Fault tolerant quantum computation with very high threshold for loss errors

Barrett, Sean D.; Stace, Thomas M.

doi:10.48550/arxiv.1005.2456

Cited by 5 publications

(6 citation statements)

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“…The efficiencies for detectors and photon emission needed in order to get a connected cluster are, however, extremely high. In future work we will consider a slightly different approach to the error correction which incorporates probabilistic gates into a framework similar to that of [32], in the hope of alleviating these stringent requirements. The introduction of coupled quantum dots in [33] can be exploited to obtain 2-dimensional cluster states, thus reducing our dependence on fusion gates.…”

Section: Discussionmentioning

confidence: 99%

Photonic implementation for the topological cluster-state quantum computer

et al. 2010

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A new implementation of the topological cluster state quantum computer is suggested, in which the basic elements are linear optics, measurements, and a two-dimensional array of quantum dots. This overcomes the need for non-linear devices to create a lattice of entangled photons. We give estimates of the minimum efficiencies needed for the detectors, fusion gates and quantum dots, from a numerical simulation.

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Section: Discussionmentioning

confidence: 99%

Photonic implementation for the topological cluster-state quantum computer

et al. 2010

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“…Furthermore, there are practical limitations on the ability to construct perfect unitary gates [49]. The depolarizing and erasure channels are two classes of noisy models for qubit quantum processors that are widely considered (see [50][51][52]).…”

Section: Theoremmentioning

confidence: 99%

Extendibility Limits the Performance of Quantum Processors

et al. 2019

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Resource theories in quantum information science are helpful for the study and quantification of the performance of information-processing tasks that involve quantum systems. These resource theories also find applications in other areas of study; e.g., the resource theories of entanglement and coherence have found use and implications in the study of quantum thermodynamics and memory effects in quantum dynamics. In this paper, we introduce the resource theory of unextendibility, which is associated to the inability of extending quantum entanglement in a given quantum state to multiple parties. The free states in this resource theory are the k-extendible states, and the free channels are k-extendible channels, which preserve the class of k-extendible states. We make use of this resource theory to derive non-asymptotic, upper bounds on the rate at which quantum communication or entanglement preservation is possible by utilizing an arbitrary quantum channel a finite number of times, along with the assistance of k-extendible channels at no cost. We then show that the bounds we obtain are significantly tighter than previously known bounds for both the depolarizing and erasure channels.

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“…Large lattice sizes have been simulated [11], however only by assuming that 4-qubit operators can be measured perfectly. Small lattices have been simulated fault-tolerantly [7,9,12,13], however these works used the code of Kolmogorov [14] which does not support continuous processing of an arbitrary number of rounds of QEC. Our code now supports continuous fault-tolerant processing, using constant memory and with processing rate independent of the number of rounds.…”

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confidence: 99%

Towards Practical Classical Processing for the Surface Code

Fowler¹,

Whiteside²,

Hollenberg³

2012

Phys. Rev. Lett.

168

181

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The surface code is unarguably the leading quantum error correction code for 2-D nearest neighbor architectures, featuring a high threshold error rate of approximately 1%, low overhead implementations of the entire Clifford group, and flexible, arbitrarily long-range logical gates. These highly desirable features come at the cost of significant classical processing complexity. We show how to perform the processing associated with an n × n lattice of qubits, each being manipulated in a realistic, fault-tolerant manner, in O(n 2 ) average time per round of error correction. We also describe how to parallelize the algorithm to achieve O(1) average processing per round, using only constant computing resources per unit area and local communication. Both of these complexities are optimal.Quantum computing promises exponentially faster processing of certain problems, including factoring [1] and simulating quantum physics [2]. Many quantum algorithms are now known [3]. The primary challenges are to mitigate and cope with the imperfections of quantum devices. The surface code [4,5] supports a powerful quantum computing scheme [6][7][8] featuring an experimentally realistic threshold error rate of approximately 1% [9] and requiring only a 2-D square lattice of qubits with nearest neighbor interactions. In this work, we describe how to perform the complex classical processing associated with the full, fault-tolerant scheme in a complexity-optimal manner. Using the current version of our code, we can simulate the fault-tolerant operation of millions of qubits, four orders of magnitude more than in any previous work.

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Fault tolerant quantum computation with very high threshold for loss errors

Cited by 5 publications

References 0 publications

Photonic implementation for the topological cluster-state quantum computer

Photonic implementation for the topological cluster-state quantum computer

Extendibility Limits the Performance of Quantum Processors

Towards Practical Classical Processing for the Surface Code

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