Comparison of ancilla preparation and measurement procedures for the Steane [[7,1,3]] code on a model ion-trap quantum computer

Tomita, Yu; Gutiérrez, Mauricio; Kabytayev, Chingiz; Brown, Kenneth R.; Hutsel, Michael R.; Morris, Alexander; Stevens, Kelly E.; Mohler, Greg

doi:10.1103/physreva.88.042336

Cited by 15 publications

(16 citation statements)

References 40 publications

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“…A model with faster ancilla movement or longer ancilla encoding time could easily change this. We note that an explicit analysis of the effect of decoding in a proposed layout for trapped-ion-based quantum computing has recently been published [13].…”

Section: Discussionmentioning

confidence: 99%

Relative performance of ancilla verification and decoding in the [[7,1,3]] Steane code

2014

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Ancilla post-selection is a common means of achieving fault-tolerance in quantum error-correction. However, it can lead to additional data errors due to movement or wait operations. Alternatives to post-selection may achieve lower overall failure rates due to avoiding such errors. We present numerical simulation results comparing the logical error rates for the fault-tolerant [[7,1,3]] Steane code using techniques of ancilla verification vs. the newer method of ancilla decoding, as described in [1]. We simulate QEC procedures in which rhe possibility of ancilla verification failures requires the creation and storage of additional ancillas and/or additional waiting of the data until a new ancilla can be created. We find that the decoding method, which avoids verification failures, is advantageous in terms of overall error rate in various cases, even when measurement operations are no slower than others. We analyze the effect of different classes of physical error on the relative performance of these two methods.

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Section: Discussionmentioning

confidence: 99%

Relative performance of ancilla verification and decoding in the [[7,1,3]] Steane code

2014

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“…The proposed setup consists of a 1D segmented highoptical-access (HOA) ion trap fabricated by Sandia National Laboratories [19], and operated in a cryogenic environment (see Fig.1). We consider 40 Ca + ions for hosting the qubits, and 88 Sr + ions for providing the capabilities for sympathetic cooling, and mixed-species readout for syndrome extraction. We consider that ions undergoing the quantum logic operations can be separated and shuttled across the segmented trap array by using high-speed (diabatic), low-excitation protocols in order to minimize cross-talk on neighboring qubits.…”

Section: A Experimental Architecturementioning

confidence: 99%

“…Hence, it would be desirable to define a set of intermediate QEC goals, which are necessary for the progress towards the fully-fledged fault-tolerant quantum computer, and can serve as a guiding principle in the experimental design by benchmarking the progress in building Figure 1. The Sandia HOA2 trap as a QEC platform: In our envisioned scheme, 40 Ca + ions (blue and red dots) are co-trapped with 88 Sr + ions (green dots) in a quantum zone divided in three storage regions S 1 , S 2 , S 3 and two manipulations zones M 1 , M 2 . Some of the 40 Ca + ions can be used as data qubits to encode quantum information according to a QEC code (blue dots), while others (red dots) can be used as ancilla qubits for syndrome extraction.…”

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confidence: 99%

“…Some of the 40 Ca + ions can be used as data qubits to encode quantum information according to a QEC code (blue dots), while others (red dots) can be used as ancilla qubits for syndrome extraction. The 88 Sr + ions (green dots) are used as sympathetic coolants to reduce the number of phonons prior to the entangling gates. Possible crystal reconfiguration operations are shown in the panel of the lower right corner: (a) Splitting of an ion crystal, (b) shuttling of an ion and subsequent merging with another ion to form a crystal, and (c) rotation (swapping) of a mixed species crystal.…”

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Assessing the Progress of Trapped-Ion Processors Towards Fault-Tolerant Quantum Computation

et al. 2017

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A quantitative assessment of the progress of small prototype quantum processors towards fault-tolerant quantum computation is a problem of current interest in experimental and theoretical quantum information science. We introduce a necessary and fair criterion for quantum error correction (QEC), which must be achieved in the development of these quantum processors before their sizes are sufficiently big to consider the well-known QEC threshold. We apply this criterion to benchmark the ongoing effort in implementing QEC with topological color codes using trapped-ion quantum processors and, more importantly, to guide the future hardware developments that shall be required in order to demonstrate beneficial QEC with small topological quantum codes. In doing so, we present a thorough description of a realistic trapped-ion toolbox for QEC, and a physically-motivated error model that goes beyond standard simplifications in the QEC literature. We focus on laser-based quantum gates realised in two-species trapped-ion crystals in high-optical aperture segmented traps. Our large-scale numerical analysis shows that, with the foreseen technological improvements hereby described, this platform is a very promising candidate for fault-tolerant quantum computation.

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“…Shor's method requires a w-qubit cat state to measure a weight-w stabilizer [11]. An extra qubit is needed to verify the ancillary qubit, but this is not a strict requirement [12,13]. Steane's method requires the fault-tolerant preparation of a logical state [14], while Knill's method relies on the fault-tolerant preparation of a logical Bell pair [15].…”

Section: Introductionmentioning

confidence: 99%

Fault tolerance with bare ancillary qubits for a [[7,1,3]] code

Gutiérrez

David

et al. 2017

Phys. Rev. A

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We present a [[7, 1, 3]] quantum error-correcting code that is able to achieve fault-tolerant syndrome measurement using one ancillary qubit per stabilizer for an error model of independent single-qubit Pauli errors. All single-qubit Pauli errors on the ancillary qubits propagate to form exclusively correctable errors on the data qubits. The situation changes for error models with two-qubit Pauli errors. We compare the level-1 logical error rates under two noise models: the standard Pauli symmetric depolarizing error model and an anisotropic error model. The anisotropic model is motivated by control errors on two-qubit gates commonly applied to trapped ion qubits. We find that one ancillary qubit per syndrome measurement is sufficient for fault-tolerance for the anisotropic error, but is not sufficient for the standard depolarizing errors. We then show how to achieve fault tolerance for the standard depolarizing errors by adding flag qubits to check for errors on select ancilary qubits. Our results on this [[7, 1, 3]] code demonstrates how physically motivated noise models may simplify fault-tolerent protocols.

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Comparison of ancilla preparation and measurement procedures for the Steane [[7,1,3]] code on a model ion-trap quantum computer

Cited by 15 publications

References 40 publications

Relative performance of ancilla verification and decoding in the [[7,1,3]] Steane code

Relative performance of ancilla verification and decoding in the [[7,1,3]] Steane code

Assessing the Progress of Trapped-Ion Processors Towards Fault-Tolerant Quantum Computation

Fault tolerance with bare ancillary qubits for a [[7,1,3]] code

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