Realization of three-qubit quantum error correction with superconducting circuits

Reed, Matthew; DiCarlo, L.; Nigg, Simon E.; Sun, Luyan; Frunzio, Luigi; Girvin, S. M.; Schoelkopf, Robert

doi:10.1038/nature10786

Cited by 571 publications

(560 citation statements)

References 29 publications

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“…Note that the coupling rate g is defined such that strength of the level splitting on resonance (swap rate) is 2g (Ref. 11 ).…”

Section: Device Parametersmentioning

confidence: 99%

“…We define n-th order fault-tolerance to mean that any combination of n errors is tolerable. Previous experiments based on nuclear magnetic resonance 8,9 , ion traps 10 , and superconducting circuits [11][12][13] have demonstrated multi-qubit states that are first-order tolerant to one type of error. Recently, experiments with ion traps and superconducting circuits have shown the simultaneous detection of multiple types of errors 14,15 .…”

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confidence: 99%

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State preservation by repetitive error detection in a superconducting quantum circuit

Kelly

Barends

Fowler

et al. 2015

Nature

875

1,004

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Quantum computing becomes viable when a quantum state can be preserved from environmentally-induced error. If quantum bits (qubits) are sufficiently reliable, errors are sparse and quantum error correction (QEC) 1-6 is capable of identifying and correcting them. Adding more qubits improves the preservation by guaranteeing increasingly larger clusters of errors will not cause logical failure -a key requirement for large-scale systems. Using QEC to extend the qubit lifetime remains one of the outstanding experimental challenges in quantum computing. Here, we report the protection of classical states from environmental bit-flip errors and demonstrate the suppression of these errors with increasing system size. We use a linear array of nine qubits, which is a natural precursor of the twodimensional surface code QEC scheme 7 , and track errors as they occur by repeatedly performing projective quantum non-demolition (QND) parity measurements. Relative to a single physical qubit, we reduce the failure rate in retrieving an input state by a factor of 2.7 for five qubits and a factor of 8.5 for nine qubits after eight cycles. Additionally, we tomographically verify preservation of the non-classical Greenberger-Horne-Zeilinger (GHZ) state. The successful suppression of environmentally-induced errors strongly motivates further research into the many exciting challenges associated with building a large-scale superconducting quantum computer.The ability to withstand multiple errors during computation is a critical aspect of error correction. We define n-th order fault-tolerance to mean that any combination of n errors is tolerable. Previous experiments based on nuclear magnetic resonance 8,9 , ion traps 10 , and superconducting circuits [11][12][13] have demonstrated multi-qubit states that are first-order tolerant to one type of error. Recently, experiments with ion traps and superconducting circuits have shown the simultaneous detection of multiple types of errors 14,15 . The above hallmark experiments demonstrate error correction in a single round; however, quantum information must be preserved throughout computation using multiple error correction cycles. The basics of repeating cycles have been shown in ion traps 16 and superconducting circuits 17 . Until now, it has been an open challenge to combine these elements to make the information stored in a quantum system robust against errors which intrinsically arise from the environment.The key to detecting errors in quantum information is to perform QND parity measurements. In the surface code, this is done by arranging qubits in a chequerboard pattern -with data qubits corresponding to the white, and measure qubits to the black squares (see Fig. 1) -and using these ancilla measure qubits to repetitively perform parity measurements to detect bit-flip (X) and phase-flip (Ẑ) errors 7 . A square chequerboard with (4n + 1) 2 qubits is n-th order fault tolerant, meaning at least n+1 errors must occur to cause failure in preserving a state if fidelities are above a threshold. W...

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“…Note that the coupling rate g is defined such that strength of the level splitting on resonance (swap rate) is 2g (Ref. 11 ).…”

Section: Device Parametersmentioning

confidence: 99%

mentioning

confidence: 99%

State preservation by repetitive error detection in a superconducting quantum circuit

Kelly

Barends

Fowler

et al. 2015

Nature

875

1,004

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“…While our results depend heavily on the Chimera architecture of the D-Wave devices, it is only possible to make progress in the field of experimental quantum error correction by studying specific devices that provide snapshots of evolving technologies (e.g., Refs. [1,2,47]). With this caveat in mind, our study contains several valuable long-term lessons.…”

Section: Discussionmentioning

confidence: 99%

Performance of two different quantum annealing correction codes

Mishra

Albash

Lidar

2015

Quantum Inf Process

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Quantum annealing is a promising approach for solving optimization problems, but like all other quantum information processing methods, it requires error correction to ensure scalability. In this work we experimentally compare two quantum annealing correction codes in the setting of antiferromagnetic chains, using two different quantum annealing processors. The lower temperature processor gives rise to higher success probabilities. The two codes differ in a number of interesting and important ways, but both require four physical qubits per encoded qubit. We find significant performance differences, which we explain in terms of the effective energy boost provided by the respective redundantly encoded logical operators of the two codes. The code with the higher energy boost results in improved performance, at the expense of a lower degree encoded graph. Therefore, we find that there exists an important tradeoff between encoded connectivity and performance for quantum annealing correction codes.

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“…The first experimental realization of the quantum Toffoli gate was presented in an ion-trap quantum computer, in 2009 at the University of Innsbruck, Austria [20]. Then, the Toffoli gate was realized in linear optics [21] and superconducting circuits [22,31,32].Due to its significance in quantum computing, the theoretical pursuit of efficient implementation of the Toffoli gate using a sequence of single-and two-qubit gates has a quite long history [7,8,11,12,[33][34][35][36][37]. It was explicitly stated as an open problem by Nielsen and Chuang in their influential textbook on quantum computation [14]: How many general two-qubit gates (or CNOT gates) are required to implement the Toffoli gate (see [14], p. 213, Problem 4.4)?…”

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confidence: 99%

Five two-qubit gates are necessary for implementing the Toffoli gate

Duan

Ying

2013

Phys. Rev. A

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In this Rapid Communication, we consider the open problem of the minimum cost of two-qubit gates for simulating the Toffoli gate and show that five two-qubit gates are necessary. Before our work, it was known that five two-qubit gates are sufficient to implement the Toffoli gate, and numerical evidence indicates that five two-qubit gates are also necessary. The idea introduced here can also be used to solve the problem of optimal simulation of Deutsch three-qubit gates. Since quantum computation provides the possibility of solving certain problems much faster than any classical computer using the best currently known algorithms [1][2][3][4][5], a huge amount of effort has been devoted to building functional and scalable quantum computers over the last two decades. The quantum circuit model is one popular model of quantum computer hardware [6][7][8][9][10][11][12][13][14][15][16][17][18]. In order to be a general purpose computational device, a quantum computer must implement a small set of quantum logical gates [14], which are universal, that is, can serve as the basic building blocks of quantum circuits, in the same way as do classical logical gates for conventional digital circuits. It is quite natural to choose certain gates operating on a small number of qubits as the basic gates.Theoretically, any two-qubit gate that can create entanglement, like the controlled-NOT (CNOT) gate, together with all single-qubit gates, is universal [18]. It has also been experimentally demonstrated that two-qubit gates can be realized with high fidelity using the current technology, for example, two-qubit gates with superconducting qubits have been presented with fidelities higher than 90% [19]. Finding more efficient ways to implement quantum gates may allow small-scale quantum computing tasks to be demonstrated on a shorter time scale. More precisely, it would be quite helpful for defeating quantum decoherence to realize multiqubit gates with the least number of possible basic gates. Thus an important problem is how to implement multiqubit gates using only two-qubit gates. Indeed, a study of the minimum cost of two-qubit gates for simulating a multiqubit gate is not only of theoretical importance, but also an experimental requirement: to accomplish a quantum algorithm, even at a small size, one has to implement a relatively high level of control over the multiqubit quantum system. A lot of experiments demonstrate multiqubit controlled-NOT gates in ion traps [20] Making controlled unitaries is an essential task for many algorithms in quantum computing [1]. Among all quantum controlled gates, those highly controlled unitaries (i.e., unitaries controlled on more than one other qubit) are useful in numerous quantum algorithms including the oracle in the * nengkunyu@gmail.com binary welded tree algorithm [5] and quantum simulation [24]. The Toffoli gate is perhaps one of the most important highly controlled unitaries for three reasons: (1) The Toffoli gate is universal for classical reversible computation in the sense that all con...

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Realization of three-qubit quantum error correction with superconducting circuits

Cited by 571 publications

References 29 publications

State preservation by repetitive error detection in a superconducting quantum circuit

State preservation by repetitive error detection in a superconducting quantum circuit

Performance of two different quantum annealing correction codes

Five two-qubit gates are necessary for implementing the Toffoli gate

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