scholarly journals The small stellated dodecahedron code and friends

2018 ◽  
Vol 376 (2123) ◽  
pp. 20170323 ◽  
Author(s):  
J. Conrad ◽  
C. Chamberland ◽  
N. P. Breuckmann ◽  
B. M. Terhal
Keyword(s):  
Quantum Mechanics ◽  
Fault Tolerant ◽  
Three Dimensional ◽  
Foundations Of Quantum Mechanics ◽  
Quantum Code ◽  
Contemporary Society ◽  
Parity Check ◽  
Logical Qubits ◽  
Surface Code ◽  
Logical Qubit

We explore a distance-3 homological CSS quantum code, namely the small stellated dodecahedron code, for dense storage of quantum information and we compare its performance with the distance-3 surface code. The data and ancilla qubits of the small stellated dodecahedron code can be located on the edges respectively vertices of a small stellated dodecahedron, making this code suitable for three-dimensional connectivity. This code encodes eight logical qubits into 30 physical qubits (plus 22 ancilla qubits for parity check measurements) in contrast with one logical qubit into nine physical qubits (plus eight ancilla qubits) for the surface code. We develop fault-tolerant parity check circuits and a decoder for this code, allowing us to numerically assess the circuit-based pseudo-threshold. This article is part of a discussion meeting issue ‘Foundations of quantum mechanics and their impact on contemporary society’.

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 The surface code with a twist

Quantum ◽  
2017 ◽  
Vol 1 ◽  
pp. 2 ◽  
Author(s):  
Theodore J. Yoder ◽  
Isaac H. Kim
Keyword(s):  
Quantum Error Correction ◽  
New Variety ◽  
Near Surface ◽  
Topological Quantum ◽  
Clifford Group ◽  
Logical Qubits ◽  
Surface Code ◽  
Quantum Error ◽  
Qubit Efficiency ◽  
Logical Qubit

The surface code is one of the most successful approaches to topological quantum error-correction. It boasts the smallest known syndrome extraction circuits and correspondingly largest thresholds. Defect-based logical encodings of a new variety called twists have made it possible to implement the full Clifford group without state distillation. Here we investigate a patch-based encoding involving a modified twist. In our modified formulation, the resulting codes, called triangle codes for the shape of their planar layout, have only weight-four checks and relatively simple syndrome extraction circuits that maintain a high, near surface-code-level threshold. They also use 25% fewer physical qubits per logical qubit than the surface code. Moreover, benefiting from the twist, we can implement all Clifford gates by lattice surgery without the need for state distillation. By a surgical transformation to the surface code, we also develop a scheme of doing all Clifford gates on surface code patches in an atypical planar layout, though with less qubit efficiency than the triangle code. Finally, we remark that logical qubits encoded in triangle codes are naturally amenable to logical tomography, and the smallest triangle code can demonstrate high-pseudothreshold fault-tolerance to depolarizing noise using just 13 physical qubits.

scholarly journals Extracontextuality and extravalence in quantum mechanics

2018 ◽  
Vol 376 (2123) ◽  
pp. 20170311 ◽  
Author(s):  
Alexia Auffèves ◽  
Philippe Grangier
Keyword(s):  
Quantum Mechanics ◽  
Quantum System ◽  
Foundations Of Quantum Mechanics ◽  
Point Of View ◽  
Contemporary Society ◽  
The Continuum

We develop the point of view where quantum mechanics results from the interplay between the quantized number of ‘modalities’ accessible to a quantum system, and the continuum of ‘contexts’ that are required to define these modalities. We point out the specific roles of ‘extracontextuality’ and ‘extravalence’ of modalities, and relate them to the Kochen–Specker and Gleason theorems. This article is part of a discussion meeting issue ‘Foundations of quantum mechanics and their impact on contemporary society’.

scholarly journals Operational locality in global theories

2018 ◽  
Vol 376 (2123) ◽  
pp. 20170321 ◽  
Author(s):  
Lea Krämer ◽  
Lídia del Rio
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Physical Theory ◽  
Foundations Of Quantum Mechanics ◽  
Building Blocks ◽  
Contemporary Society ◽  
Operational Model ◽  
State Spaces ◽  
Local Functions ◽  
Generalized Probability

Within a global physical theory, a notion of locality allows us to find and justify information-processing primitives, like non-signalling between distant agents. Here, we propose exploring the opposite direction: to take agents as the basic building blocks through which we test a physical theory, and recover operational notions of locality from signalling conditions. First, we introduce an operational model for the effective state spaces of individual agents, as well as the range of their actions. We then formulate natural secrecy conditions between agents and identify the aspects of locality relevant for signalling. We discuss the possibility of taking commutation of transformations as a primitive of physical theories, as well as applications to quantum theory and generalized probability frameworks. This ‘it from bit’ approach establishes an operational connection between local actions and local observations, and gives a global interpretation to concepts like discarding a subsystem or composing local functions. This article is part of a discussion meeting issue ‘Foundations of quantum mechanics and their impact on contemporary society’.

scholarly journals Locality and quantum mechanics

2018 ◽  
Vol 376 (2123) ◽  
pp. 20170320 ◽  
Author(s):  
W. G. Unruh
Keyword(s):  
Quantum Mechanics ◽  
Foundations Of Quantum Mechanics ◽  
Contemporary Society ◽  
Non Local

It is argued that it is best not to think of quantum mechanics as non-local, but rather that it is non-realistic. This article is part of a discussion meeting issue ‘Foundations of quantum mechanics and their impact on contemporary society’.

scholarly journals ‘Space is blue and birds fly through it’

2018 ◽  
Vol 376 (2123) ◽  
pp. 20170312 ◽  
Author(s):  
Carlo Rovelli
Keyword(s):  
Quantum Mechanics ◽  
Foundations Of Quantum Mechanics ◽  
Quantum States ◽  
Contemporary Society ◽  
Physical Variables

Quantum mechanics is not about ‘quantum states’: it is about values of physical variables. I give a short fresh presentation and update on the relational perspective on the theory, and a comment on its philosophical implications. This article is part of a discussion meeting issue ‘Foundations of quantum mechanics and their impact on contemporary society’.

scholarly journals Fault-Tolerant quantum computation with constant overhead

2014 ◽  
Vol 14 (15&16) ◽  
pp. 1339-1371
Author(s):  
Daniel Gottesman
Keyword(s):  
Fault Tolerant ◽  
Quantum Circuit ◽  
Error Correcting Codes ◽  
Parity Check ◽  
Low Density Parity Check ◽  
The Family ◽  
Minimum Number ◽  
Logical Qubits ◽  
Quantum Error ◽  
Parity Check Codes

What is the minimum number of extra qubits needed to perform a large fault-tolerant quantum circuit? Working in a common model of fault-tolerance, I show that in the asymptotic limit of large circuits, the ratio of physical qubits to logical qubits can be a constant. The construction makes use of quantum low-density parity check codes, and the asymptotic overhead of the protocol is equal to that of the family of quantum error-correcting codes underlying the fault-tolerant protocol.

scholarly journals A fault-tolerant non-Clifford gate for the surface code in two dimensions

2020 ◽  
Vol 6 (21) ◽  
pp. eaay4929 ◽  
Author(s):  
Benjamin J. Brown
Keyword(s):  
Fault Tolerant ◽  
Error Correcting Code ◽  
Three Dimensional ◽  
Logic Gates ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Decoding Algorithms ◽  
Future Technology ◽  
Surface Code ◽  
Three Dimensional Models

Fault-tolerant logic gates will consume a large proportion of the resources of a two-dimensional quantum computing architecture. Here we show how to perform a fault-tolerant non-Clifford gate with the surface code; a quantum error-correcting code now under intensive development. This alleviates the need for distillation or higher-dimensional components to complete a universal gate set. The operation uses both local transversal gates and code deformations over a time that scales with the size of the qubit array. An important component of the gate is a just-in-time decoder. These decoding algorithms allow us to draw upon the advantages of three-dimensional models using only a two-dimensional array of live qubits. Our gate is completed using parity checks of weight no greater than four. We therefore expect it to be amenable with near-future technology. As the gate circumvents the need for magic-state distillation, it may reduce the resource overhead of surface-code quantum computation considerably.

scholarly journals What is quantum in quantum randomness?

2018 ◽  
Vol 376 (2123) ◽  
pp. 20170322 ◽  
Author(s):  
P. Grangier ◽  
A. Auffèves
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Quantum Physics ◽  
Foundations Of Quantum Mechanics ◽  
Quantum Systems ◽  
Contemporary Society ◽  
Quantum Thermodynamics ◽  
Quantum Randomness ◽  
Classical World ◽  
The Impact

It is often said that quantum and classical randomness are of different nature, the former being ontological and the latter epistemological. However, so far the question of ‘What is quantum in quantum randomness?’, i.e. what is the impact of quantization and discreteness on the nature of randomness, remains to be answered. In a first part, we make explicit the differences between quantum and classical randomness within a recently proposed ontology for quantum mechanics based on contextual objectivity. In this view, quantum randomness is the result of contextuality and quantization. We show that this approach strongly impacts the purposes of quantum theory as well as its areas of application. In particular, it challenges current programmes inspired by classical reductionism, aiming at the emergence of the classical world from a large number of quantum systems. In a second part, we analyse quantum physics and thermodynamics as theories of randomness, unveiling their mutual influences. We finally consider new technological applications of quantum randomness that have opened up in the emerging field of quantum thermodynamics. This article is part of a discussion meeting issue ‘Foundations of quantum mechanics and their impact on contemporary society’.

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