Magic-state distillation with the four-qubit code

Meier, Adam; Eastin, Bryan; Knill, Emanuel

doi:10.26421/qic13.3-4-2

Cited by 47 publications

(85 citation statements)

References 8 publications

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“…Second, at the required TOF error rate it suffices to implement the top-down protocol using a mixture of repetition codes and surface codes, which dramatically reduces the factory footprint. In contrast, the best performing T state factories (in architectures without biased noise) rely completely on surface codes and either require multiple rounds of distillation to achieve the same error suppression [30][31][32] or only produce 1 T state at a time so that 8 rounds are needed to realize 2 TOF gates [33].…”

Section: A Overview Of Main Resultsmentioning

confidence: 99%

“…For κ φ = 10κ 1 and n th = 0.01, we find that the perturbation theory predicts the optimal gate time for the Toffoli gate is 1.25 times that of the CNOT gate by comparing Eqs. (31) and (37). Also, at the optimal gate time of the CNOT gate (predicted by the perturbation theory), the Z error rates of the Toffoli gate are predicted to be…”

Section: Toffolimentioning

confidence: 97%

“…In magic state distillation schemes, the goal is to distill magic states with circuits that require only stabilizer operations [30,31,33]. The circuits used to distill such magic states are typically not fault-tolerant to all Clifford gate errors and thus must be implemented using a sufficiently large error-correcting code.…”

Section: Toffoli Distillation: Bottom-up Schemementioning

confidence: 99%

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Building a fault-tolerant quantum computer using concatenated cat codes

Chamberland,

Noh,

Arrangoiz-Arriola

et al. 2020

Preprint

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We present a comprehensive architectural analysis for a fault-tolerant quantum computer based on cat codes concatenated with outer quantum error-correcting codes. For the physical hardware, we propose a system of acoustic resonators coupled to superconducting circuits with a two-dimensional layout. Using estimated near-term physical parameters for electro-acoustic systems, we perform a detailed error analysis of measurements and gates, including CNOT and Toffoli gates. Having built a realistic noise model, we numerically simulate quantum error correction when the outer code is either a repetition code or a thin rectangular surface code. Our next step toward universal fault-tolerant quantum computation is a protocol for fault-tolerant Toffoli magic state preparation that significantly improves upon the fidelity of physical Toffoli gates at very low qubit cost. To achieve even lower overheads, we devise a new magic-state distillation protocol for Toffoli states. Combining these results together, we obtain realistic full-resource estimates of the physical error rates and overheads needed to run useful fault-tolerant quantum algorithms. We find that with around 1,000 superconducting circuit components, one could construct a fault-tolerant quantum computer that can run circuits which are intractable for classical supercomputers. Hardware with 32,000 superconducting circuit components, in turn, could simulate the Hubbard model in a regime beyond the reach of classical computing.

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Section: A Overview Of Main Resultsmentioning

confidence: 99%

Section: Toffolimentioning

confidence: 97%

Section: Toffoli Distillation: Bottom-up Schemementioning

confidence: 99%

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Building a fault-tolerant quantum computer using concatenated cat codes

Chamberland,

Noh,

Arrangoiz-Arriola

et al. 2020

Preprint

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“…A standard setting is that of the resource theory of magic [1,2], in which preparation of stabilizer states, Clifford unitaries and Pauli measurements are fault-tolerant and hence 'free', while magic states are a 'resource' that needs to be injected to achieve universality. Magic states may come at a limited rate, since their preparation involves complex distillation schemes [3][4][5][6][7][8]. Also, much of the residual noise in an error-corrected computation would ideally originate from these elements.…”

mentioning

confidence: 99%

Error mitigation and quantum-assisted simulation in the error corrected regime

Lostaglio,

Ciani

2021

Preprint

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We extend error mitigation to the case where the qubits are logically encoded in a quantum error correcting code. Here the noise to be corrected enters through the magic states needed to achieve universality. In this setting, we generalize the concept of robustness of magic to the quantum-assisted robustness of magic (QRoM), which is a magic measure relative to the available quantum resources. We show how the QRoM quantifies the sampling overhead of (quasiprobability-based) error mitigation algorithms as a function of the noise parameter, interpolating between classical simulation based on the Gottesman-Knill theorem and an ideal quantum computer. Furthermore, classical simulation and error mitigation can be seen as special instances of quantum-assisted simulation. In this task, fewer, noisier quantum resources boost classical simulations of a larger, ideal quantum computation with an overhead quantified by the QRoM. Finally we extend the error mitigation protocol beyond the ideal scenario by allowing residual noise on the fault-tolerant components of the circuit.

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“…Stabilizer operations can be promoted to universality by injecting magic states, which are thus a "resource" for quantum computation. Magic states may come at a limited rate, since their fault-tolerant preparation involves complex distillation schemes [6][7][8][9][10][11]. Also, much of the residual noise in an error corrected computation can originate from these elements.…”

mentioning

confidence: 99%