scholarly journals The XZZX surface code

2020 ◽  
Author(s):  
J. Bonilla Ataides ◽  
David Tuckett ◽  
Stephen Bartlett ◽  
Steven Flammia ◽  
Benjamin Brown
Keyword(s):  
Quantum Computation ◽  
High Performance ◽  
Fault Tolerant ◽  
Small Scale ◽  
Single Qubit ◽  
The Common ◽  
Surface Code ◽  
Random Codes ◽  
Relevant Range ◽  
Common Situation

Abstract We show that a variant of the surface code—the XZZX code—offers remarkable performance for fault-tolerant quantum computation. The error threshold of this code matches what can be achieved with random codes (hashing) for every single-qubit Pauli noise channel; it is the first explicit code shown to have this universal property. We present numerical evidence that the threshold even exceeds this hashing bound for an experimentally relevant range of noise parameters. Focusing on the common situation where qubit dephasing is the dominant noise, we show that this code has a practical, high-performance decoder and surpasses all previously known thresholds in the realistic setting where syndrome measurements are unreliable. We go on to demonstrate the favorable sub-threshold resource scaling that can be obtained by specializing a code to exploit structure in the noise. We show that it is possible to maintain all of these advantages when we perform fault-tolerant quantum computation. We finally suggest some small-scale experiments that could exploit noise bias to reduce qubit overhead in two-dimensional architectures

scholarly journals The XZZX surface code

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
J. Pablo Bonilla Ataides ◽  
David K. Tuckett ◽  
Stephen D. Bartlett ◽  
Steven T. Flammia ◽  
Benjamin J. Brown
Keyword(s):  
Quantum Computation ◽  
High Performance ◽  
Quantum Computer ◽  
Fault Tolerant ◽  
Error Correcting Codes ◽  
The Common ◽  
Surface Code ◽  
Random Codes ◽  
Quantum Error ◽  
Relevant Range

AbstractPerforming large calculations with a quantum computer will likely require a fault-tolerant architecture based on quantum error-correcting codes. The challenge is to design practical quantum error-correcting codes that perform well against realistic noise using modest resources. Here we show that a variant of the surface code—the XZZX code—offers remarkable performance for fault-tolerant quantum computation. The error threshold of this code matches what can be achieved with random codes (hashing) for every single-qubit Pauli noise channel; it is the first explicit code shown to have this universal property. We present numerical evidence that the threshold even exceeds this hashing bound for an experimentally relevant range of noise parameters. Focusing on the common situation where qubit dephasing is the dominant noise, we show that this code has a practical, high-performance decoder and surpasses all previously known thresholds in the realistic setting where syndrome measurements are unreliable. We go on to demonstrate the favourable sub-threshold resource scaling that can be obtained by specialising a code to exploit structure in the noise. We show that it is possible to maintain all of these advantages when we perform fault-tolerant quantum computation.

scholarly journals Lattice Surgery with a Twist: Simplifying Clifford Gates of Surface Codes

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 62 ◽  
Author(s):  
Daniel Litinski ◽  
Felix von Oppen
Keyword(s):  
Quantum Computation ◽  
Long Range ◽  
Fault Tolerant ◽  
Planar Surface ◽  
Single Qubit ◽  
Control Target ◽  
Surface Code ◽  
Time Overhead

We present a planar surface-code-based scheme for fault-tolerant quantum computation which eliminates the time overhead of single-qubit Clifford gates, and implements long-range multi-target CNOT gates with a time overhead that scales only logarithmically with the control-target separation. This is done by replacing hardware operations for single-qubit Clifford gates with a classical tracking protocol. Inter-qubit communication is added via a modified lattice surgery protocol that employs twist defects of the surface code. The long-range multi-target CNOT gates facilitate magic state distillation, which renders our scheme fault-tolerant and universal.

scholarly journals Path-optimized nonadiabatic geometric quantum computation on superconducting qubits

2021 ◽  
Author(s):  
Cheng-Yun Ding ◽  
Li-Na Ji ◽  
Tao Chen ◽  
Zheng-Yuan Xue
Keyword(s):  
Quantum Computation ◽  
Large Scale ◽  
Fault Tolerant ◽  
High Fidelity ◽  
Noise Resistance ◽  
Geometric Phases ◽  
Single Qubit ◽  
Phase Gate ◽  
New Perspective ◽  
Geometric Quantum Computation

Abstract Quantum computation based on nonadiabatic geometric phases has attracted a broad range of interests, due to its fast manipulation and inherent noise resistance. However, it is limited to some special evolution paths, and the gate-times are typically longer than conventional dynamical gates, resulting in weakening of robustness and more infidelities of the implemented geometric gates. Here, we propose a path-optimized scheme for geometric quantum computation on superconducting transmon qubits, where high-fidelity and robust universal nonadiabatic geometric gates can be implemented, based on conventional experimental setups. Specifically, we find that, by selecting appropriate evolution paths, the constructed geometric gates can be superior to their corresponding dynamical ones under different local errors. Numerical simulations show that the fidelities for single-qubit geometric Phase, $\pi/8$ and Hadamard gates can be obtained as $99.93\%$, $99.95\%$ and $99.95\%$, respectively. Remarkably, the fidelity for two-qubit control-phase gate can be as high as $99.87\%$. Therefore, our scheme provides a new perspective for geometric quantum computation, making it more promising in the application of large-scale fault-tolerant quantum computation.

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 The boundaries and twist defects of the color code and their applications to topological quantum computation

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 101 ◽  
Author(s):  
Markus S. Kesselring ◽  
Fernando Pastawski ◽  
Jens Eisert ◽  
Benjamin J. Brown
Keyword(s):  
Quantum Computation ◽  
Domain Walls ◽  
Fault Tolerant ◽  
Error Correcting Codes ◽  
Two Dimensions ◽  
Abstract Theory ◽  
Color Code ◽  
Topological Quantum ◽  
Multiple Copies ◽  
Surface Code

The color code is both an interesting example of an exactly solved topologically ordered phase of matter and also among the most promising candidate models to realize fault-tolerant quantum computation with minimal resource overhead. The contributions of this work are threefold. First of all, we build upon the abstract theory of boundaries and domain walls of topological phases of matter to comprehensively catalog the objects realizable in color codes. Together with our classification we also provide lattice representations of these objects which include three new types of boundaries as well as a generating set for all 72 color code twist defects. Our work thus provides an explicit toy model that will help to better understand the abstract theory of domain walls. Secondly, we discover a number of interesting new applications of the cataloged objects for quantum information protocols. These include improved methods for performing quantum computations by code deformation, a new four-qubit error-detecting code, as well as families of new quantum error-correcting codes we call stellated color codes, which encode logical qubits at the same distance as the next best color code, but using approximately half the number of physical qubits. To the best of our knowledge, our new topological codes have the highest encoding rate of local stabilizer codes with bounded-weight stabilizers in two dimensions. Finally, we show how the boundaries and twist defects of the color code are represented by multiple copies of other phases. Indeed, in addition to the well studied comparison between the color code and two copies of the surface code, we also compare the color code to two copies of the three-fermion model. In particular, we find that this analogy offers a very clear lens through which we can view the symmetries of the color code which gives rise to its multitude of domain walls.

Ḥadith ‘Āishah fī Man’i al-Nisā’ Min al-Masājid; Niqāsh ‘Ulamā’ Bangladesh Ḥaulahu

2020 ◽  
Vol 9 (1) ◽  
pp. 97-115
Author(s):  
Syed Mahmudul Hasan
Keyword(s):  
Analytical Method ◽  
Inductive Method ◽  
The Common ◽  
The Difference ◽  
Common Situation

The Narration of Aisyah (May Allah be pleased with her), is the main focus of the controversy among Bangladeshi scholars on the issue of women's prayer in the mosque. The reason for the dispute is that a group of them issued the ruling based on the phenomenon of the text, and the others explained the ruling of Hadith according to the common situation in the society. If the circumstances change, the ruling will change along with it, because the originality of the issue is permissible, that is proven from other texts. This research adopts an inductive method to survey the Prophetic hadiths that talk about the prayer of women in the Mosque in terms of permissibility and prohibition and analytical method to analyze the difference in opinion of Bangladeshi scholars related to this issue. The research finds that the ruling of Shari’ah is a process that is continuous and permanent. But in necessity and emergency, it has the notion of flexibility and explanation. In the issue of women’s presence in the mosque, they should be allowed if they abide by the suggestions of Prophet (s) and should not if they don’t. So, Prohibition is not from the prophet (s), but it is from their obedience to the ruling.

Student Perceptions of Community: A Different Perspective

NASPA Journal ◽  
1998 ◽  
Vol 35 (4) ◽  
Author(s):  
Jackie Clark ◽  
Joan Hirt
Keyword(s):  
Student Perceptions ◽  
Large Scale ◽  
Research University ◽  
Small Scale ◽  
Social Environments ◽  
Common Assumption ◽  
Small Communities ◽  
Public Research University ◽  
The Common ◽  
Using Data

The creation of small communities has been proposed as a way of enhancing the educational experience of students at large institutions. Using data from a survey of students living in large and small residences at a public research university, this study does not support the common assumption that small-scale social environments are more conducive to positive community life than large-scale social environments.

scholarly journals Blind quantum computation where a user only performs single-qubit gates

2021 ◽  
Vol 142 ◽  
pp. 107190
Author(s):  
Qin Li ◽  
Chengdong Liu ◽  
Yu Peng ◽  
Fang Yu ◽  
Cai Zhang
Keyword(s):  
Quantum Computation ◽  
Single Qubit ◽  
Blind Quantum Computation

scholarly journals Fast Comparison of High-Precision Time Scales Using GNSS Receivers

2017 ◽  
Vol 2017 ◽  
pp. 1-4
Author(s):  
Vojtech Vigner ◽  
Jaroslav Roztocil
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
High Performance ◽  
Data Format ◽  
Common View ◽  
Log Files ◽  
Gnss Receivers ◽  
Precision Time ◽  
The Common ◽  
The Difference

Comparison of high-performance time scales generated by atomic clocks in laboratories of time and frequency metrology is usually performed by means of the Common View method. Laboratories are equipped with specialized GNSS receivers which measure the difference between a local time scale and a time scale of the selected satellite. Every receiver generates log files in CGGTTS data format to record measured differences. In order to calculate time differences recorded by two receivers, it is necessary to obtain these logs from both receivers and process them. This paper deals with automation and speeding up of these processes.

Sign in / Sign up

Export Citation Format

Share Document