scholarly journals Optimally combining dynamical decoupling and quantum error correction

2013 ◽  
Vol 3 (1) ◽  
Author(s):  
Gerardo A. Paz-Silva ◽  
D. A. Lidar
Keyword(s):  
Error Correction ◽  
Quantum Error Correction ◽  
Dynamical Decoupling ◽  
Quantum Error

ROBUST DYNAMICAL DECOUPLING: FEEDBACK-FREE ERROR CORRECTION

2005 ◽  
Vol 03 (supp01) ◽  
pp. 41-52
Author(s):  
D. A. LIDAR ◽  
K. KHODJASTEH
Keyword(s):  
Error Correction ◽  
Efficiency Analysis ◽  
Error Correcting Codes ◽  
Quantum Error Correction ◽  
Dynamical Decoupling ◽  
Protection Scheme ◽  
Basic Concepts ◽  
Quantum Error

Dynamical decoupling is a feed-back free scheme for quantum error correction against noise and decoherence errors. An efficiency analysis of dynamical decoupling is performed. Furthermore we provide the basic concepts of dynamical decoupling and quantum error correcting codes, and give an example of a hybrid protection scheme. Some interesting extensions of dynamical decoupling are discussed at the end.

Stabilizing qubit coherence via tracking-control

2005 ◽  
Vol 5 (4&5) ◽  
pp. 350-363
Author(s):  
D.A. Lidar ◽  
S. Schneider
Keyword(s):  
Error Correction ◽  
Finite Time ◽  
Tracking Control ◽  
Quantum Error Correction ◽  
The State ◽  
Control Field ◽  
Dynamical Decoupling ◽  
Single Qubit ◽  
Quantum Error

We consider the problem of stabilizing the coherence of a single qubit subject to Markovian decoherence, via the application of a control Hamiltonian, without any additional resources. In this case neither quantum error correction/avoidance, nor dynamical decoupling applies. We show that using tracking-control, i.e., the conditioning of the control field on the state of the qubit, it is possible to maintain coherence for finite time durations, until the control field diverges.

scholarly journals 2-designs and redundant syndrome extraction for quantum error correction

2021 ◽  
Vol 20 (3) ◽  
Author(s):  
Vickram N. Premakumar ◽  
Hele Sha ◽  
Daniel Crow ◽  
Eric Bach ◽  
Robert Joynt
Keyword(s):  
Error Correction ◽  
Quantum Error Correction ◽  
Quantum Error

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.

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