scholarly journals Systematic distillation of composite Fibonacci anyons using one mobile quasiparticle

2012 ◽  
Vol 12 (9&10) ◽  
pp. 876-892
Author(s):  
Ben W. Reichardt
Keyword(s):  
Quantum Computation ◽  
Quantum Computer ◽  
Fault Tolerant ◽  
Success Probability ◽  
Quantum Algorithm ◽  
Systematic Construction ◽  
Topological Quantum ◽  
Universal Quantum ◽  
Measurement Devices ◽  
Topological Quantum Computation

A topological quantum computer should allow intrinsically fault-tolerant quantum computation, but there remains uncertainty about how such a computer can be implemented. It is known that topological quantum computation can be implemented with limited quasiparticle braiding capabilities, in fact using only a single mobile quasiparticle, if the system can be properly initialized by measurements. It is also known that measurements alone suffice without any braiding, provided that the measurement devices can be dynamically created and modified. We study a model in which both measurement and braiding capabilities are limited. Given the ability to pull nontrivial Fibonacci anyon pairs from the vacuum with a certain success probability, we show how to simulate universal quantum computation by braiding one quasiparticle and with only one measurement, to read out the result. The difficulty lies in initializing the system. We give a systematic construction of a family of braid sequences that initialize to arbitrary accuracy nontrivial composite anyons. Instead of using the Solovay-Kitaev theorem, the sequences are based on a quantum algorithm for convergent search.

scholarly journals GEOMETRIC PHASES AND TOPOLOGICAL QUANTUM COMPUTATION

2003 ◽  
Vol 01 (01) ◽  
pp. 1-23 ◽  
Author(s):  
VLATKO VEDRAL
Keyword(s):  
Quantum Computation ◽  
Large Scale ◽  
Quantum Computer ◽  
Fault Tolerant ◽  
Geometric Phases ◽  
Quantum Phases ◽  
Topological Quantum ◽  
Universal Quantum ◽  
The Subject ◽  
Topological Quantum Computation

In the first part of this review we introduce the basics theory behind geometric phases and emphasize their importance in quantum theory. The subject is presented in a general way so as to illustrate its wide applicability, but we also introduce a number of examples that will help the reader understand the basic issues involved. In the second part we show how to perform a universal quantum computation using only geometric effects appearing in quantum phases. It is then finally discussed how this geometric way of performing quantum gates can lead to a stable, large scale, intrinsically fault-tolerant quantum computer.

scholarly journals Optimizing Clifford gate generation for measurement-only topological quantum computation with Majorana zero modes

2020 ◽  
Vol 8 (6) ◽  
Author(s):  
Alan Tran ◽  
Alex Bocharov ◽  
Bela Bauer ◽  
Parsa Bonderson
Keyword(s):  
Quantum Computation ◽  
Nearest Neighbor ◽  
Quantum Computer ◽  
Quantum Algorithm ◽  
Zero Modes ◽  
Topological Quantum ◽  
Different Types ◽  
Computer Based ◽  
Surface Code ◽  
Topological Quantum Computation

One of the main challenges for quantum computation is that while the number of gates required to perform a non-trivial quantum computation may be very large, decoherence and errors in realistic quantum architectures limit the number of physical gate operations that can be performed coherently. Therefore, an optimal mapping of the quantum algorithm into the physically available set of operations is of crucial importance. We examine this problem for a measurement-only topological quantum computer based on Majorana zero modes, where gates are performed through sequences of measurements. Such a scheme has been proposed as a practical, scalable approach to process quantum information in an array of topological qubits built using Majorana zero modes. Building on previous work that has shown that multi-qubit Clifford gates can be enacted in a topologically protected fashion in such qubit networks, we discuss methods to obtain the optimal measurement sequence for a given Clifford gate under the constraints imposed by the physical architecture, such as layout and the relative difficulty of implementing different types of measurements. Our methods also provide tools for comparative analysis of different architectures and strategies, given experimental characterizations of particular aspects of the systems under consideration. As a further non-trivial demonstration, we discuss an implementation of the surface code in Majorana-based topological qubits. We use the techniques developed here to obtain an optimized measurement sequence that implements the stabilizer measurements using only fermionic parity measurements on nearest-neighbor topological qubit islands.

scholarly journals Competing ν = 5/2 fractional quantum Hall states in confined geometry

2016 ◽  
Vol 113 (44) ◽  
pp. 12386-12390 ◽  
Author(s):  
Hailong Fu ◽  
Pengjie Wang ◽  
Pujia Shan ◽  
Lin Xiong ◽  
Loren N. Pfeiffer ◽  
...  
Keyword(s):  
Quantum Computation ◽  
Filling Factor ◽  
Fault Tolerant ◽  
Quantum Hall ◽  
Point Contact ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Topological Quantum ◽  
Quantum Point ◽  
Topological Quantum Computation

Some theories predict that the filling factor 5/2 fractional quantum Hall state can exhibit non-Abelian statistics, which makes it a candidate for fault-tolerant topological quantum computation. Although the non-Abelian Pfaffian state and its particle-hole conjugate, the anti-Pfaffian state, are the most plausible wave functions for the 5/2 state, there are a number of alternatives with either Abelian or non-Abelian statistics. Recent experiments suggest that the tunneling exponents are more consistent with an Abelian state rather than a non-Abelian state. Here, we present edge-current–tunneling experiments in geometrically confined quantum point contacts, which indicate that Abelian and non-Abelian states compete at filling factor 5/2. Our results are consistent with a transition from an Abelian state to a non-Abelian state in a single quantum point contact when the confinement is tuned. Our observation suggests that there is an intrinsic non-Abelian 5/2 ground state but that the appropriate confinement is necessary to maintain it. This observation is important not only for understanding the physics of the 5/2 state but also for the design of future topological quantum computation devices.

TOWARDS A QUANTUM ALGORITHM FOR THE PERMANENT

2007 ◽  
Vol 05 (01n02) ◽  
pp. 223-228 ◽  
Author(s):  
ANNALISA MARZUOLI ◽  
MARIO RASETTI
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Computation ◽  
Quantum Computer ◽  
Quantum Algorithm ◽  
Topological Quantum Field Theory ◽  
Quantum Field ◽  
Topological Quantum

We resort to considerations based on topological quantum field theory to outline the development of a possible quantum algorithm for the evaluation of the permanent of a 0 - 1 matrix. Such an algorithm might represent a breakthrough for quantum computation, since computing the permanent is considered a "universal problem", namely, one among the hardest problems that a quantum computer can efficiently handle.

scholarly journals Quantum software engineering. Pt. I: Quantum Circuit (Gate) Model based Computing – education Lectures and pedagogical workshop

2020 ◽  
pp. 129-201
Author(s):  
Sergey Ulyanov ◽  
Andrey Reshetnikov ◽  
Olga Tyatyushkina ◽  
Vladimir Korenkov
Keyword(s):  
Software Engineering ◽  
Quantum Computation ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Quantum Circuit ◽  
Circuit Model ◽  
Topological Quantum ◽  
Definition Of ◽  
Topological Quantum Computation ◽  
Main Ideas

All the quantum algorithms are based on a certain quantum computing model, varying from the quantum circuit, one-way quantum computation, adiabatic quantum computation and topological quantum computation. These four models are equivalent in computational power; among them, the quantum circuit model is most frequently used. In the circuit model, it has been proved that arbitrary single-qubit rotations plus twoqubit controlled-NOT gates are universal, i.e. they can provide a set of gates to implement any quantum algorithm. This article discusses the goal for this research: it is to given a lightning-fast (as-barebones-as-possible) definition of the quantum circuit model computing and leisurely development of quantum computation before actually getting around to sophisticated algorithms. In this article the main ideas of quantum software engineering is described.

Majorana Zero Modes in Networks of Cooper-Pair Boxes: Topologically Ordered States and Topological Quantum Computation

2020 ◽  
Vol 11 (1) ◽  
pp. 397-420 ◽  
Author(s):  
Yuval Oreg ◽  
Felix von Oppen
Keyword(s):  
Quantum Computation ◽  
Coulomb Blockade ◽  
Cooper Pair ◽  
Quantum Computer ◽  
Zero Modes ◽  
Topological Superconductors ◽  
Topological Quantum ◽  
Recent Developments ◽  
Universal Quantum ◽  
Coulomb Effects

Recent experimental progress introduced devices that can combine topological superconductivity with Coulomb-blockade effects. Experiments with these devices have already provided additional evidence for Majorana zero modes in proximity-coupled semiconductor wires. They also stimulated numerous ideas for how to exploit interactions between Majorana zero modes generated by Coulomb charging effects in networks of Majorana wires. Coulomb effects promise to become a powerful tool in the quest for a topological quantum computer as well as for driving topological superconductors into topologically ordered insulating states. Here, we present a focused review of these recent developments, including discussions of recent experiments, designs of topological qubits, Majorana-based implementations of universal quantum computation, and topological quantum error correction. Motivated by the analogy between a qubit and a spin-1/2 degree of freedom, we also review how coupling between Cooper-pair boxes leads to emergent topologically ordered insulating phases.

scholarly journals Majorana zero modes in impurity-assisted vortex of LiFeAs superconductor

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Lingyuan Kong ◽  
Lu Cao ◽  
Shiyu Zhu ◽  
Michał Papaj ◽  
Guangyang Dai ◽  
...  
Keyword(s):  
Quantum Computation ◽  
Zero Mode ◽  
Scanning Tunneling ◽  
Homogeneous Material ◽  
Dirac Fermions ◽  
Tunneling Microscopy ◽  
Zero Modes ◽  
Topological Quantum ◽  
One Step ◽  
Topological Quantum Computation

AbstractThe iron-based superconductor is emerging as a promising platform for Majorana zero mode, which can be used to implement topological quantum computation. One of the most significant advances of this platform is the appearance of large vortex level spacing that strongly protects Majorana zero mode from other low-lying quasiparticles. Despite the advantages in the context of physics research, the inhomogeneity of various aspects hampers the practical construction of topological qubits in the compounds studied so far. Here we show that the stoichiometric superconductor LiFeAs is a good candidate to overcome this obstacle. By using scanning tunneling microscopy, we discover that the Majorana zero modes, which are absent on the natural clean surface, can appear in vortices influenced by native impurities. Our detailed analysis reveals a new mechanism for the emergence of those Majorana zero modes, i.e. native tuning of bulk Dirac fermions. The discovery of Majorana zero modes in this homogeneous material, with a promise of tunability, offers an ideal material platform for manipulating and braiding Majorana zero modes, pushing one step forward towards topological quantum computation.

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