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Chinese Physics B

Majorana noise model and its influence on the power spectrum

Shumeng 书梦 Chen 陈, Sifan 思凡 Ding 丁, Zhen-Tao 振涛 Zhang 张, Dong E. Liu

Published Sep 26, 2023• 0 citations
Publisher

Abstract

Majorana quantum computation offers a potential approach to securely manipulating and storing quantum data in a topological manner that may effectively resist the decoherence induced by local noise. However, actual Majorana qubit setups are susceptible to noise. In this study, from a quantum dynamics perspective, we develop a noise model for Majorana qubits that accounts for quasi-particle poisoning and Majorana overlapping with fluctuation. Furthermore, we focus on Majorana parity readout methodologies, specifically those leveraging an ancillary quantum dot, and carry out an in-depth exploration of continuous measurement techniques founded on the quantum jump model of a quantum point contact. Utilizing these methodologies, we proceed to analyze the influence of noise on the afore-mentioned noise model, employing numerical computation to evaluate the power spectrum and frequency curve. In the culmination of our study, we put forward a strategy to benchmark the presence and detailed properties of noise in Majorana qubits.

DOI
10.1088/1674-1056/acfd19

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Majorana quantum computation offers a potential approach to securely manipulating and storing quantum data in a topological manner that may effectively resist the decoherence induced by local noise. However, actual Majorana qubit setups are susceptible to noise. In this study, from a quantum dynamics perspective, we develop a noise model for Majorana qubits that accounts for quasi-particle poisoning and Majorana overlapping with fluctuation. Furthermore, we focus on Majorana parity readout methodologies, specifically those leveraging an ancillary quantum dot, and carry out an in-depth exploration of continuous measurement techniques founded on the quantum jump model of a quantum point contact. Utilizing these methodologies, we proceed to analyze the influence of noise on the afore-mentioned noise model, employing numerical computation to evaluate the power spectrum and frequency curve. In the culmination of our study, we put forward a strategy to benchmark the presence and detailed properties of noise in Majorana qubits.
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Majorana-based quantum computing seeks to use the non-local nature of Majorana zero modes to store and manipulate quantum information in a topologically protected way. While noise is anticipated to be significantly suppressed in such systems, finite temperature and system size result in residual errors. In this work, we connect the underlying physical error processes in Majorana-based systems to the noise models used in a fault tolerance analysis. Standard qubit-based noise models built from Pauli operators do not capture leading order noise processes arising from quasiparticle poisoning events, thus it is not obvious a priori that such noise models can be usefully applied to a Majorana-based system. We develop stochastic Majorana noise models that are generalizations of the standard qubit-based models and connect the error probabilities defining these models to parameters of the physical system. Using these models, we compute pseudo-thresholds for the d=5 Bacon-Shor subsystem code. Our results emphasize the importance of correlated errors induced in multi-qubit measurements. Moreover, we find that for sufficiently fast quasiparticle relaxation the errors are well described by Pauli operators. This work bridges the divide between physical errors in Majorana-based quantum computing architectures and the significance of these errors in a quantum error correcting code.
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Majorana qubits offer a promising way to store and manipulate quantum information by encoding it into the state of Majorana zero modes. As the information is stored in a topological property of the system, local noise cannot lead to decoherence. Manipulation of the information is achieved by braiding the zero modes. The measurement, however, is challenging as the information is well hidden and thus inherently hard to access. Here, we discuss a setup for measuring the state of a Majorana qubit by employing standard tools of microwave engineering. The basic physical effect that we employ is the fact that a voltage-biased Josephson junction hosting Majorana fermions allows photons to be emitted and absorbed at half the Josephson frequency. We show that in the dispersive regime, our setup allows us to perform a quantum nondemolition measurement and to reach the quantum limit. An appealing feature of our setup is that the interaction of the Majorana qubit with the measurement device can be turned on and off at will by changing the dc bias of the junction.
Building a fault-tolerant quantum computer requires physical qubits with exceptionally low error rates. An exciting proposal for achieving this goal is to employ Majorana-based qubits, which may have error rates that are exponentially suppressed in macroscopic system parameters. Specifically, for Majorana qubits based on topological superconducting nanowires, errors are expected to be exponentially suppressed in the nanowire length, superconducting gap, and decreasing temperature. This thesis investigates errors in Majorana-based qubits from excited quasiparticles due to changes in chemical potentials and 1/f charge noise, and shows that such errors are not exponentially suppressed and can be quite substantial. In the first study of this thesis, we show that small temporal variations of the chemical potential can cause errors that grow linearly with the length of the nanowire. These errors stem from leakage into excited bulk quasiparticle states, which poison Majorana modes at opposite ends of the nanowire. We further demonstrate that the dynamics of this leakage are captured by the half Landau-Zener effect, which dictates its dependence on key parameters such as the superconducting gap, chemical potential variations, and dynamic changes in the spatial profile of Majorana modes. In the second study we investigate quasiparticle excitations due to high-frequency components of 1/f charge noise, which is ubiquitous in the materials surrounding the nanowire. We model 1/f noise as arising from two level fluctuators which cause chemical potential fluctuations following random telegraph noise. We demonstrate that 1/f noise causes error rates which grow linearly with the system size and are not exponentially suppressed in the superconducting gap. For existing tetron qubit designs, we estimate decoherence times to be an order of magnitude shorter than the target 1μs measurement time. This thesis also develops an algorithmic framework for applying the covariance matrix method to the time-dependent Kitaev chain model. This extends upon existing approaches, providing a key numerical tool used throughout this thesis. This work motivates engineering strategies to reduce coupling to two level systems in Majorana qubits, such as increasing the nanowire capacitance. Beyond Majoranas, a promising avenue is to investigate the impact of this quasiparticle excitation mechanism on superconducting circuits, such as superconducting qubits, resonators, and single-photon detectors.
Robustness of edge states and non-Abelian excitations of topological states of matter promises quantum memory and quantum processing, which are naturally immune to microscopic imperfections such as static disorder. However, topological properties will not in general protect quantum systems from time-dependent disorder or noise. Here we take the example of a network of Kitaev wires with Majorana edge modes storing qubits to investigate the effects of classical noise in the crossover from the quasistatic to the fast fluctuation regime. We present detailed results for the Majorana edge correlations, and fidelity of braiding operations for both global and local noise sources preserving parity symmetry, such as random chemical potentials and phase fluctuations. While in general noise will induce heating and dephasing, we identify examples of long-lived quantum correlations in the presence of fast noise due to motional narrowing, where external noise drives the system rapidly between the topological and nontopological phases.