Dissipative quantum computing with majorana fermions. We establish a unified framework for majoranabased faulttolerant quantum computation with majorana surface codes and majorana color codes. Novel gate may enhance power of majoranabased quantum. The chiral majorana fermion, also known as the majorana weyl fermion, is a massless fermionic particle being its own antiparticle proposed long ago in theoretical physics.
Braiding in a system hosting majorana fermions zero modes or. New material shows high potential for quantum computing news. Pdf braiding, majorana fermions, fibonacci particles and. Majorana fermions and topological materials science. This is done by introducing a protocol for pauli product measurements with tetrons and hexons which only requires local 4 majorana parity measurements. I believe that much of the existing literature on this question has been unnecessarily confused by reference to the alleged negativeenergy solutions to the bdg equations. Topological quantum computation using majorana fermions youtube.
Majorana fermion surface code for universal quantum. Keywords braiding fermions majorana fermions quantum process quantum computing 1 introduction. Jul 11, 2018 exotic particles called majorana fermions have potential applications in quantum computing, but their existence has yet to be definitively confirmed. From systems where the\fundamental particle is an nstate system, socalled z n z nz parafermions can emerge.
Creating majorana fermions in topological insulators. May 11, 2016 however, even if the majorana fermions at the ends of wires were easy to braid around one another, they still would not support a universal quantum computera device capable of performing any. Pdf topological quantum computationfrom basic concepts to. Researchers develop error correction method for quantum. Scalable fermionic error correction in majorana surface codes. December, 20 one of the main problems with experimental realizations of quantum computation is performing the required operationsresiliently. Kitaev toy model although majorana fermions were originally predicted in the context of elementary particle physics, they can. These majorana fermions are separated in xdirection and are all coupled to another lead e. Sep 07, 2017 this new proof of majorana fermions is going to be massive for quantum devices. The chiral majorana fermion, also known as the majorana. Sep 22, 2011 i will show that such a topological state emerging at the interface can be occupied by exotic quasiparticles, called majorana fermions, that obey unconventional exchange statistics. The majorana fermions cthat satisfy c cso that they are their own antiparticles. There is a lot of interest in these as quasiparticles and they are relatedto braiding and to topological quantum computing.
Although all are tied tightly to majoranas pioneering insights some examples rather stretch the original. We study the dynamical process of braiding majorana bound states mbs in the presence of the coupling to photons in a microwave cavity. Focus on majorana fermions in condensed matter new journal. It is these majorana fermions with their interactions amongst closest neighbors that lead to quantum entanglement.
Majorana fermions for quantum computer majorana fermions are particles that could potentially be used as information units for a quantum computer. The concept of majorana fermions has its roots in a celebrated equation discovered in the late 1920s by physicist paul dirac. Zero energy majorana bound state at vortex h2e sqshim junction zero energy majorana bound state at junction k e m s. Majorana fermions forming in certain real systems can be thought of as ising anyons. This paper is an introduction to relationships between quantum topology and quantum computing. Majorana fermions and topological quantum computing the degenerate states associated with majorana zero modes define a topologically protected quantum memory kitaev. Knot logic and topological quantum computing with majorana. This paper is an introduction to relationships between topology, quantum computing, and the properties of fermions. Majorana fermions exist at the boundary of special superconductors called topological superconductors, which have a superconducting gap in their interiors and harbor majorana fermions outside, at their boundaries. The property of a system to have boundary majorana. Majorana fermions are quasiparticles, theoretically predicted to form as excitations in.
Quantum computation possible with majorana fermions youtube. Properties of majoran fermions will have to be investigated in detail in both experiments and theories, to reach the goal of the controllable manipulation of majorana fermions in quantum computing. Their unique properties can be exploited for implementing faulttolerant topological quantum computation schemes that are inherently decoherencefree. Periodic table of topological insulators and superconductors. Apr 01, 2018 theoretically predicted about decades ago, the majorana is expected to revolutionize quantum computing, particularly the topologicalbased, more stable approach, which is being led by microsoft. Topological quantum computation is an approach to storing and manipulating quantum infor. Quantum computing uses quantum phenomena to perform computations.
In magnetic fields, the emergence of majorana edge current is predicted to manifest itself in the form of a finite thermal hall effect 1,2, a feature. Microsoft edges closer to quantum computer based on elusive. Topological quantum computation based on chiral majorana fermions. Creation and detection of majorana fermions in laboratories are only the beginning to study these particles for the application in quantum computing. Now, socalled topological qubits could potentially be used for decoherencefree quantum computing. Braiding, majorana fermions, fibonacci particles and. Topological superconductors, majorana fermions and topological quantum computation 1.
Topological quantum computing with majorana fermions. Majorana operators are paired up with an energy gap while few ones localized at the boundary or defects remain free. Hsieh, and liang fu department of physics, massachusetts institute of technology, cambridge, massachusetts 029, usa received 8 april 2015. A fundamental property of quantum computing is the ability of a quantum bit to simultaneously hold both a 0 and a 1 until a calculation or other logical operation fixes it as a 0 or a 1, at which. Theoretically predicted about decades ago, the majorana is expected to revolutionize quantum computing, particularly the topologicalbased, more stable approach, which is. Pdf quantum computation requires controlled engineering of quantum. We introduce an exactly solvable model of interacting majorana fermions realizing z2 topological order with a z2 fermion parity grading and lattice symmetries permuting the three fundamental anyon types. Quantum bits with macroscopic topologically protected. Dissipative quantum computing, phonon interaction, majorana fermions, universal quantum computation 1. Unpaired majorana fermions in quantum wires iopscience. Faulttolerant fermionic quantum computation based on color code. The creation operator creates a fermion in quantum state described by a real wave function, whereas the annihilation operator annihilates it or, equivalently. It has been theoretically predicted and experimentally observed in a hybrid device of a quantum anomalous hall. We will show that majorana fermions can also occur at the ends of quantum wires.
Pdf this paper is an introduction to relationships between topology, quantum computing, and the properties of fermions. Pdf knot logic and topological quantum computing with. The dirac equation seamlessly brings together quantum mechanics and the special theory of relativity and provides the quantum mechanical description of spinhalf fermions, such as electrons, protons, and neutrons. Braiding of majorana fermions in a cavity request pdf. For example, unpaired majorana fermions exist on vortices inchiraltwodimensionalpwavesuperconductors9,10. It has been theoretically predicted and experimentally observed in a hybrid device of a quantum anomalous hall insulator and a conventional superconductor. Introduction majorana fermions in superconducting heterostructures provide one of the most challenging but also interesting candidates for quantum computation 14. We establish a unified framework for majorana based faulttolerant quantum computation with majorana surface codes and majorana color codes. Majorana fermions can also be used for implementing the fermionic quantum computation, in which fermionic modes instead of qubits are the. We propose a concrete physical realization by utilizing quantum phase slips in an array of josephsoncoupled mesoscopic topological superconductors, which can be implemented in a wide range of. Majorana fermion surface code for universal quantum computation sagar vijay, timothy h. The term is sometimes used in opposition to a dirac fermion, which describes fermions that are not their own antiparticles. This paper is an introduction to relationships between topology, quantum computing and the properties of fermions.
The simplest chiral majorana fermion is predicted in 1d space, where it propagates unidirectionally. The chiral majorana fermion is a massless selfconjugate fermion which can arise as the edge state of certain 2d topological matters. This talk will discuss the braiding structure of majorana fermions and possible applications to topological quantum computing. Dwavesys do you believe that the discovery of majorana fermions can lead to another quantum computing breakthrough. The difference between majorana fermions and dirac fermions can be expressed mathematically in terms of the creation and annihilation operators of second quantization. This is done by introducing a protocol for pauli product measurements with tetrons and hexons which only requires local 4majorana parity measurements. This thesis deals with some of the physics of majorana fermions and how they may be applied to quantum computing. Mar, 2017 video on use of majorana bound states for topological quantum computation as part of ese 523 quantum engineering, spring 2017. Apr 19, 20 now, socalled topological qubits could potentially be used for decoherencefree quantum computing. All logical clifford gates are implemented with zero time overhead. Majorana fermions bound to domain wall vortex in 2d sc. We study tunneling conductance at finite bias g ev 0 for a system with a pair of almost decoupled majorana fermions and derive the conditions for the universal zerobias peak with the height 2 e 2 h to be observed in a realistic system which always hosts an even number of majorana fermions.
Majorana fermions are sometimes called\half a fermion. Topological quantum computation based on chiral majorana. We take a foundational approach, showing how knots are related not just to braiding and quantum operators, but to quantum set theoretical foundations and. Braiding of majorana fermions and topological quantum. However, even if the majorana fermions at the ends of wires were easy to braid around one another, they still would not support a universal quantum computera device. We say partial here because a universal topological gate. Majorana fermions and representations of the braid group. Topological quantum materials for realizing majorana.
Majorana fermions in condensedmatter physics international. I will show that such a topological state emerging at the interface can be occupied by exotic quasiparticles, called majorana fermions, that obey unconventional exchange statistics. Exotic particles called majorana fermions have potential applications in quantum computing, but their existence has yet to be definitively confirmed. A corbino ring junction of the hybrid device can use quantum coherent chiral majorana fermions to implement the hadamard gate and the phase gate, and the junction conductance yields a natural readout for the qubit state. Topological quantum computing is an approach to construct qubits that survive for the. This new proof of majorana fermions is going to be massive. This shows how majorana fermions can appear at the base of partial topological quantum computing. Topological quantum computation using majorana fermions. Majorana fermions and quantum matter for quantum computing. In a one dimensional topological superconductor, a single. The condition is satisfied in the presence of an arbitrary small energy gap induced by proximity of a threedimensional pwave superconductor, provided that the normal spectrum has an odd number. Video on use of majorana bound states for topological quantum computation as part of ese 523 quantum engineering, spring 2017.
Majorana zero modes and topological quantum computation npj. Just like the quantum spin used in all other forms of quantum computing. Pdf majorana fermion surface code for universal quantum. Mar 28, 2018 researchers make majorana fermions, but now must try to control them. This new proof of majorana fermions is going to be massive for quantum devices. Majorana fermions and quantum matter for quantum computing chairmen. A short introduction to topological quantum computation.
Majorana fermions in particle physics, solid state and. Mar 01, 2014 creation and detection of majorana fermions in laboratories are only the beginning to study these particles for the application in quantum computing. Majorana fermions have recently garnered a great attention outside the field of particle physics, in condensed matter physics. Kramers pairs of majorana fermions and parafermions in. Researchers make majorana fermions, but now must try to control them. Louis h kauffman received a bs in mathematics from mit in 1966 and a phd in mathematics from princeton university in 1972. Microsoft quantum computing scientists have captured a. In contrast to their particle physics counterparts, majorana fermions. In particular, we study the remarkable unitary braid group representations associated with majorana fermions. In particular we study the remarkable unitary braid group representations associated with majorana fermions. By contrast, majorana fermions, as originally conceived, obey ordinary fermidirac statistics, and are simply a particular type of fermion. Jun 28, 2019 quantum computing uses quantum phenomena to perform computations. Five majorana fermions are present in strongly spin orbit coupled quantum wires on top of a superconductor. The property of a system to have boundary majorana fermions is expressed as a condition on the bulk electron spectrum.
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