participate. In the latter case, rapid transitions organize the spectrum into two long-lived manifolds that approximately correspond to sectors of the combined dot-tetron X-loop parity, yielding effective two-state switching despite the underlying multilevel structure. Our results show that measurement-induced stabilization can substantially enhance the observed X-parity switching lifetime, such that the lifetime measured under continuous readout can greatly exceed the intrinsic idle T2∗ coherence time of the isolated Majorana tetron qubit.
Quantum computers can solve some problems exponentially faster than classical computers. Unfortunately, the computational power of quantum computers is currently limited by the number of working qubits. It is difficult to scale up these systems, because qubits are easily affected by noise in their environment. This noise leads to decoherence: loss of the qubit’s encoded information. A possible solution to diminish decoherence is using Majorana box qubits, as these qubits are predicted to be insensitive to local noise. However, this promising type of qubit does not exist yet. With the research described in this thesis, we aim to contribute to the development of Majorana box qubits (MBQs). In these qubits, Majorana zero modes, the basic elements of MBQs, are contained within a superconducting island to suppress Majorana parity fluctuations caused by quasiparticle poisoning. To enable parity readout of the MBQ, these modes are coupled to quantum dots within a nanowire network. To help realize MBQs, we need a better understanding of quasiparticles in superconducting islands, parity-readout techniques, and ways to fabricate nanowire networks. These three aspects are the focus of the experiments presented in this thesis. To study superconducting islands and readout techniques, we used InAs semiconductor nanowires with an epitaxially grown Al shell. Majorana signatures have already been observed in such nanowires. We addressed quasiparticle dynamics in superconducting islands by measuring the gate-charge modulation of the switching current. We found a consistent 2e-periodic modulation at zero magnetic field, and an exponential decrease of parity lifetime with increasing magnetic field. We explored MBQ readout, using a quantum dot level as a proxy for a Majorana zero mode, and measured its charge hybridization with another dot using gate-based readout. We showed that we can rapidly discriminate between two settings with different tunnel couplings, demonstrating the potential of gate-based readout to measure MBQs. And, using gate-based readout, we could study charge-transfer processes occurring in hybrid structures of superconducting islands coupled to quantum dots. Finally, to find a good material platform for nanowire networks, we characterized two two-dimensional systems. We realized quantum point contacts in InSb, which we used to measure the g-factor anisotropy, and effective electron mass in this system. And, we studied the spin-orbit interaction in InAs/GaSb by extracting the difference in density between electrons with different spin orientations. This thesis finishes with a proposal for a series experiments to realize MBQs. These experiments make use of superconducting islands and the reflectometry setup we developed for gate-based readout.
We present a theoretical analysis of a Majorana-based qubit consisting of two topological superconducting islands connected via a Josephson junction. The qubit is operated by electrostatic gates which control the coupling of two of the four Majorana zero modes. At the end of the operation, readout is performed in the charge basis. Even though the operations are not topologically protected, the proposed experiment can potentially shed light on the coherence of the parity degree of freedom in Majorana devices and serve as a first step towards topological Majorana qubits. We discuss in detail the charge-stability diagram and its use for characterizing the parameters of the devices, including the overlap of the Majorana edge states. We describe the multilevel spectral properties of the system and present a detailed study of its controlled coherent oscillations, as well as decoherence resulting from coupling to a non-Markovian environment. In particular, we study a gate-controlled protocol where conversion between Coulomb-blockade and transmon regimes generates coherent oscillations of the qubit state due to the overlap of Majorana modes. We show that, in addition to fluctuations of the Majorana coupling, considerable measurement errors may be accumulated during the conversion intervals when electrostatic fluctuations in the superconducting islands are present. These results are also relevant for several proposed implementations of topological qubits which rely on readout based on charge detection.
We theoretically study a scheme to distinguish the two ground states of a one-dimensional topological superconductor, which could serve as a basis for the readout of Majorana qubits. The scheme is based on parity-to-charge conversion, i.e., the ground-state parity of the superconductor is converted to the charge occupation on a tunnel-coupled auxiliary quantum dot. We describe how certain error mechanisms degrade the quality of the parity-to-charge conversion process. We consider (i) leakage due to a strong readout tunnel pulse, (ii) incomplete charge Rabi oscillations due to slow charge noise, and (iii) charge relaxation due to phonon emission and absorption. To describe these effects, we use simple model Hamiltonians based on the ideal Kitaev chain, and draw conclusions to generic one-dimensional topological superconductors wherever possible. In general, the effects of the error mechanisms can be minimized by choosing a smooth shape and an optimal strength for the readout tunnel pulse. In a case study based on InAs heterostructure device parameters, we estimate that the parity-to-charge conversion error is mainly due to slow charge noise for weak tunnel pulses and leakage for strong tunnel pulses.
The fusion of non-Abelian anyons is a fundamental operation in measurement-only topological quantum computation1. In one-dimensional topological superconductors (1DTSs)2–4, fusion amounts to a determination of the shared fermion parity of Majorana zero modes (MZMs). Here we introduce a device architecture5 that is compatible with future tests of fusion rules. We implement a single-shot interferometric measurement of fermion parity6–11 in indium arsenide–aluminium heterostructures with a gate-defined superconducting nanowire12–14. The interferometer is formed by tunnel-coupling the proximitized nanowire to quantum dots. The nanowire causes a state-dependent shift of the quantum capacitance of these quantum dots of up to 1 fF. Our quantum-capacitance measurements show flux h/2e-periodic bimodality with a signal-to-noise ratio (SNR) of 1 in 3.6 μs at optimal flux values. From the time traces of the quantum-capacitance measurements, we extract a dwell time in the two associated states that is longer than 1 ms at in-plane magnetic fields of approximately 2 T. We discuss the interpretation of our measurements in terms of both topologically trivial and non-trivial origins. The large capacitance shift and long poisoning time enable a parity measurement with an assignment error probability of 1%. A device architecture based on indium arsenide–aluminium heterostructures with a gate-defined superconducting nanowire allows single-shot interferometric measurement of fermion parity and demonstrates an assignment error probability of 1%.