scholarly journals Probabilistic Fault-Tolerant Universal Quantum Computation and sampling problems in Continuous Variables

2019 ◽  
Author(s):  
Tom Douce ◽  
Damian Markham ◽  
Elham Kashefi ◽  
Peter van Loock ◽  
Giulia Ferrini
Keyword(s):  
Quantum Computation ◽  
Fault Tolerant ◽  
Continuous Variables ◽  
Universal Quantum ◽  
Sampling Problems

scholarly journals Probabilistic fault-tolerant universal quantum computation and sampling problems in continuous variables

2019 ◽  
Vol 99 (1) ◽  
Author(s):  
Tom Douce ◽  
Damian Markham ◽  
Elham Kashefi ◽  
Peter van Loock ◽  
Giulia Ferrini
Keyword(s):  
Quantum Computation ◽  
Fault Tolerant ◽  
Continuous Variables ◽  
Universal Quantum ◽  
Sampling Problems

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
Keyword(s):  
Quantum Computation ◽  
Fault Tolerant ◽  
Universal Quantum

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 Theory of decoherence-free fault-tolerant universal quantum computation

2001 ◽  
Vol 63 (4) ◽  
Author(s):  
J. Kempe ◽  
D. Bacon ◽  
D. A. Lidar ◽  
K. B. Whaley
Keyword(s):  
Quantum Computation ◽  
Fault Tolerant ◽  
Universal Quantum

Graphical algorithms and threshold error rates for the 2d color code

2010 ◽  
Vol 10 (9&10) ◽  
pp. 780-802
Author(s):  
David S. Wang ◽  
Austin G. Fowler ◽  
Charles D. Hill ◽  
Lloyd C.L. Hollenberg
Keyword(s):  
Quantum Computation ◽  
Error Rate ◽  
Graph Matching ◽  
Fault Tolerant ◽  
Error Rates ◽  
Color Code ◽  
Clifford Group ◽  
Universal Quantum ◽  
Surface Code ◽  
Topological Error

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\%.

scholarly journals Deterministic generation of a two-dimensional cluster state

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
Keyword(s):  
Quantum Computation ◽  
Quantum Information Processing ◽  
Fault Tolerant ◽  
Cluster State ◽  
Two Dimensional ◽  
Cluster States ◽  
Squeezed Light ◽  
Universal Quantum ◽  
Speed Up ◽  
Quantum Error

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.

scholarly journals Author Correction: Roads towards fault-tolerant universal quantum computation

Nature ◽  
2018 ◽  
Vol 559 (7713) ◽  
pp. E6-E6
Author(s):  
Earl T. Campbell ◽  
Barbara M. Terhal ◽  
Christophe Vuillot
Keyword(s):  
Quantum Computation ◽  
Fault Tolerant ◽  
Universal Quantum

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 Nonadaptive fault-tolerant verification of quantum supremacy with noise

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 164 ◽  
Author(s):  
Theodoros Kapourniotis ◽  
Animesh Datta
Keyword(s):  
Error Detection ◽  
Fault Tolerant ◽  
Square Lattice ◽  
Verification Scheme ◽  
Universal Quantum ◽  
Near Term ◽  
Quantum Polynomial ◽  
Sampling Problems ◽  
Qubit States

Quantum samplers are believed capable of sampling efficiently from distributions that are classically hard to sample from. We consider a sampler inspired by the classical Ising model. It is nonadaptive and therefore experimentally amenable. Under a plausible conjecture, classical sampling upto additive errors from this model is known to be hard. We present a trap-based verification scheme for quantum supremacy that only requires the verifier to prepare single-qubit states. The verification is done on the same model as the original sampler, a square lattice, with only a constant overhead. We next revamp our verification scheme in two distinct ways using fault tolerance that preserves the nonadaptivity. The first has a lower overhead based on error correction with the same threshold as universal quantum computation. The second has a higher overhead but an improved threshold (1.97%) based on error detection. We show that classically sampling upto additive errors is likely hard in both these schemes. Our results are applicable to other sampling problems such as the Instantaneous Quantum Polynomial-time (IQP) computation model. They should also assist near-term attempts at experimentally demonstrating quantum supremacy and guide long-term ones.

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