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.

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 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 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 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 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.

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).

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