scholarly journals A heterometallic [LnLn′Ln] lanthanide complex as a qubit with embedded quantum error correction

2020 ◽  
Vol 11 (38) ◽  
pp. 10337-10343
Author(s):  
Emilio Macaluso ◽  
Marcos Rubín ◽  
David Aguilà ◽  
Alessandro Chiesa ◽  
Leoní A. Barrios ◽  
...  
Keyword(s):  
Error Correction ◽  
Coordination Compound ◽  
Lanthanide Complex ◽  
Quantum Error Correction ◽  
Error Correction Code ◽  
Magnetic Molecules ◽  
Pure Dephasing ◽  
Quantum Error

We show that a [Er–Ce–Er] molecular trinuclear coordination compound is a promising platform to implement the three-qubit quantum error correction code protecting against pure dephasing, the most important error in magnetic molecules.

Fault-tolerant quantum error correction code preparation in UBQC

2020 ◽  
Vol 19 (8) ◽  
Author(s):  
Qiang Zhao ◽  
Qiong Li ◽  
Haokun Mao ◽  
Xuan Wen ◽  
Qi Han ◽  
...  
Keyword(s):  
Error Correction ◽  
Fault Tolerant ◽  
Quantum Error Correction ◽  
Error Correction Code ◽  
Quantum Error

scholarly journals Experimental demonstration of a graph state quantum error-correction code

2014 ◽  
Vol 5 (1) ◽  
Author(s):  
B. A. Bell ◽  
D. A. Herrera-Martí ◽  
M. S. Tame ◽  
D. Markham ◽  
W. J. Wadsworth ◽  
...  
Keyword(s):  
Error Correction ◽  
Quantum Error Correction ◽  
Experimental Demonstration ◽  
Graph State ◽  
Error Correction Code ◽  
Quantum Error

scholarly journals Entropy of a Quantum Error Correction Code

2008 ◽  
Vol 15 (04) ◽  
pp. 329-343 ◽  
Author(s):  
David W. Kribs ◽  
Aron Pasieka ◽  
Karol Życzkowski
Keyword(s):  
Error Correction ◽  
Detailed Analysis ◽  
Quantum Channel ◽  
Error Correcting Codes ◽  
Quantum Error Correction ◽  
Maximal Entropy ◽  
Initial State ◽  
Error Correction Code ◽  
Quantum Error ◽  
Decoherence Free Subspaces

We define and investigate the notion of entropy for quantum error correcting codes. The entropy of a code for a given quantum channel has a number of equivalent realisations, such as through the coefficients associated with the Knill-Laflamme conditions and the entropy exchange computed with respect to any initial state supported on the code. In general the entropy of a code can be viewed as a measure of how close it is to the minimal entropy case, which is given by unitarily correctable codes (including decoherence-free subspaces), or the maximal entropy case, which from dynamical Choi matrix considerations corresponds to non-degenerate codes. We consider several examples, including a detailed analysis of the case of binary unitary channels, and we discuss an extension of the entropy to operator quantum error correcting subsystem codes.

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 Fault-tolerant quantum error correction code conversion

2013 ◽  
Vol 13 (5&6) ◽  
pp. 439-451
Author(s):  
Charles D. Hill ◽  
Austin G. Fowler ◽  
David S. Wang ◽  
Lloyd C.L. Hollenberg
Keyword(s):  
Error Correction ◽  
Fault Tolerant ◽  
Quantum Error Correction ◽  
Error Correction Code ◽  
Computational Search ◽  
Quantum Error

In this paper we demonstrate how data encoded in a five-qubit quantum error correction code can be converted, fault-tolerantly, into a seven-qubit Steane code. This is achieved by progressing through a series of codes, each of which fault-tolerantly corrects at least one error. Throughout the conversion the encoded qubit remains protected. We found, through computational search, that the method used to convert between codes given in this paper is optimal.

scholarly journals Encoding an arbitrary state in a [7,1,3] quantum error correction code

2012 ◽  
Vol 12 (2) ◽  
pp. 699-719 ◽  
Author(s):  
Sidney D. Buchbinder ◽  
Channing L. Huang ◽  
Yaakov S. Weinstein
Keyword(s):  
Error Correction ◽  
Quantum Error Correction ◽  
Error Correction Code ◽  
Arbitrary State ◽  
Quantum Error
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