scholarly journals Roads towards fault-tolerant universal quantum computation

Nature ◽  
2017 ◽  
Vol 549 (7671) ◽  
pp. 172-179 ◽  
Author(s):  
Earl T. Campbell ◽  
Barbara M. Terhal ◽  
Christophe Vuillot
2003 ◽  
Vol 01 (01) ◽  
pp. 1-23 ◽  
Author(s):  
VLATKO VEDRAL

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.


2001 ◽  
Vol 63 (4) ◽  
Author(s):  
J. Kempe ◽  
D. Bacon ◽  
D. A. Lidar ◽  
K. B. Whaley

2010 ◽  
Vol 10 (9&10) ◽  
pp. 780-802
Author(s):  
David S. Wang ◽  
Austin G. Fowler ◽  
Charles D. Hill ◽  
Lloyd C.L. Hollenberg

Recent work on fault-tolerant quantum computation making use of topological error correction shows great potential, with the 2d surface code possessing a threshold error rate approaching 1\%. However, the 2d surface code requires the use of a complex state distillation procedure to achieve universal quantum computation. The color code of is a related scheme partially solving the problem, providing a means to perform all Clifford group gates transversally. We review the color code and its error correcting methodology, discussing one approximate technique based on graph matching. We derive an analytic lower bound to the threshold error rate of 6.25\% under error-free syndrome extraction, while numerical simulations indicate it may be as high as 13.3\%. Inclusion of faulty syndrome extraction circuits drops the threshold to approximately 0.10 \pm 0.01\%.


Science ◽  
2019 ◽  
Vol 366 (6463) ◽  
pp. 369-372 ◽  
Author(s):  
Mikkel V. Larsen ◽  
Xueshi Guo ◽  
Casper R. Breum ◽  
Jonas S. Neergaard-Nielsen ◽  
Ulrik L. Andersen

Measurement-based quantum computation offers exponential computational speed-up through simple measurements on a large entangled cluster state. We propose and demonstrate a scalable scheme for the generation of photonic cluster states suitable for universal measurement-based quantum computation. We exploit temporal multiplexing of squeezed light modes, delay loops, and beam-splitter transformations to deterministically generate a cylindrical cluster state with a two-dimensional (2D) topological structure as required for universal quantum information processing. The generated state consists of more than 30,000 entangled modes arranged in a cylindrical lattice with 24 modes on the circumference, defining the input register, and a length of 1250 modes, defining the computation depth. Our demonstrated source of two-dimensional cluster states can be combined with quantum error correction to enable fault-tolerant quantum computation.


Nature ◽  
2018 ◽  
Vol 559 (7713) ◽  
pp. E6-E6
Author(s):  
Earl T. Campbell ◽  
Barbara M. Terhal ◽  
Christophe Vuillot

2012 ◽  
Vol 12 (9&10) ◽  
pp. 876-892
Author(s):  
Ben W. Reichardt

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.


2019 ◽  
Vol 99 (1) ◽  
Author(s):  
Tom Douce ◽  
Damian Markham ◽  
Elham Kashefi ◽  
Peter van Loock ◽  
Giulia Ferrini

2021 ◽  
Author(s):  
Atsushi Sakguchi ◽  
Shunya Konno ◽  
Fumiya Hanamura ◽  
Hisashi Ogawa ◽  
Kan Takase ◽  
...  

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