Hybrid Quantum Computing Apocalypse

Chinese scientists won a major victory, by proving that the Majorana fermions – a particle we’ve found tantalizing hints for years – genuinely exists. This discovery has huge implications for quantum computing, and it might change the world. Don Lincoln, a senior physicist at Fermi lab, does research using the Large Hadrons Collider. He is the author of “The Large Hadrons Collider: The Extraordinary Story of the Higgs Boson and Other Stuff That Will Blow Your Mind”, and produces a series of science education videos. To the question: Why is there (in our Universe) something including cancer, rather than nothing? He is giving the simplest scientific answer: We shouldn’t exist at all.

Majorana fermions, exotic particles with potential applications in quantum computing, have garnered significant interest in condensed matter physics. The Kitaev model serves as a fundamental framework for investigating the emergence of Majorana fermions in one-dimensional systems. We explore the intriguing question of whether Majorana fermions can arise in a normal metal (NM) side-coupled to a Kitaev chain (KC) in the topologically trivial phase. Our findings reveal affirmative evidence, further demonstrating that the KC, when in the topological phase, can induce additional Majorana fermions in the neighboring NM region. Through extensive parameter analysis, we uncover the potential for zero, one, or two pairs of Majorana fermions in a KC side-coupled to an NM. Additionally, we investigate the impact of magnetic flux on the system and calculate the winding number -a topological invariant used to characterize topological phases.

We relax one of the requirements for topological quantum computation with Majorana fermions. Topological quantum computation was discussed so far as manipulation of the wave function within degenerate many-body ground state. The simplest particles providing degenerate ground state, Majorana fermions, often coexist with extremely low-energy excitations so keeping the system in the ground state may be hard. We show that the topological protection extends to the excited states, as long as the Majorana fermions do not interact neither directly nor via the excited states. This protection relies on the fermion parity conservation and so it is generic to any implementation of Majorana fermions.

Majorana fermions (MFs), quantum particles that are their own antiparticles, are not only of fundamental importance in elementary particle physics and dark matter, but also building blocks for fault-tolerant quantum computation. Recently MFs have been intensively studied in solid state and cold atomic systems. These studies are generally based on superconducting pairing with zero total momentum. On the other hand, finite total momentum Cooper pairings, known as Fulde-Ferrell (FF) Larkin-Ovchinnikov (LO) states, were widely studied in many branches of physics. However, whether FF and LO superconductors can support MFs has not been explored. Here we show that MFs can exist in certain types of gapped FF states, yielding a new quantum matter: topological FF superfluids/superconductors. We demonstrate the existence of such topological FF superfluids and the associated MFs using spin-orbit-coupled degenerate Fermi gases and derive their parameter regions. The implementation of topological FF superconductors in semiconductor/superconductor heterostructures is also discussed.

Majorana fermions are zero-energy quasiparticles that may exist in superconducting vortices and interfaces, but their detection is problematic since they have no charge. This is an obstacle to the realization of topological quantum computation, which relies on Majorana fermions to store qubits in a way which is insensitive to decoherence. We show how a pair of neutral Majorana fermions can be converted reversibly into a charged Dirac fermion. These two types of fermions are predicted to exist on the metallic surface of a topological insulator (such as Bi2Se3). Our Dirac-Majorana fermion converter enables electrical detection of a qubit by an interferometric measurement.

Verifying non-Abelian statistics by numerical braiding Majorana fermions

: Spin has long been known to have the potential to perform universal quantum computation. To realize quantum computation with spins one needs an extraordinary amount of control over the spins so we can set, manipulate, and read out the various processes required in information processing. This is a daunting task as these processes are not immune from decoherence. While one can manipulate single spins with high-fidelity and long coherence times, there is no clear path to move from single spin manipulation to many spins. Recent advances have revealed a new type of information processing, topological quantum computation, which is immune from environment related decoherence. Topological information processing relies on the manipulation of anyons, particles which obey non-Abelian statistics. The simplest of these particles, Majorana fermions, are believed to exist as excitations in exotic materials under extreme conditions. Additionally, Majorana fermions have been proposed to exist in a new class of materials commonly referred to as topological insulators coupled with superconducting contacts under much less extreme conditions. In this work, we propose to theoretically investigate the formation, manipulation, entanglement and detection of Majorana fermions in diamond-topological insulator-superconductor heterojunctions. Furthermore, we propose to further investigate the relationship between superconducting elements and 2D and 3D topological insulators. The tasks we outline in this proposal will be undertaken using a variety of analytical tools to provide insight into the system behavior at the theoretical limits and numerical techniques to yield results in experimentally realistic conditions. The goal is to make significant and measurable advances towards transformative information processing technologies that have the potential to vastly increase operational capabilities of multiple Air Force applications.

Majorana fermions in condensed matter: An outlook

In January 2018, the China Reform and Development Committee (led by President Jinping Xi) had the meeting, and passed the plan of “Chinese Initiated International Large Scientific Plan and Large Scientific Project”. In March 2018, it was released by Chinese government. The 14th five years plan will start in 2021 and it is very important to have a historical review of China’s large science projects in order to help in future large science projects’ planning and implementation, such as Circular Electron Positron Collider (CEPC), as Higgs factory proposed in September 2012 by Chinese scientists after the Higgs boson was discovered on July 4, 2012 at CERN on Large Hadron Collider (LHC). In November 2018, the Conceptual Design Report (CDR) of CEPC was released formally and Technical Design Report (TDR) phase started in 2019. It is planned that CEPC TDR will be completed at the end of 2022 and CEPC will be proved by Chinese government during 14th five year plan and completed around 2030. As China’s first large science project, Beijing Electron Positron Collider (BEPC), which was completed in October 1988, its success and experiences are very precious and useful for the realization of CEPC. In 1993, the year of 20th anniversary of Institute of High Energy Physics (IHEP), Chinese Academy of Sciences (CAS), Professor Jialin Xie, Academician of CAS and the first director of BEPC, has written an article recalling the planning, design, R&D and construction of BEPC. In this article, Jialin Xie recalled firstly the Beijing Proton Synchrotron (BPS), so called “87 Project”, in late 1970’s, which was a <sc>50 GeV</sc> synchrotron, and Jialin Xie was the project leader of BPS. During BPS planning and R&D, many trips were to Fermi National Accelerator Laboratory (FNAL), Brookhaven National Laboratory (BNL) and CERN. At the end of 1970’s, due to Chinese economy situation, BPS was suspended. During a collaboration meeting initiated by Professor T. D. Lee of Columbia University and Nobel Prize winner in 1957, between China and USA held at FNAL in March 1981, Professor Wolfgan K. H. Panofsky from SLAC proposed to Chinese delegation a <sc>2.2 GeV</sc> electron positron collider instead of proton synchrotron as BPS. After careful discussions among scientists and the following evaluations from CAS, it was finally decided that China will build Beijing Electron Positron Collider, so called BEPC. BEPC was started in 1984 and completed in October 1988. In the article of Jialin Xie, he recalled many detailed difficulties in design, R&D and construction phases, and many supports from international collaboration with US scientists and government under China-US scientific collaboration agreement. This article revealed many decision making process, design philosophy, technology choice and R&D issues, team training, project management in time and cost controls, etc. He also recalled the doubts and objection voices towards BEPC. BEPC has not only laid a solid ground but also accumulated many precious experiences for the high energy physics and many other large science projects which follow in China. By recalling, keeping and carrying forwards these precious experiences and pioneering spirits, it is believed that CEPC as a successor of BEPC, will be realized successfully in the future. In addition to high energy physics project CEPC, other two long term key directions are exploration to Manned Mars Project and Chinese Fussion Experimental Test Reactor (CFETRE), and three of them should be the strategic parallel Chinese large science and technology projects in the future.

The Kitaev chain model exhibits topological order that manifests as topological degeneracy, Majorana edge modes and Z2 topological invariant of the bulk spectrum. This model can be obtained from a transverse field Ising model(TFIM) using the Jordan–Wigner transformation. TFIM has neither topological degeneracy nor any edge modes. Topological degeneracy associated with topological order is central to topological quantum computation. In this paper, we explore topological protection of the ground state manifold in the case of Majorana fermion models which exhibit Z2 topological order. We show that there are at least two different ways to understand this topological protection of Majorana fermion qubits: one way is based on fermionic mode operators and the other is based on anti-commuting symmetry operators. We also show how these two different ways are related to each other. We provide a very general approach to understanding the topological protection of Majorana fermion qubits in the case of lattice Hamiltonians. We then show how in topological phases in Majorana fermion models gives rise to new braid group representations. So, we give a unifying and broad perspective of topological phases in Majorana fermion models based on anti-commuting symmetry operators and braid group representations of Majorana fermions as anyons.

Majorana bound states are interesting candidates for applications in topological quantum computation. Low energy models allowing to grasp their properties are hence conceptually important. The usual scenario in these models is that two relevant gapped phases, separated by a gapless point, exist. In one of the phases, topological boundary states are absent, while the other one supports Majorana bound states. We show that a customary model violates this paradigm. The phase that should not host Majorana fermions supports a fractional soliton exponentially localized at only one end. By varying the parameters of the model, we describe analytically the transition between the fractional soliton and two Majorana fermions. Moreover, we provide a possible physical implementation of the model. We further characterize the symmetry of the superconducting pairing, showing that the odd-frequency component is intimately related to the spatial profile of the Majorana wavefunctions.

Topological quantum computation provides an elegant way around decoherence, as one encodes quantum information in a non-local fashion that the environment finds difficult to corrupt. Here we establish that one of the key operations---braiding of non-Abelian anyons---can be implemented in one-dimensional semiconductor wire networks. Previous work [Lutchyn et al., arXiv:1002.4033 and Oreg et al., arXiv:1003.1145] provided a recipe for driving semiconducting wires into a topological phase supporting long-sought particles known as Majorana fermions that can store topologically protected quantum information. Majorana fermions in this setting can be transported, created, and fused by applying locally tunable gates to the wire. More importantly, we show that networks of such wires allow braiding of Majorana fermions and that they exhibit non-Abelian statistics like vortices in a p+ip superconductor. We propose experimental setups that enable the Majorana fusion rules to be probed, along with networks that allow for efficient exchange of arbitrary numbers of Majorana fermions. This work paves a new path forward in topological quantum computation that benefits from physical transparency and experimental realism.

1D topological systems for next-generation electronics

Exotic particles called Majorana fermions have potential applications in quantum computing, but their existence has yet to be definitively confirmed. Two groups have now glimpsed these particles. Exotic particles called Majorana fermions have potential applications in quantum computing, but their existence has yet to be definitively confirmed. Two groups have now glimpsed these particles.

This paper is an introduction to relationships between topology, quantum computing, and the properties of Fermions. In particular, we study the remarkable unitary braid group representations associated with Majorana fermions.