scholarly journals Quantum teleportation of physical qubits into logical code spaces

2021 ◽  
Vol 118 (36) ◽  
pp. e2026250118
Author(s):  
Yi-Han Luo ◽  
Ming-Cheng Chen ◽  
Manuel Erhard ◽  
Han-Sen Zhong ◽  
Dian Wu ◽  
...  
Keyword(s):  
Quantum Information ◽  
Large Scale ◽  
Fault Tolerant ◽  
Quantum Error Correction ◽  
Quantum Circuits ◽  
Entangled State ◽  
Maximally Entangled State ◽  
Universal Quantum ◽  
Quantum Error ◽  
Logical Qubit

Quantum error correction is an essential tool for reliably performing tasks for processing quantum information on a large scale. However, integration into quantum circuits to achieve these tasks is problematic when one realizes that nontransverse operations, which are essential for universal quantum computation, lead to the spread of errors. Quantum gate teleportation has been proposed as an elegant solution for this. Here, one replaces these fragile, nontransverse inline gates with the generation of specific, highly entangled offline resource states that can be teleported into the circuit to implement the nontransverse gate. As the first important step, we create a maximally entangled state between a physical and an error-correctable logical qubit and use it as a teleportation resource. We then demonstrate the teleportation of quantum information encoded on the physical qubit into the error-corrected logical qubit with fidelities up to 0.786. Our scheme can be designed to be fully fault tolerant so that it can be used in future large-scale quantum technologies.

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 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).

scholarly journals Cost-optimal single-qubit gate synthesis in the Clifford hierarchy

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 396
Author(s):  
Gary J. Mooney ◽  
Charles D. Hill ◽  
Lloyd C. L. Hollenberg
Keyword(s):  
Error Correction ◽  
Quantum Information Processing ◽  
Fault Tolerant ◽  
Quantum Error Correction ◽  
Practical Implementation ◽  
Error Correction Code ◽  
Universal Quantum ◽  
Arbitrary Precision ◽  
Qubit Gate ◽  
Quantum Error

For universal quantum computation, a major challenge to overcome for practical implementation is the large amount of resources required for fault-tolerant quantum information processing. An important aspect is implementing arbitrary unitary operators built from logical gates within the quantum error correction code. A synthesis algorithm can be used to approximate any unitary gate up to arbitrary precision by assembling sequences of logical gates chosen from a small set of universal gates that are fault-tolerantly performable while encoded in a quantum error-correction code. However, current procedures do not yet support individual assignment of base gate costs and many do not support extended sets of universal base gates. We analysed cost-optimal sequences using an exhaustive search based on Dijkstra’s pathfinding algorithm for the canonical Clifford+T set of base gates and compared them to when additionally including Z-rotations from higher orders of the Clifford hierarchy. Two approaches of assigning base gate costs were used. First, costs were reduced to T-counts by recursively applying a Z-rotation catalyst circuit. Second, costs were assigned as the average numbers of raw (i.e. physical level) magic states required to directly distil and implement the gates fault-tolerantly. We found that the average sequence cost decreases by up to 54±3% when using the Z-rotation catalyst circuit approach and by up to 33±2% when using the magic state distillation approach. In addition, we investigated observed limitations of certain assignments of base gate costs by developing an analytic model to estimate the proportion of sets of Z-rotation gates from higher orders of the Clifford hierarchy that are found within sequences approximating random target gates.

scholarly journals Key ideas in quantum error correction

2012 ◽  
Vol 370 (1975) ◽  
pp. 4541-4565 ◽  
Author(s):  
Robert Raussendorf
Keyword(s):  
Quantum Information ◽  
Error Correction ◽  
Quantum Computation ◽  
Fault Tolerant ◽  
Quantum Error Correction ◽  
Quantum Gates ◽  
Quantum Codes ◽  
Introductory Article ◽  
The Subject ◽  
Quantum Error

In this introductory article on the subject of quantum error correction and fault-tolerant quantum computation, we review three important ingredients that enter known constructions for fault-tolerant quantum computation, namely quantum codes, error discretization and transversal quantum gates. Taken together, they provide a ground on which the theory of quantum error correction can be developed and fault-tolerant quantum information protocols can be built.

scholarly journals A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 128 ◽  
Author(s):  
Daniel Litinski
Keyword(s):  
Quantum Computing ◽  
Large Scale ◽  
Fault Tolerant ◽  
Quantum Error Correction ◽  
Trade Offs ◽  
Gate Circuit ◽  
Small Set ◽  
Space Cost ◽  
Surface Code ◽  
Quantum Error

Given a quantum gate circuit, how does one execute it in a fault-tolerant architecture with as little overhead as possible? In this paper, we discuss strategies for surface-code quantum computing on small, intermediate and large scales. They are strategies for space-time trade-offs, going from slow computations using few qubits to fast computations using many qubits. Our schemes are based on surface-code patches, which not only feature a low space cost compared to other surface-code schemes, but are also conceptually simple~--~simple enough that they can be described as a tile-based game with a small set of rules. Therefore, no knowledge of quantum error correction is necessary to understand the schemes in this paper, but only the concepts of qubits and measurements.

scholarly journals Theory of quasi-exact fault-tolerant quantum computing and valence-bond-solid codes

2021 ◽  
Author(s):  
Dongsheng Wang ◽  
Yunjiang Wang ◽  
Ningping Cao ◽  
Bei Zeng ◽  
Raymond Lafflamme
Keyword(s):  
Error Correction ◽  
Quantum Computation ◽  
Fault Tolerant ◽  
Valence Bond ◽  
Quantum Error Correction ◽  
Quantum Codes ◽  
Error Correction Codes ◽  
Exact Quantum ◽  
Valence Bond Solid ◽  
Quantum Error

Abstract In this work, we develop the theory of quasi-exact fault-tolerant quantum (QEQ) computation, which uses qubits encoded into quasi-exact quantum error-correction codes (``quasi codes''). By definition, a quasi code is a parametric approximate code that can become exact by tuning its parameters. The model of QEQ computation lies in between the two well-known ones: the usual noisy quantum computation without error correction and the usual fault-tolerant quantum computation, but closer to the later. Many notions of exact quantum codes need to be adjusted for the quasi setting. Here we develop quasi error-correction theory using quantum instrument, the notions of quasi universality, quasi code distances, and quasi thresholds, etc. We find a wide class of quasi codes which are called valence-bond-solid codes, and we use them as concrete examples to demonstrate QEQ computation.

scholarly journals Universal quantum computation and quantum error correction with ultracold atomic mixtures

2021 ◽  
Author(s):  
Valentin Kasper ◽  
Daniel González-Cuadra ◽  
Apoorva Hegde ◽  
Andy Xia ◽  
Alexandre Dauphin ◽  
...  
Keyword(s):  
Error Correction ◽  
Quantum Computation ◽  
Quantum Error Correction ◽  
Universal Quantum ◽  
Quantum Error

scholarly journals Advanced exact synthesis of Clifford+T circuits

2020 ◽  
Vol 19 (9) ◽  
Author(s):  
Philipp Niemann ◽  
Robert Wille ◽  
Rolf Drechsler
Keyword(s):  
Large Scale ◽  
Fault Tolerant ◽  
Logic Synthesis ◽  
Research Problem ◽  
Quantum Systems ◽  
Quantum Circuits ◽  
Research Attention ◽  
Small Quantum ◽  
Significant Research ◽  
Important Research Problem

Abstract Quantum systems provide a new way of conducting computations based on the so-called qubits. Due to the potential for significant speed-ups, this field received significant research attention in recent years. The Clifford+T library is a very promising and popular gate library for these kinds of computations. Unlike other libraries considered so far, it consists of only a small number of gates for all of which robust, fault-tolerant realizations are known for many technologies that seem to be promising for large-scale quantum computing. As a consequence, (logic) synthesis of Clifford+T quantum circuits became an important research problem. However, previous work in this area has several drawbacks: Corresponding approaches are either only applicable to very small quantum systems or lead to circuits that are far from being optimal. The latter is mainly caused by the fact that current synthesis realizes the desired circuit by a local, i.e., column-wise, consideration of the underlying unitary transformation matrix to be synthesized. In this paper, we analyze the conceptual drawbacks of this approach and propose to overcome them by taking a global view of the matrices and perform a separation of concerns regarding individual synthesis steps. We precisely describe a corresponding algorithm as well as its efficient implementation on top of decision diagrams. Experimental results confirm the resulting benefits and show improvements of up to several orders of magnitudes in costs compared to previous work.

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