scholarly journals Quantifying magic for multi-qubit operations

2019 ◽  
Vol 475 (2227) ◽  
pp. 20190251 ◽  
Author(s):  
James R. Seddon ◽  
Earl T. Campbell
Keyword(s):  
Fault Tolerant ◽  
Sample Complexity ◽  
Intermediate Scale ◽  
Quantum Operations ◽  
Classical Simulation ◽  
Qubit Operations ◽  
Treat All ◽  
General Circuits ◽  
Qubit States ◽  
Better Than

The development of a framework for quantifying ‘non-stabilizerness’ of quantum operations is motivated by the magic state model of fault-tolerant quantum computation and by the need to estimate classical simulation cost for noisy intermediate-scale quantum (NISQ) devices. The robustness of magic was recently proposed as a well-behaved magic monotone for multi-qubit states and quantifies the simulation overhead of circuits composed of Clifford +  T gates, or circuits using other gates from the Clifford hierarchy. Here we present a general theory of the ‘non-stabilizerness’ of quantum operations rather than states, which are useful for classical simulation of more general circuits. We introduce two magic monotones, called channel robustness and magic capacity, which are well-defined for general n -qubit channels and treat all stabilizer-preserving CPTP maps as free operations. We present two complementary Monte Carlo-type classical simulation algorithms with sample complexity given by these quantities and provide examples of channels where the complexity of our algorithms is exponentially better than previously known simulators. We present additional techniques that ease the difficulty of calculating our monotones for special classes of channels.

FAULT TOLERANT ROUTING IN HYPERCUBES AND STAR GRAPHS

1996 ◽  
Vol 06 (01) ◽  
pp. 127-136 ◽  
Author(s):  
QIAN-PING GU ◽  
SHIETUNG PENG
Keyword(s):  
Free Path ◽  
Fault Tolerant ◽  
Linear Time ◽  
Time Efficiency ◽  
Routing Problem ◽  
Star Graphs ◽  
Linear Time Algorithms ◽  
Better Than

In this paper, we give two linear time algorithms for node-to-node fault tolerant routing problem in n-dimensional hypercubes Hn and star graphs Gn. The first algorithm, given at most n−1 arbitrary fault nodes and two non-fault nodes s and t in Hn, finds a fault-free path s→t of length at most [Formula: see text] in O(n) time, where d(s, t) is the distance between s and t. Our second algorithm, given at most n−2 fault nodes and two non-fault nodes s and t in Gn, finds a fault-free path s→t of length at most d(Gn)+3 in O(n) time, where [Formula: see text] is the diameter of Gn. When the time efficiency of finding the routing path is more important than the length of the path, the algorithms in this paper are better than the previous ones.

scholarly journals Degenerate Quantum LDPC Codes With Good Finite Length Performance

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 585
Author(s):  
Pavel Panteleev ◽  
Gleb Kalachev
Keyword(s):  
Minimum Distance ◽  
Belief Propagation ◽  
Fault Tolerant ◽  
Large Family ◽  
Parity Check ◽  
Product Codes ◽  
Medium Length ◽  
Surface Code ◽  
Depolarizing Channel ◽  
Better Than

We study the performance of medium-length quantum LDPC (QLDPC) codes in the depolarizing channel. Only degenerate codes with the maximal stabilizer weight much smaller than their minimum distance are considered. It is shown that with the help of OSD-like post-processing the performance of the standard belief propagation (BP) decoder on many QLDPC codes can be improved by several orders of magnitude. Using this new BP-OSD decoder we study the performance of several known classes of degenerate QLDPC codes including hypergraph product codes, hyperbicycle codes, homological product codes, and Haah's cubic codes. We also construct several interesting examples of short generalized bicycle codes. Some of them have an additional property that their syndromes are protected by small BCH codes, which may be useful for the fault-tolerant syndrome measurement. We also propose a new large family of QLDPC codes that contains the class of hypergraph product codes, where one of the used parity-check matrices is square. It is shown that in some cases such codes have better performance than hypergraph product codes. Finally, we demonstrate that the performance of the proposed BP-OSD decoder for some of the constructed codes is better than for a relatively large surface code decoded by a near-optimal decoder.

scholarly journals Unipolar magnetic field pulses as an advantageous tool for ultrafast operations in superconducting Josephson “atoms”

2019 ◽  
Vol 10 ◽  
pp. 1548-1558
Author(s):  
Daria V Popolitova ◽  
Nikolay V Klenov ◽  
Igor I Soloviev ◽  
Sergey V Bakurskiy ◽  
Olga V Tikhonova
Keyword(s):  
Magnetic Field ◽  
Theoretical Approach ◽  
Magnetization Reversal ◽  
Population Transfer ◽  
Experimental Realization ◽  
Quantum Operations ◽  
Picosecond Time Scale ◽  
On Chip ◽  
Qubit States ◽  
Full Quantum

A theoretical approach to the consistent full quantum description of the ultrafast population transfer and magnetization reversal in superconducting meta-atoms induced by picosecond unipolar pulses of a magnetic field is developed. A promising scheme based on the regime of stimulated Raman Λ-type transitions between qubit states via upper-lying levels is suggested in order to provide ultrafast quantum operations on the picosecond time scale. The experimental realization of a circuit-on-chip for the discussed ultrafast control is presented.

scholarly journals Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography

2017 ◽  
Vol 8 (1) ◽  
Author(s):  
Robin Blume-Kohout ◽  
John King Gamble ◽  
Erik Nielsen ◽  
Kenneth Rudinger ◽  
Jonathan Mizrahi ◽  
...  
Keyword(s):  
Quantum Information ◽  
Fault Tolerance ◽  
Error Correction ◽  
Error Rate ◽  
Fault Tolerant ◽  
Fast Algorithms ◽  
Quantum Error Correction ◽  
Qubit Operations ◽  
Quantum Error ◽  
Qubit Operation

Abstract Quantum information processors promise fast algorithms for problems inaccessible to classical computers. But since qubits are noisy and error-prone, they will depend on fault-tolerant quantum error correction (FTQEC) to compute reliably. Quantum error correction can protect against general noise if—and only if—the error in each physical qubit operation is smaller than a certain threshold. The threshold for general errors is quantified by their diamond norm. Until now, qubits have been assessed primarily by randomized benchmarking, which reports a different error rate that is not sensitive to all errors, and cannot be compared directly to diamond norm thresholds. Here we use gate set tomography to completely characterize operations on a trapped-Yb+-ion qubit and demonstrate with greater than 95% confidence that they satisfy a rigorous threshold for FTQEC (diamond norm ≤6.7 × 10−4).

The Study on Protection Algorithms in Multi-Domain Optical Networks

2010 ◽  
Vol 121-122 ◽  
pp. 693-698
Author(s):  
Xue Yong Li ◽  
Guo Hong Gao ◽  
Guo Yi Miao ◽  
Shi Tao Yan
Keyword(s):  
Optical Networks ◽  
Fault Tolerant ◽  
Auxiliary Graph ◽  
Simulation Results ◽  
Better Than

This paper proposes two protection algorithms SBP and PBP with the waveband grouping in fault-tolerant multi-domain optical networks. We also present the concept of layered auxiliary graph to achieve the multi-domain waveband grouping. Simulation results show that PBP performed better than SBP.

scholarly journals FPETD: Fault-Tolerant and Privacy-Preserving Electricity Theft Detection

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Siliang Dong ◽  
Zhixin Zeng ◽  
Yining Liu
Keyword(s):  
Machine Learning ◽  
Data Privacy ◽  
Fault Tolerant ◽  
Privacy Preserving ◽  
User Privacy ◽  
Accuracy Rate ◽  
Electricity Theft ◽  
User Data ◽  
Dimensionality Reduction Method ◽  
Better Than

Electricity theft occurs from time to time in the smart grid, which can cause great losses to the power supplier, so it is necessary to prevent the occurrence of electricity theft. Using machine learning as an electricity theft detection tool can quickly lock participants suspected of electricity theft; however, directly publishing user data to the detector for machine learning-based detection may expose user privacy. In this paper, we propose a real-time fault-tolerant and privacy-preserving electricity theft detection (FPETD) scheme that combines n -source anonymity and a convolutional neural network (CNN). In our scheme, we designed a fault-tolerant raw data collection protocol to collect electricity data and cut off the correspondence between users and their data, thereby ensuring the fault tolerance and data privacy during the electricity theft detection process. Experiments have proven that our dimensionality reduction method makes our model have an accuracy rate of 92.86% for detecting electricity theft, which is much better than others.

scholarly journals Incident atrial fibrillation and its risk prediction in patients developing COVID-19: A machine learning based algorithm approach

2021 ◽  
Author(s):  
Ash Genaidy
Keyword(s):  
Machine Learning ◽  
The Elderly ◽  
Adverse Outcomes ◽  
Good Prediction ◽  
Main Effect Model ◽  
Effect Model ◽  
Main Effect ◽  
Index Value ◽  
Treat All ◽  
Better Than

Background The elderly multi-morbid patient is at high risk of adverse outcomes with COVID-19 complications, and in the general population, the development of incident AF is associated with worse outcomes in such patients. We therefore investigated incident AF risks in a large prospective population of elderly patients with/without incident COVID-19 cases and baseline cardiovascular/non-cardiovascular multi-morbidities. We used two approaches: main-effect modeling and secondly, a machine-learning (ML) approach accounting for complex dynamic relationships. Methods We studied a prospective elderly US cohort of 280592 patients from medical databases in a 8-month investigation of new COVID19 cases. Incident AF outcomes were examined in relationship to diverse multi-morbid conditions, COVID-19 status and demographic variables, with ML accounting for the dynamic nature of changing multimorbidity risk factors. Results Multi-morbidity contributed to the onset of confirmed COVID-19 cases with cognitive impairment (OR 1.69; 95%CI 1.52-1.88), anemia (OR 1.41; 95%CI 1.32-1.50), diabetes mellitus (OR 1.35; 95%CI 1.27-1.44) and vascular disease (OR 1.30; 95%CI 1.21-1.39) having the highest associations. A main effect model (C-index value 0.718) showed that COVID-19 had the highest association with incident AF cases (OR 3.12; 95%CI 2.61-3.710, followed by congestive heart failure (1.72; 95%CI 1.50-1.96), then coronary artery disease (OR 1.43; 95%CI 1.27-1.60) and valvular disease (1.42; 95%CI 1.26-1.60). The ML algorithm demonstrated improved discriminatory validity incrementally over the statistical main effect model (training: C-index 0.729, 95%CI 0.718-0.740; validation: C-index 0.704, 95%CI 0.687-0.72). Calibration of ML based formulation was satisfactory and better than the main-effect model. Decision curve analysis demonstrated that the clinical utility for the ML based formulation was better than the ‘treat all’ strategy and the main effect model. Conclusion COVID-19 status has major implications for incident AF in a cohort with diverse cardiovascular/non-cardiovascular multi-morbidities. Our approach accounting for dynamic multimorbidity changes had good prediction for incident AF amongst incident COVID19 cases.

scholarly journals Message Broadcasting via a New Fault Tolerant Irregular Advance Omega Network in Faulty and Nonfaulty Network Environments

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Ved Prakash Bhardwaj ◽  
Nitin
Keyword(s):  
Fault Tolerant ◽  
Interconnection Network ◽  
High Reliability ◽  
Low Cost ◽  
Routing Algorithm ◽  
Multiple Faults ◽  
Message Broadcasting ◽  
Double Switch ◽  
Better Than

Interconnection Network (IN) is a key element for all parallel processing applications. Multistage Interconnection Network (MIN) is an efficient IN for these applications, as it has the quality of excellent performance at low cost with high reliability. MINs are effective medium for message broadcasting. Doing the same task in faulty situations is a critical challenge. In this paper, we have presented a new Fault Tolerant Interconnection Network named as Irregular Advance Omega Network (IAON); also we have presented its routing algorithm. IAON is the modified form of Advance Omega Network. The proposed MIN can endure multiple faults and provides a suitable path between every source to every destination. We have examined the fault tolerance capacity of IAON and compared its performance with other existing MINs. In order to check the performance of proposed MIN, message broadcasting was performed in three conditions as follows: (1) when network was fault free; (2) when network was Single Switch Faulty in every stage; (3) when network was Double Switch Faulty in every stage. Results showed that IAON performed better than the earlier proposed MINs.

scholarly journals Quantum Algorithms for Simulating the Lattice Schwinger Model

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 306 ◽  
Author(s):  
Alexander F. Shaw ◽  
Pavel Lougovski ◽  
Jesse R. Stryker ◽  
Nathan Wiebe
Keyword(s):  
Quantum Electrodynamics ◽  
Quantum Computer ◽  
Fault Tolerant ◽  
Quantum Algorithms ◽  
Gauge Field Theories ◽  
Coupling Constant ◽  
Schwinger Model ◽  
Pair Density ◽  
Trotter Formula ◽  
Better Than

The Schwinger model (quantum electrodynamics in 1+1 dimensions) is a testbed for the study of quantum gauge field theories. We give scalable, explicit digital quantum algorithms to simulate the lattice Schwinger model in both NISQ and fault-tolerant settings. In particular, we perform a tight analysis of low-order Trotter formula simulations of the Schwinger model, using recently derived commutator bounds, and give upper bounds on the resources needed for simulations in both scenarios. In lattice units, we find a Schwinger model on N/2 physical sites with coupling constant x−1/2 and electric field cutoff x−1/2Λ can be simulated on a quantum computer for time 2xT using a number of T-gates or CNOTs in O~(N3/2T3/2xΛ) for fixed operator error. This scaling with the truncation Λ is better than that expected from algorithms such as qubitization or QDRIFT. Furthermore, we give scalable measurement schemes and algorithms to estimate observables which we cost in both the NISQ and fault-tolerant settings by assuming a simple target observable–the mean pair density. Finally, we bound the root-mean-square error in estimating this observable via simulation as a function of the diamond distance between the ideal and actual CNOT channels. This work provides a rigorous analysis of simulating the Schwinger model, while also providing benchmarks against which subsequent simulation algorithms can be tested.

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