Exponential suppression of bit or phase errors with cyclic error correction

Realizing 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.

Rectangular surface code under biased noise

To date, the surface code has become a promising candidate for quantum error correcting codes because it achieves a high threshold and is composed of only the nearest gate operations and low-weight stabilizers. Here, we have exhibited that the logical failure rate can be enhanced by manipulating the lattice size of surface codes that they can show an enormous improvement in the number of physical qubits for a noise model where dephasing errors dominate over relaxation errors. We estimated the logical error rate in terms of the lattice size and physical error rate. When the physical error rate was high, the parameter estimation method was applied, and when it was low, the most frequently occurring logical error cases were considered. By using the minimum weight perfect matching decoding algorithm, we obtained the optimal lattice size by minimizing the number of qubits to achieve the required failure rates when physical error rates and bias are provided .

Introduction

This introductory chapter provides an overview of suicide in the military, detailing the author’s experience in Iraq. The prevailing method for suicide prevention was limited by survival bias, a logical error wherein we focus on the people or things that survive some selection process while overlooking those who did not. This book challenges some of the core assumptions about suicide and typical practices that may not be so helpful or useful after all. It also presents alternative perspectives that implicate different approaches that may work better than prevailing methods. These alternative perspectives have been heavily influenced by the many suicidal individuals who have shared their experiences, trials, and triumphs.

Leakage detection for a transmon-based surface code

Leakage outside of the qubit computational subspace, present in many leading experimental platforms, constitutes a threatening error for quantum error correction (QEC) for qubits. We develop a leakage-detection scheme via Hidden Markov models (HMMs) for transmon-based implementations of the surface code. By performing realistic density-matrix simulations of the distance-3 surface code (Surface-17), we observe that leakage is sharply projected and leads to an increase in the surface-code defect probability of neighboring stabilizers. Together with the analog readout of the ancilla qubits, this increase enables the accurate detection of the time and location of leakage. We restore the logical error rate below the memory break-even point by post-selecting out leakage, discarding less than half of the data for the given noise parameters. Leakage detection via HMMs opens the prospect for near-term QEC demonstrations, targeted leakage reduction and leakage-aware decoding and is applicable to other experimental platforms.

On the Issue of the Substitution of Concepts in Determining the Subjects of the Political System of Society (Based on a Critical Analysis of Modern Legal Literature on the Theory of State and Law)

This scientific article is devoted to some theoretical problems of the theory of the political system of society. The purpose of the article is to show the true, objective position in relation to the subjects of the political system. To solve this goal, the following tasks were set: a critical analysis of the opinions of those authors who consider as such: 1) criminal communities; 2) public organizations with an insignificant political aspect. Moreover, both in the first and in the second case, it has been proven that scientists are engaged in the substitution of concepts, that is, they commit a logical error. Result: 1) criminal associations are not subjects of the political system of society; 2) according to the political criterion, it is necessary to distinguish only proper political and not proper political organizations; 3) general theoretical provisions, opposite to those stated, differing in illogicality, do not contribute to improving the quality of educational literature on the theory of state and law.

ANALISIS KESALAHAN MAHASISWA PGSD DALAM MENYELESAIKAN MASALAH GEOMETRI

One of the courses have often difficult by pre service teacher in primary education is Geometry, evidently by learning outcome that are still low. Difficulties experienced by students led to an error occurred in solving problem in geometry. Errors that occur when students solve problems in geometry really need to be known, especially the type of error. One of procedure that can be used to reveal the student error is Newman procedure. This research employed a descriptive qualitative method that aimed to analyze the errors of pre service teacher in primary education when solve the problems in geometry. Participants in this research were two students who have taken the courses of Geometry and meet the criteria which is experiencing a mathematical error. Data collection technique use a question sheet and interviews. Question sheet given in order to analyze student errors that appear. While the interviews were conducted to confirm the results of student work. The results showed that the four stages of the procedure of Newman Error Analyze that comprehension, transformation, process skill and encoding occur mathematical error, logical error and strategic error. Furthermore, as new findings in this research, the error experienced by the students at this stage of the procedure Newman can cause errors in the later stages.

Multiple Keyword Searching Method Implementation for Data Searching on Data Center Application at P4M Stmik Dipanegara Makassar

Center for Development of Research and Community Service (P4M) is a place where the entire academic community, especially at the Dipanegara School of Informatics and Computer Management (STMIK Dipanegara) Makassar, is looking for data on writing about the development of research and community service that has been done. However, until now there is no system that manages all the data in Center for Development of Research and Community Service (P4M) STMIK Dipanegara Makassar, so the academic community is still having difficulty searching for data related to P4M in the forms of journal data, Plus Field Work Lecture (KKLP) data and all data handled by P4M STMIK Dipanegara Makassar. To fulfil these needs, a system that can manage the data is required, a system that has an effective and more efficient search. The effective search referred to in this case is a search that can trace all data related to keywords entered by the user, commonly referred to as Multiple Keyword Searching. With this system, it will be very easy for the user (academic community) to browse Data/Documents related to P4M STMIK Dipanegara Makassar and from the results of white box testing, there is no logical error in the application of Multiple Keyword Searching.