scholarly journals Quantum gates for Majoranas zero modes in topological superconductors in one-dimensional geometry

2021 ◽  
Vol 103 (20) ◽  
Author(s):  
Marek Narożniak ◽  
Matthieu C. Dartiailh ◽  
Jonathan P. Dowling ◽  
Javad Shabani ◽  
Tim Byrnes
Keyword(s):  
Quantum Gates ◽  
One Dimensional ◽  
Zero Modes ◽  
Topological Superconductors

scholarly journals Suppression of2πphase slip due to hidden zero modes in one-dimensional topological superconductors

2013 ◽  
Vol 87 (6) ◽  
Author(s):  
David Pekker ◽  
Chang-Yu Hou ◽  
Doron L. Bergman ◽  
Sam Goldberg ◽  
İnanç Adagideli ◽  
...  
Keyword(s):  
One Dimensional ◽  
Zero Modes ◽  
Topological Superconductors

scholarly journals Flux-stabilized Majorana zero modes in coupled one-dimensional Fermi wires

2018 ◽  
Vol 98 (16) ◽  
Author(s):  
Chun Chen ◽  
Wei Yan ◽  
C. S. Ting ◽  
Yan Chen ◽  
F. J. Burnell
Keyword(s):  
One Dimensional ◽  
Zero Modes

scholarly journals Assessing Bound States in a One-Dimensional Topological Superconductor: Majorana versus Tamm

2021 ◽  
Author(s):  
Niccolò Traverso Ziani ◽  
Lucia Vigliotti ◽  
Matteo Carrega ◽  
Fabio Cavaliere
Keyword(s):  
Quantum Computation ◽  
Bound States ◽  
Research Activity ◽  
One Dimensional ◽  
Majorana Bound States ◽  
Topological Superconductors ◽  
Topological Quantum ◽  
Tamm State ◽  
Topological Quantum Computation ◽  
Intense Research

Majorana bound states in topological superconductors have attracted intense research activity in view of applications in topological quantum computation. However, they are not the only example of topological bound states that can occur in such systems. We here study a model in which both Majorana and Tamm bound states compete. We show both numerically and analytically that, surprisingly, the Tamm state remains partially localized even when the spectrum becomes gapless. Despite this fact, we demonstrate that the Majorana polarization shows a clear transition between the two regimes.

scholarly journals Majorana zero modes in one-dimensional quantum wires without long-ranged superconducting order

2011 ◽  
Vol 84 (19) ◽  
Author(s):  
Lukasz Fidkowski ◽  
Roman M. Lutchyn ◽  
Chetan Nayak ◽  
Matthew P. A. Fisher
Keyword(s):  
Quantum Wires ◽  
One Dimensional ◽  
Zero Modes

scholarly journals Characterizations of topological superconductors: Chern numbers, edge states and Majorana zero modes

2017 ◽  
Vol 19 (9) ◽  
pp. 093018 ◽  
Author(s):  
Xiao-Ping Liu ◽  
Yuan Zhou ◽  
Yi-Fei Wang ◽  
Chang-De Gong
Keyword(s):  
Edge States ◽  
Zero Modes ◽  
Topological Superconductors ◽  
Chern Numbers

scholarly journals Quantum Implementation of Powell’s Conjugate Direction Method

2019 ◽  
Vol 23 (4) ◽  
pp. 726-734
Author(s):  
Kehan Chen ◽  
Fei Yan ◽  
Kaoru Hirota ◽  
Jianping Zhao ◽  
◽  
...  
Keyword(s):  
Search Algorithm ◽  
Quantum Circuit ◽  
Data Fitting ◽  
Quadratic Equation ◽  
Quantum Circuits ◽  
Quantum Gates ◽  
Circuit Implementation ◽  
One Dimensional ◽  
Conjugate Direction ◽  
Conjugate Direction Method

A quantum circuit implementation of Powell’s conjugate direction method (“Powell’s method”) is proposed based on quantum basic transformations in this study. Powell’s method intends to find the minimum of a function, including a sequence of parameters, by changing one parameter at a time. The quantum circuits that implement Powell’s method are logically built by combining quantum computing units and basic quantum gates. The main contributions of this study are the quantum realization of a quadratic equation, the proposal of a quantum one-dimensional search algorithm, the quantum implementation of updating the searching direction array (SDA), and the quantum judgment of stopping the Powell’s iteration. A simulation demonstrates the execution of Powell’s method, and future applications, such as data fitting and image registration, are discussed.

scholarly journals Synthesis of quantum circuits in Linear Nearest neighbor Model using Positive Davio Lattices

2011 ◽  
Vol 24 (1) ◽  
pp. 71-87 ◽  
Author(s):  
Marek Perkowski ◽  
Martin Lukac ◽  
Dipal Shah ◽  
Michitaka Kameyama
Keyword(s):  
Nearest Neighbor ◽  
Dimensional Space ◽  
Synthesis Method ◽  
Logic Synthesis ◽  
Quantum Circuits ◽  
Quantum Gates ◽  
Synthesis Methods ◽  
Cost Models ◽  
Quantum Cost ◽  
One Dimensional

We present a logic synthesis method based on lattices that realize quantum arrays in One-Dimensional Ion Trap technology. This means that all gates are built from 2x2 quantum primitives that are located only on neighbor qubits in a one-dimensional space (called also vector of qubits or Linear Nearest Neighbor (LNN) architecture). The Logic circuits designed by the proposed method are realized only with 3*3 Toffoli, Feynman and NOT quantum gates and the usage of the commonly used multi-input Toffoli gates is avoided. This realization method of quantum circuits is different from most of reversible circuits synthesis methods from the literature that use only high level quantum cost based on the number of quantum gates. Our synthesis approach applies to both standard and LNN quantum cost models. It leads to entirely new CAD algorithms for circuit synthesis and substantially decreases the quantum cost for LNN quantum circuits. The drawback of synthesizing circuits in the presented LNN architecture is the addition of ancilla qubits.

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