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 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 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.

scholarly journals Path-optimized nonadiabatic geometric quantum computation on superconducting qubits

2021 ◽  
Author(s):  
Cheng-Yun Ding ◽  
Li-Na Ji ◽  
Tao Chen ◽  
Zheng-Yuan Xue
Keyword(s):  
Quantum Computation ◽  
Large Scale ◽  
Fault Tolerant ◽  
High Fidelity ◽  
Noise Resistance ◽  
Geometric Phases ◽  
Single Qubit ◽  
Phase Gate ◽  
New Perspective ◽  
Geometric Quantum Computation

Abstract Quantum computation based on nonadiabatic geometric phases has attracted a broad range of interests, due to its fast manipulation and inherent noise resistance. However, it is limited to some special evolution paths, and the gate-times are typically longer than conventional dynamical gates, resulting in weakening of robustness and more infidelities of the implemented geometric gates. Here, we propose a path-optimized scheme for geometric quantum computation on superconducting transmon qubits, where high-fidelity and robust universal nonadiabatic geometric gates can be implemented, based on conventional experimental setups. Specifically, we find that, by selecting appropriate evolution paths, the constructed geometric gates can be superior to their corresponding dynamical ones under different local errors. Numerical simulations show that the fidelities for single-qubit geometric Phase, $\pi/8$ and Hadamard gates can be obtained as $99.93\%$, $99.95\%$ and $99.95\%$, respectively. Remarkably, the fidelity for two-qubit control-phase gate can be as high as $99.87\%$. Therefore, our scheme provides a new perspective for geometric quantum computation, making it more promising in the application of large-scale fault-tolerant quantum computation.

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 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 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.

scholarly journals MEASUREMENT-BASED QUANTUM COMPUTATION WITH CLUSTER STATES

2009 ◽  
Vol 07 (06) ◽  
pp. 1053-1203 ◽  
Author(s):  
ROBERT RAUßENDORF
Keyword(s):  
Computational Model ◽  
Quantum Computation ◽  
Quantum Logic ◽  
Network Model ◽  
Quantum Computer ◽  
Fault Tolerant ◽  
Cluster State ◽  
Building Blocks ◽  
Network Simulator ◽  
Classical Level

In this thesis, we describe the one-way quantum computer [Formula: see text], a scheme of universal quantum computation that consists entirely of one-qubit measurements on a highly entangled multiparticle state, i.e. the cluster state. We prove the universality of the [Formula: see text], describe the underlying computational model and demonstrate that the [Formula: see text] can be operated fault-tolerantly. In Sec. 2, we show that the [Formula: see text] can be regarded as a simulator of quantum logic networks. In this way, we prove the universality and establish the link to the network model — the common model of quantum computation. We also indicate that the description of the [Formula: see text] as a network simulator is not adequate in every respect. In Sec. 3, we derive the computational model underlying the [Formula: see text], which is very different from the quantum logic network model. The [Formula: see text] has no quantum input, no quantum output and no quantum register, and the unitary gates from some universal set are not the elementary building blocks of [Formula: see text] quantum algorithms. Further, all information that is processed with the [Formula: see text] is the outcomes of one-qubit measurements and thus processing of information exists only at the classical level. The [Formula: see text] is nevertheless quantum-mechanical, as it uses a highly entangled cluster state as the central physical resource. In Sec. 4, we show that there exist nonzero error thresholds for fault-tolerant quantum computation with the [Formula: see text]. Further, we outline the concept of checksums in the context of the [Formula: see text], which may become an element in future practical and adequate methods for fault-tolerant [Formula: see text] computation.

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