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arXiv:2403.02481 · Physical Review Letters

Characterizing Dynamic Hybridization of Majorana Zero Modes for Universal Quantum Computing

Themba Hodge, Eric Mascot, Daniel Crawford, Stephan Rachel

Published Mar 6, 2025• 12 citations
arXivHTMLPDF

Abstract

Qubits built out of Majorana zero modes (MZMs) have long been theorized as a potential pathway toward fault-tolerant topological quantum computation. Almost unavoidable in these processes is Majorana wave function overlap, known as hybridization, which arises throughout the process when Majorana modes get close to each other. This breaks the ground state degeneracy, leading to qubit errors in the braiding process. This work presents a simple but precise method to predict qubit errors for dynamic hybridization which varies in space and time. This includes hybridization between four or more MZMs through topological or trivial regions or both of them. As an illustration, we characterize qubit errors for an X gate. We demonstrate how to utilize the hybridization to implement not only arbitrary one-qubit rotations but also a two-qubit controlled variable phase gate, providing a demonstration of universal quantum computing.

DOI
10.1103/physrevlett.134.096601

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Qubits built out of Majorana zero modes (MZMs) have long been theorized as a potential pathway toward fault-tolerant topological quantum computation. Almost unavoidable in these processes is Majorana wave function overlap, known as hybridization, which arises throughout the process when Majorana modes get close to each other. This breaks the ground state degeneracy, leading to qubit errors in the braiding process. This work presents a simple but precise method to predict qubit errors for dynamic hybridization which varies in space and time. This includes hybridization between four or more MZMs through topological or trivial regions or both of them. As an illustration, we characterize qubit errors for an X gate. We demonstrate how to utilize the hybridization to implement not only arbitrary one-qubit rotations but also a two-qubit controlled variable phase gate, providing a demonstration of universal quantum computing.
Majorana zero modes, the elementary building blocks for the quantum bits of topological quantum computers, are known to suffer from hybridization as their wavefunctions begin to overlap. This breaks the ground-state degeneracy, splitting their energy levels and leading to an accumulation of error when performing topological quantum gates. Here, we show that the energy splitting of the Majorana zero modes can become , which can be utilized to reduce the average hybridization energy of the total gate. We present two illustrative examples where suppresses gate errors to such an extent that they remain below the fault-tolerance threshold. As an intrinsic property of Majorana zero modes, negative hybridization enables systems based on imperfect Majorana zero modes to regain functionality for quantum information processing.
Majorana zero modes, the elementary building blocks for the quantum bits of topological quantum computers, are known to suffer from hybridization as their wavefunctions begin to overlap. This breaks the ground state degeneracy, splitting their energy levels and leading to an accumulation of error when performing topological quantum gates. Here we show that the energy splitting of the Majorana zero modes can become negative, which can be utilized to reduce the average hybridization energy of the total gate. We present two illustrative examples where negative hybridization suppresses gate errors to such an extent that they remain below the fault-tolerance threshold. As an intrinsic property of Majorana zero modes, negative hybridization enables systems based on imperfect Majorana zero modes to regain functionality for quantum information processing.
Qubits built out of Majorana zero modes constitute the primary path toward topologically protected quantum computing. Simulating the braiding process of multiple Majorana zero modes corresponds to the quantum dynamics of a superconducting many-body system. It is crucial to study the Majorana dynamics both in the presence of all other quasiparticles and for reasonably large system sizes. We present a method to calculate arbitrary many-body wave functions as well as their expectation values, correlators, and overlaps from time evolved single-particle states of a superconductor, allowing for significantly larger system sizes. We calculate the fidelity, transition probabilities, and joint parities of Majorana pairs to track the quality of the braiding process. We show how the braiding success depends on the speed of the braid. Moreover, we demonstrate the topological CNOT two-qubit gate as an example of two-qubit entanglement. Our Letter opens the path to test and analyze the many theoretical implementations of Majorana qubits. Moreover, this method can be used to study the dynamics of any noninteracting superconductor.
Topological qubits composed of unpaired Majorana zero modes are under intense experimental and theoretical scrutiny in efforts to realize practical quantum computation schemes. In this work, we show that the minimum four Majorana zero modes required for a topological qubit according to braiding schemes and control of entanglement for gate operations are inherent to multiplicative topological phases, which realize symmetry-protected tensor products—and maximally entangled Bell states—of unpaired Majorana zero modes. We construct and characterize both one-dimensional and two-dimensional multiplicative topological phases with two parent Kitaev chain Hamiltonians. We furthermore characterize topology in the bulk and on the boundary with established methods while also introducing techniques to overcome challenges in characterizing multiplicative topology. In the process, we explore the potential of these multiplicative topological phases for an alternative to braiding-based topological quantum computation schemes, in which gate operations are performed through topological phase transitions. Published by the American Physical Society 2024
Topological quantum computation aims to employ anyonic quasiparticles with exotic braiding statistics to encode and manipulate quantum information in a fault-tolerant way. Majorana zero modes are experimentally the simplest realisation of anyons that can non-trivially process quantum information. However, their braiding evolutions, necessary for realising topological gates, still remain beyond current technologies. Here we report the experimental encoding of four Majorana zero modes in an all-optical quantum simulator that give rise to a fault-tolerant qubit. We experimentally simulate their braiding and demonstrate both the non-Abelian character and the topological nature of the resulting geometric phase. We realise a full set of topological and non-topological gates that can arbitrarily rotate the encoded qubit. As an application, we implement the Deutsch-Jozsa algorithm exclusively by topological gates. Our experiment indicates the intriguing possibility of the experimental simulation of Majorana-based quantum computation with scalable technologies.
Topology-related ideas might lead to noise-resilient quantum computing. For example, it is expected that the slow spatial exchange (``braiding'') of Majorana zero modes in superconductors yields quantum gates that are robust against disorder. Here, we report our numerical experiments, which describe the dynamics of a Majorana qubit built from quantum dots controlled by time-dependent gate voltages. Our protocol incorporates nonprotected control, braiding-based protected control, and readout of the Majorana qubit. We use the Kitaev chain model for the simulations, and we focus on the case when the main source of errors is quasistatic charge noise affecting the hybridization energy splitting of the Majorana modes. We provide quantitative guidelines to suppress both diabatic errors and disorder-induced qubit dephasing, such that a fidelity plateau is observed as the hallmark of the topological quantum gate. Our simulations predict realistic features that are expected to be seen in future braiding experiments with Majorana zero modes and other topological qubit architectures.