Universal fault tolerant quantum computation on bilinear nearest neighbor arrays

2008 ◽  
Vol 8 (3&4) ◽  
pp. 330-344
Author(s):  
A.M. Stephens ◽  
A.G. Fowler ◽  
L.C.L. Hollenberg
Keyword(s):  
Lower Bound ◽  
Quantum Computation ◽  
Error Rate ◽  
Nearest Neighbor ◽  
Fault Tolerant ◽  
Quantum Code ◽  
Memory Errors ◽  
Memory Failure ◽  
Qubit Gate ◽  
Readout Error

Assuming an array that consists of two parallel lines of qubits and that permits only nearest neighbor interactions, we construct physical and logical circuitry to enable universal fault tolerant quantum computation under the $[[7,1,3]]$ quantum code. A rigorous lower bound to the fault tolerant threshold for this array is determined in a number of physical settings. Adversarial memory errors, two-qubit gate errors and readout errors are included in our analysis. In the setting where the physical memory failure rate is equal to one-tenth of the physical gate error rate, the physical readout error rate is equal to the physical gate error rate, and the duration of physical readout is ten times the duration of a physical gate, we obtain a lower bound to the asymptotic threshold of $1.96\times10^{-6}$.

scholarly journals Accuracy threshold for postselected quantum computation

2008 ◽  
Vol 8 (3&4) ◽  
pp. 181-244 ◽  
Author(s):  
P. Aliferis ◽  
D. Gottesman ◽  
J. Preskill
Keyword(s):  
Lower Bound ◽  
Quantum Computation ◽  
Error Detection ◽  
Fault Tolerant ◽  
Error Correcting Codes ◽  
Stochastic Noise ◽  
Strongly Correlated ◽  
Error Detecting ◽  
Error Detecting Code

We prove an accuracy threshold theorem for fault-tolerant quantum computation based on error detection and postselection. Our proof provides a rigorous foundation for the scheme suggested by Knill, in which preparation circuits for ancilla states are protected by a concatenated error-detecting code and the preparation is aborted if an error is detected. The proof applies to independent stochastic noise but (in contrast to proofs of the quantum accuracy threshold theorem based on concatenated error-correcting codes) not to strongly-correlated adversarial noise. Our rigorously established lower bound on the accuracy threshold, $1.04\times 10^{-3}$, is well below Knill's numerical estimates.

Polyestimate: a library for near-instantaneous surface code analysis

2015 ◽  
Vol 15 (1&2) ◽  
pp. 1034-1444
Author(s):  
Austin G. Fowler
Keyword(s):  
Quantum Computation ◽  
Error Rate ◽  
Nearest Neighbor ◽  
Careful Analysis ◽  
Error Rates ◽  
Code Analysis ◽  
Logical Error ◽  
Surface Code ◽  
User Friendly ◽  
Library User

The surface code is highly practical, enabling arbitrarily reliable quantum computation given a 2-D nearest-neighbor coupled array of qubits with gate error rates below approximately 1\%. We describe an open source library, Polyestimate, enabling a user with no knowledge of the surface code to specify realistic physical quantum gate error models and obtain logical error rate estimates. Functions allowing the user to specify simple depolarizing error rates for each gate have also been included. Every effort has been made to make this library user-friendly. Polyestimate provides data essentially instantaneously that previously required hundreds to thousands of hours of simulation, statements which we discuss and make precise. This advance has been made possible through careful analysis of the error structure of the surface code and extensive pre-simulation.

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 Threshold error penalty for fault-tolerant quantum computation with nearest neighbor communication

2006 ◽  
Vol 5 (1) ◽  
pp. 42-49 ◽  
Author(s):  
T. Szkopek ◽  
P.O. Boykin ◽  
Heng Fan ◽  
V.P. Roychowdhury ◽  
E. Yablonovitch ◽  
...  
Keyword(s):  
Quantum Computation ◽  
Nearest Neighbor ◽  
Fault Tolerant

scholarly journals ERROR THRESHOLD ESTIMATION BY MEANS OF THE [[7,1,3]] CSS QUANTUM CODE

2005 ◽  
Vol 03 (02) ◽  
pp. 371-393 ◽  
Author(s):  
P. J. SALAS ◽  
A. L. SANZ
Keyword(s):  
Quantum Computation ◽  
Error Probability ◽  
Fault Tolerant ◽  
Error Correcting Codes ◽  
Quantum Code ◽  
Threshold Estimation ◽  
Control Error ◽  
Threshold Conditions ◽  
Quantum Error ◽  
Depolarizing Channel

The states needed in quantum computation are extremely affected by decoherence. Several methods have been proposed to control error spreading. They use two main tools: fault-tolerant constructions and concatenated quantum error correcting codes. In this work, we estimate the threshold conditions necessary to make a long enough quantum computation. The [[7,1,3]] CSS quantum code together with the Shor method to measure the error syndrome is used. No concatenation is included. The decoherence is introduced by means of the depolarizing channel error model, obtaining several thresholds from the numerical simulation. Regarding the maintenance of a qubit stabilized in the memory, the error probability must be smaller than 2.9 × 10-5. In order to implement a one or two-qubit encoded gate in an effective fault-tolerant way, it is possible to choose an adequate non-encoded noisy gate if the memory error probability is smaller than 1.3 × 10-5. In addition, fulfilling this last condition permits us to assume a more efficient behavior compared to the equivalent non-encoded process.

scholarly journals Fault-Tolerant Quantum Computation with Constant Error Rate

2008 ◽  
Vol 38 (4) ◽  
pp. 1207-1282 ◽  
Author(s):  
Dorit Aharonov ◽  
Michael Ben-Or
Keyword(s):  
Quantum Computation ◽  
Error Rate ◽  
Constant Error ◽  
Fault Tolerant

A method of mapping and nearest neighbor optimization for 2-D quantum circuits

2020 ◽  
Vol 20 (3&4) ◽  
pp. 194-212
Author(s):  
Yuxin Zhang ◽  
Zhijin Guan ◽  
Longyong Ji ◽  
Qin Fang Luan ◽  
Yizhen Wang
Keyword(s):  
Quantum Computation ◽  
Nearest Neighbor ◽  
Quantum Circuit ◽  
Mapping Method ◽  
Quantum Circuits ◽  
Grid Structure ◽  
Quantum Bits ◽  
Physical Constraints ◽  
Swap Gate ◽  
Qubit Gate

In some practical quantum physical architectures, the qubits need to be distributed on 2-dimensional (2-D) grid structure to implement quantum computation. In order to map an 1-dimensional (1-D) quantum circuit into a 2-D grid structure and satisfy the nearest neighbor constraint of qubit interaction in the grid structure, a mapping method from 1-D quantum circuit to 2-D grid structure is proposed in this paper. This method firstly determines the order of placing qubits, and then presents the layout strategy of qubits in 2-D grid. We also proposed an algorithm for establishing interaction paths between non-adjacent qubits in 2-D grid structure, which can satisfy the physical constraints of the interaction of quantum bits in the grid in the process of mapping an 1-D quantum circuit to a 2-D grid structure. For some benchmark circuits, after using the method of this paper to place qubits, it is possible to make every 2-qubit gate in the circuit have a nearest neighbor, so that there is no need to use SWAP gate to establish channel routing. Compared with the latest available methods, the average optimization rate is 82.38%.

Quantum accuracy threshold for concatenated distance-3 code

2006 ◽  
Vol 6 (2) ◽  
pp. 97-165 ◽  
Author(s):  
P. Aliferis ◽  
D. Gottesman ◽  
J. Preskill
Keyword(s):  
Lower Bound ◽  
Fault Tolerant ◽  
Combinatorial Analysis ◽  
Noise Model ◽  
Computer Assisted ◽  
Quantum Code ◽  
Stochastic Noise ◽  
Noise Models ◽  
New Criteria ◽  
Inductive Analysis

We prove a new version of the quantum threshold theorem that applies to concatenation of a quantum code that corrects only one error, and we use this theorem to derive a rigorous lower bound on the quantum accuracy threshold $\varepsilon_0$. Our proof also applies to concatenation of higher-distance codes, and to noise models that allow faults to be correlated in space and in time. The proof uses new criteria for assessing the accuracy of fault-tolerant circuits, which are particularly conducive to the inductive analysis of recursive simulations. Our lower bound on the threshold, $\varepsilon_0 \ge 2.73\times 10^{-5}$ for an adversarial independent stochastic noise model, is derived from a computer-assisted combinatorial analysis; it is the best lower bound that has been rigorously proven so far.

scholarly journals Optimal two-qubit circuits for universal fault-tolerant quantum computation

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Andrew N. Glaudell ◽  
Neil J. Ross ◽  
Jacob M. Taylor
Keyword(s):  
Lower Bound ◽  
Normal Form ◽  
Quantum Computation ◽  
Normal Forms ◽  
Fault Tolerant ◽  
Quantum Circuits ◽  
Worst Case ◽  
Synthesis Algorithm ◽  
Phase Gate ◽  
Controlled Phase Gate

AbstractWe study two-qubit circuits over the Clifford+CS gate set, which consists of the Clifford gates together with the controlled-phase gate CS = diag(1, 1, 1, i). The Clifford+CS gate set is universal for quantum computation and its elements can be implemented fault-tolerantly in most error-correcting schemes through magic state distillation. Since non-Clifford gates are typically more expensive to perform in a fault-tolerant manner, it is often desirable to construct circuits that use few CS gates. In the present paper, we introduce an efficient and optimal synthesis algorithm for two-qubit Clifford+CS operators. Our algorithm inputs a Clifford+CS operator U and outputs a Clifford+CS circuit for U, which uses the least possible number of CS gates. Because the algorithm is deterministic, the circuit it associates to a Clifford+CS operator can be viewed as a normal form for that operator. We give an explicit description of these normal forms and use this description to derive a worst-case lower bound of $$5{{\rm{log}}}_{2}(\frac{1}{\epsilon })+O(1)$$ 5 log 2 ( 1 ϵ ) + O ( 1 ) on the number of CS gates required to ϵ-approximate elements of SU(4). Our work leverages a wide variety of mathematical tools that may find further applications in the study of fault-tolerant quantum circuits.

Optimizing Error Rate in Intrusion Detection System Using Artificial Neural Network Algorithm

2018 ◽  
Vol 6 (9) ◽  
pp. 152
Author(s):  
S. Vijaya Rani ◽  
G. N. K. Suresh Babu
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Intrusion Detection ◽  
Error Rate ◽  
Learning Process ◽  
Nearest Neighbor ◽  
Detection System ◽  
Support Vector ◽  
K Nearest Neighbor ◽  
Artificial Neural

The illegal hackers  penetrate the servers and networks of corporate and financial institutions to gain money and extract vital information. The hacking varies from one computing system to many system. They gain access by sending malicious packets in the network through virus, worms, Trojan horses etc. The hackers scan a network through various tools and collect information of network and host. Hence it is very much essential to detect the attacks as they enter into a network. The methods  available for intrusion detection are Naive Bayes, Decision tree, Support Vector Machine, K-Nearest Neighbor, Artificial Neural Networks. A neural network consists of processing units in complex manner and able to store information and make it functional for use. It acts like human brain and takes knowledge from the environment through training and learning process. Many algorithms are available for learning process This work carry out research on analysis of malicious packets and predicting the error rate in detection of injured packets through artificial neural network algorithms.

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