Noise threshold for a fault-tolerant two-dimensional lattice architecture

2007 ◽  
Vol 7 (4) ◽  
pp. 297-318
Author(s):  
K.M. Svore ◽  
D.P. DiVincenzo ◽  
B.M. Terhal
Keyword(s):  
Nearest Neighbor ◽  
Ion Trap ◽  
Fault Tolerant ◽  
Error Rates ◽  
Local Model ◽  
Dimensional Lattice ◽  
Coding Scheme ◽  
Local Setting ◽  
Noise Threshold ◽  
Model Affect

We consider a model of quantum computation in which the set of operations is limited to nearest-neighbor interactions on a 2D lattice. We model movement of qubits with noisy \SWAP\ operations. For this architecture we design a fault-tolerant coding scheme using the concatenated $[[7,1,3]]$ Steane code. Our scheme is potentially applicable to ion-trap and solid-state quantum technologies. We calculate a lower bound on the noise threshold for our local model using a detailed failure probability analysis. We obtain a threshold of $1.85 \times 10^{-5}$ for the local setting, where memory error rates are one-tenth of the failure rates of gates, measurement, and preparation steps. For the analogous nonlocal setting, we obtain a noise threshold of $3.61 \times 10^{-5}$. Our results thus show that the additional \SWAP\ operations required to move qubits in the local model affect the noise threshold only moderately.

scholarly journals Very low overhead fault-tolerant magic state preparation using redundant ancilla encoding and flag qubits

2020 ◽  
Vol 6 (1) ◽  
Author(s):  
Christopher Chamberland ◽  
Kyungjoo Noh
Keyword(s):  
Quantum Computing ◽  
Nearest Neighbor ◽  
Fault Tolerant ◽  
Error Correcting Code ◽  
Error Rates ◽  
High Quality ◽  
Color Code ◽  
Order Of Magnitude ◽  
Computing Platforms ◽  
Classical Computing

Abstract Fault-tolerant quantum computing promises significant computational speedup over classical computing for a variety of important problems. One of the biggest challenges for realizing fault-tolerant quantum computing is preparing magic states with sufficiently low error rates. Magic state distillation is one of the most efficient schemes for preparing high-quality magic states. However, since magic state distillation circuits are not fault-tolerant, all the operations in the distillation circuits must be encoded in a large distance error-correcting code, resulting in a significant resource overhead. Here, we propose a fault-tolerant scheme for directly preparing high-quality magic states, which makes magic state distillation unnecessary. In particular, we introduce a concept that we call redundant ancilla encoding. The latter combined with flag qubits allows for circuits to both measure stabilizer generators of some code, while also being able to measure global operators to fault-tolerantly prepare magic states, all using nearest neighbor interactions. We apply such schemes to a planar architecture of the triangular color code family and demonstrate that our scheme requires at least an order of magnitude fewer qubits and space–time overhead compared to the most competitive magic state distillation schemes. Since our scheme requires only nearest-neighbor interactions in a planar architecture, it is suitable for various quantum computing platforms currently under development.

scholarly journals Exponential suppression of bit or phase errors with cyclic error correction

Nature ◽  
2021 ◽  
Vol 595 (7867) ◽  
pp. 383-387
Author(s):  
◽  
Zijun Chen ◽  
Kevin J. Satzinger ◽  
Juan Atalaya ◽  
Alexander N. Korotkov ◽  
...  
Keyword(s):  
Error Correction ◽  
Error Detection ◽  
Fault Tolerant ◽  
Error Rates ◽  
Quantum Error Correction ◽  
Superconducting Qubits ◽  
Two Dimensional ◽  
Logical Error ◽  
Quantum Error ◽  
Logical Qubit

AbstractRealizing the potential of quantum computing requires sufficiently low logical error rates1. Many applications call for error rates as low as 10−15 (refs. 2–9), but state-of-the-art quantum platforms typically have physical error rates near 10−3 (refs. 10–14). Quantum error correction15–17 promises to bridge this divide by distributing quantum logical information across many physical qubits in such a way that errors can be detected and corrected. Errors on the encoded logical qubit state can be exponentially suppressed as the number of physical qubits grows, provided that the physical error rates are below a certain threshold and stable over the course of a computation. Here we implement one-dimensional repetition codes embedded in a two-dimensional grid of superconducting qubits that demonstrate exponential suppression of bit-flip or phase-flip errors, reducing logical error per round more than 100-fold when increasing the number of qubits from 5 to 21. Crucially, this error suppression is stable over 50 rounds of error correction. We also introduce a method for analysing error correlations with high precision, allowing us to characterize error locality while performing quantum error correction. Finally, we perform error detection with a small logical qubit using the 2D surface code on the same device18,19 and show that the results from both one- and two-dimensional codes agree with numerical simulations that use a simple depolarizing error model. These experimental demonstrations provide a foundation for building a scalable fault-tolerant quantum computer with superconducting qubits.

scholarly journals Predicting ionizing radiation exposure using biochemically-inspired genomic machine learning

F1000Research ◽  
2018 ◽  
Vol 7 ◽  
pp. 233
Author(s):  
Jonathan Z.L. Zhao ◽  
Eliseos J. Mucaki ◽  
Peter K. Rogan
Keyword(s):  
Machine Learning ◽  
Ionizing Radiation ◽  
Radiation Exposure ◽  
Large Scale ◽  
Nearest Neighbor ◽  
Error Rates ◽  
Support Vector ◽  
Dose Estimation ◽  
Gene Signatures ◽  
Ionizing Radiation Exposure

Background: Gene signatures derived from transcriptomic data using machine learning methods have shown promise for biodosimetry testing. These signatures may not be sufficiently robust for large scale testing, as their performance has not been adequately validated on external, independent datasets. The present study develops human and murine signatures with biochemically-inspired machine learning that are strictly validated using k-fold and traditional approaches. Methods: Gene Expression Omnibus (GEO) datasets of exposed human and murine lymphocytes were preprocessed via nearest neighbor imputation and expression of genes implicated in the literature to be responsive to radiation exposure (n=998) were then ranked by Minimum Redundancy Maximum Relevance (mRMR). Optimal signatures were derived by backward, complete, and forward sequential feature selection using Support Vector Machines (SVM), and validated using k-fold or traditional validation on independent datasets. Results: The best human signatures we derived exhibit k-fold validation accuracies of up to 98% (DDB2,  PRKDC, TPP2, PTPRE, and GADD45A) when validated over 209 samples and traditional validation accuracies of up to 92% (DDB2,  CD8A,  TALDO1,  PCNA,  EIF4G2,  LCN2,  CDKN1A,  PRKCH,  ENO1,  and PPM1D) when validated over 85 samples. Some human signatures are specific enough to differentiate between chemotherapy and radiotherapy. Certain multi-class murine signatures have sufficient granularity in dose estimation to inform eligibility for cytokine therapy (assuming these signatures could be translated to humans). We compiled a list of the most frequently appearing genes in the top 20 human and mouse signatures. More frequently appearing genes among an ensemble of signatures may indicate greater impact of these genes on the performance of individual signatures. Several genes in the signatures we derived are present in previously proposed signatures. Conclusions: Gene signatures for ionizing radiation exposure derived by machine learning have low error rates in externally validated, independent datasets, and exhibit high specificity and granularity for dose estimation.

Thermal conduction in a quasi-stationary one-dimensional lattice system

2019 ◽  
Vol 33 (17) ◽  
pp. 1950178
Author(s):  
Mohammad Khorrami ◽  
Amir Aghamohammadi
Keyword(s):  
Heat Transfer ◽  
Ising Model ◽  
Diffusion Equation ◽  
Thermal Conduction ◽  
Nearest Neighbor ◽  
Entropy Change ◽  
Neighbor Interaction ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Special Case

A system of nearest-neighbor interaction on a one-dimensional lattice is investigated, which has a quasi-stationary (and position-dependent) temperature profile. The rates of heat transfer and entropy change, as well as the diffusion equation for the temperature are studied. A q-state Potts model, and its special case, a two-state Ising model, are considered as an example.

scholarly journals The connection between vortex-like topological excitations and conventional excitations in quantum ferromagnetic spin systems on two-dimensional lattice and their stability

2015 ◽  
Vol 29 (29) ◽  
pp. 1550209
Author(s):  
Subhajit Sarkar ◽  
Ranjan Chaudhury ◽  
Samir K. Paul
Keyword(s):  
Nearest Neighbor ◽  
Magnetic Measurements ◽  
Spin Dynamics ◽  
Threshold Value ◽  
System Size ◽  
Heisenberg Ferromagnet ◽  
Two Dimensional ◽  
Stable States ◽  
Dimensional Lattice ◽  
Topological Excitations

In this paper, we present a scheme for the construction of quantum states of vortex-like topological excitations corresponding to spin-1/2 strongly XY-anisotropic nearest neighbor Heisenberg ferromagnet on two-dimensional lattice. The procedure involving Pauli spin basis states is carried out corresponding to both infinite dilute limit and finite density limit of vortex/anti-vortex. It is found that the corresponding quantum mechanical states representing charge 1 quantum vortices/anti-vortices can be expressed as linear combinations of single magnon states, composite multi-magnon states and the ground state. Detailed calculations show that these states are quantum mechanically stable states of the Hamiltonian only when the system size exceeds certain threshold value. Our analysis indicates that the interactions between different magnon modes can very well generate these topological excitations. Possible applications of our calculations to real magnetic systems are also discussed. Magnetic measurements probing spin dynamics may be undertaken to verify the existence of the threshold size for the stability of vortices.

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