Logical error rate scaling of the toric code

Watson, Fern H. E.; Barrett, S. D.

doi:10.1088/1367-2630/16/9/093045

Cited by 23 publications

(27 citation statements)

References 45 publications

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“…[64][65][66]. In our case, one can find that this function provides a good fit to our numerical data.…”

Section: Appendix F: the Error Model And Charge Tunnelling Errorssupporting

confidence: 72%

Noise Threshold and Resource Cost of Fault-Tolerant Quantum Computing with Majorana Fermions in Hybrid Systems

2016

Phys. Rev. Lett.

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Fault-tolerant quantum computing in systems composed of both Majorana fermions and topologically unprotected quantum systems, e.g. superconducting circuits or quantum dots, is studied in this paper. Errors caused by topologically unprotected quantum systems need to be corrected with error correction schemes, for instance, the surface code. We find that the error-correction performance of such a hybrid topological quantum computer is not superior to a normal quantum computer unless the topological charge of Majorana fermions is insusceptible to noise. If errors changing the topological charge are rare, the fault-tolerance threshold is much higher than the threshold of a normal quantum computer, and a surface-code logical qubit could be encoded in only tens of topological qubits instead of about a thousand normal qubits.

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“…[64][65][66]. In our case, one can find that this function provides a good fit to our numerical data.…”

Section: Appendix F: the Error Model And Charge Tunnelling Errorssupporting

confidence: 72%

Noise Threshold and Resource Cost of Fault-Tolerant Quantum Computing with Majorana Fermions in Hybrid Systems

2016

Phys. Rev. Lett.

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“…We determine the threshold p (d) th using a rescaling method [19,34]. Selecting data close to the point where the curves of different L cross (for fixed qudit dimension) we perform a fit to a function of the form…”

Section: Thresholds Estimation and Percolation Limitationmentioning

confidence: 99%

Fast fault-tolerant decoder for qubit and qudit surface codes

2015

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The surface code is one of the most promising candidates for combating errors in large scale fault-tolerant quantum computation. A fault-tolerant decoder is a vital part of the error correction process-it is the algorithm which computes the operations needed to correct or compensate for the errors according to the measured syndrome, even when the measurement itself is error prone. Previously decoders based on minimum-weight perfect matching have been studied. However, these are not immediately generalizable from qubit to qudit codes. In this work, we develop a fault-tolerant decoder for the surface code, capable of efficient operation for qubits and qudits of any dimension, generalizing the decoder first introduced by Bravyi and Haah [Phys. Rev. Lett. 111, 200501 (2013)]. We study its performance when both the physical qudits and the syndromes measurements are subject to generalized uncorrelated bit-flip noise (and the higher-dimensional equivalent). We show that, with appropriate enhancements to the decoder and a high enough qudit dimension, a threshold at an error rate of more than 8% can be achieved. I. OVERVIEWTopological quantum codes built from qubits [twodimensional (2D) quantum systems] play a central role in architectures for fault-tolerant quantum computing at the forefront of current research [1][2][3][4]. The surface code [5] and the related toric code [6,7] are prominent examples of such codes. Compared with other quantum error correcting codes, they posses the key experimental benefit of requiring only local interactions and yet, under realistic noise models, they have been shown to achieve the highest reported fault-tolerant thresholds [8,9].Recent developments have shown that employing ddimensional quantum systems, or qudits, as the building blocks for fault-tolerant schemes may offer some important advantages. For example, an integral part of many faulttolerant schemes is the distillation of magic states [10]-a procedure necessary to achieve universal computation-where generalization to higher dimensions has resulted in improved distillation thresholds and lower overheads in the number of qudit magic states [11][12][13]. Moreover, threshold investigations of the qudit toric code with noise-free syndrome measurements have shown that, for a standard independent noise model, the error correction threshold increases significantly with increasing qudit dimension [14][15][16], although we caution that it is difficult to fairly compare noise rates between systems of different dimensions. Although it is more challenging to realize qudit quantum systems experimentally, recent work has demonstrated the ability to coherently control and perform operations in single 16-dimensional atomic systems with high fidelity [17,18], with the implementation of high-fidelity multiqudit interactions still to be achieved.A surface code is a stabilizer code with local stabilizer generators. Qudits are associated with the edges of a 2D square lattice. In order to store the encoded information for * fern.watson10@imperial...

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“…The question of how these protocols behave when well below threshold (i.e., the regime where a device would realistically operate) requires a different approach to the Monte Carlo simulations performed here, as considered in several recent works [31,32]. While this is beyond the scope of this paper, we note that using the medium protocol at half the threshold network error (7%) with a lattice size of L ¼ 16 yields a logical error rate per L stabilizer rounds of fewer than 1 in 10 6 .…”

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confidence: 99%

Freely Scalable Quantum Technologies Using Cells of 5-to-50 Qubits with Very Lossy and Noisy Photonic Links

2014

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Exquisite quantum control has now been achieved in small ion traps, in nitrogen-vacancy centers and in superconducting qubit clusters. We can regard such a system as a universal cell with diverse technological uses from communication to large-scale computing, provided that the cell is able to network with others and overcome any noise in the interlinks. Here, we show that loss-tolerant entanglement purification makes quantum computing feasible with the noisy and lossy links that are realistic today: With a modestly complex cell design, and using a surface code protocol with a network noise threshold of 13.3%, we find that interlinks that attempt entanglement at a rate of 2 MHz but suffer 98% photon loss can result in kilohertz computer clock speeds (i.e., rate of high-fidelity stabilizer measurements). Improved links would dramatically increase the clock speed. Our simulations employ local gates of a fidelity already achieved in ion trap devices. DOI: 10.1103/PhysRevX.4.041041 Subject Areas: Quantum PhysicsWithin the past year, there have been remarkable advances in the fidelity with which small quantum devices can be controlled. The two most mature systems are ion traps and superconducting qubits. In ion trap devices, single-qubit fidelities [1] have reached 99.9999%, with combined preparation and measurement of 99.93%. Moreover, two-qubit operations [2] have been reported with fidelities up to 99.9%. Meanwhile, a superconducting qubit device (SQD) containing five qubits [3] has been demonstrated with all qubit manipulations above 99.3%. At the same time, there has been rapid progress in the study of nitrogen-vacancy (NV) centers in diamond-single electron spin manipulation is possible with 99% fidelity [4], and it is possible to manipulate nuclei that are relatively far from the center, so that each NV center may be thought of as a group of several qubits interacting with an optically active core [5].These prototype systems are small; none of them contain as many as 20 qubits. But importantly in each case, it is possible to bridge between small systems using photonic channels, albeit with lower entanglement fidelities and in a probabilistic way that may require many attempts. In the ion trap community, there are well-established methods for entangling ions in separate traps, and recent progress associated with projects such as the MUSIQC initiative [6] have led to successful entanglement at a rate of hertz [7]. This can be improved by orders of magnitude by hardware advances and by loss-adapted protocols, as we describe in this paper. In SQDs, a well-established means of interfacing qubits is to exploit microwave photons in cavities [8]. This suffices for short-range bridging, and, moreover, remote entanglement of two superconducting qubits separated by more than a meter of coaxial cable has recently been demonstrated [9]. In the case of NV center research, successful optical linking of qubits can occur either within the same sample [4] or over meters of separation [10], and teleportation [11] with fidelity ...

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Logical error rate scaling of the toric code

Cited by 23 publications

References 45 publications

Noise Threshold and Resource Cost of Fault-Tolerant Quantum Computing with Majorana Fermions in Hybrid Systems

Noise Threshold and Resource Cost of Fault-Tolerant Quantum Computing with Majorana Fermions in Hybrid Systems

Fast fault-tolerant decoder for qubit and qudit surface codes

Freely Scalable Quantum Technologies Using Cells of 5-to-50 Qubits with Very Lossy and Noisy Photonic Links

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