Universal fault-tolerant quantum computation using fault-tolerant conversion schemes

Luo, Liang; Ma, Zhi

doi:10.1088/1367-2630/ab3378

Cited by 2 publications

(5 citation statements)

References 27 publications

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“…In particular, S gate can obtain a higher threshold on QRM (1,3) than CNOT [45,90,91], since there are fewer kinds of error-prone positions in the former gate circuit (with only one logical qubit involved). [44]) coding on them. The CNOT operations between the second and the sixth steps correspond to the following X stabilizer generators respectively.…”

Section: H-type Msdmentioning

confidence: 99%

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Magic state distillation and cost analysis in fault-tolerant universal quantum computation

Liu¹,

Luo²,

Ma³

et al. 2023

Quantum Sci. Technol.

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Magic states have been widely studied in recent years as resource states that help quantum computers achieve fault-tolerant universal quantum computing. The fault-tolerant quantum computing requires fault-tolerant implementation of a set of universal logical gates. Stabilizer code, as a commonly used error correcting code with good properties, can apply the Clifford gates transversally which is fault tolerant. But only Clifford gates can not realize universal computation. Magic states are introduced to construct non-Clifford gates that combine with Clifford operations to achieve universal quantum computing. Since the preparation of quantum states is inevitably accompanied by noise, preparing the magic state with high fidelity and low overhead is the crucial problem to realizing universal quantum computation. In this paper, we survey the related literature in the past 20 years and introduce the common types of magic states, the protocols to obtain high-fidelity magic states, and overhead analysis for these protocols. Finally, we discuss the future directions of this field.

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Section: H-type Msdmentioning

confidence: 99%

“…There are three mainstream models for implementing FTUQC, the magic state model [11,26,37,38], the concatenation mode [39][40][41], and the fault-tolerant conversion model [42][43][44][45]. As the earliest proposal to realize FTUQC, the magic distillation scheme has been extensively studied.…”

Section: Introductionmentioning

confidence: 99%

Magic state distillation and cost analysis in fault-tolerant universal quantum computation

Liu¹,

Luo²,

Ma³

et al. 2023

Quantum Sci. Technol.

Self Cite

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“…We begin by briefly reviewing the two fault-tolerant schemes based on QRM codes. For more details, please refer to references [15,16,28].…”

Section: Scheme Overviewmentioning

confidence: 99%

“…Similar to QRM(1, 3), QRM (2,5) has transversal H and CNOT gates, and can realize the non-transversal T gate by first converting to QRM(2, 7) (with QRM (2,6) being an intermediate code), transversally applying T gates, and then converting the code back to QRM (2,5). Different from reference [28], we pick all syndrome bits from the common stabilizer generators of QRM(2, 5) (combined with The conversion from QRM (2,6) to QRM(2, 7) completes in a similar way. Using the stabilizer overlapping method, we present all types of locations in the encoding circuits for ancillary states in table 1.…”

Section: The 31-qubit Code Qrm(2 5)mentioning

confidence: 99%

“…Later, Choi [27] computed the average gate cost of a logical T gate on QRM (1,3) in a post-selected quantum computation model. In the work of reference [28], the conversion schemes between higher-order QRM codes QRM(r, m) are provided, along with the analysis on the logical error rate of a logical T gate on QRM (2,5). The reduction of the logical error rate, however, has not been clearly investigated in their work as a function of concatenation level.…”

Section: Introductionmentioning

confidence: 99%

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Fault-tolerance thresholds for code conversion schemes with quantum Reed–Muller codes

Luo¹,

Ma²,

Lin³

et al. 2020

Quantum Sci. Technol.

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Code concatenation and conversion are two prominent methods to realize universal fault-tolerant quantum computation without the need for magic state distillation. In this paper, we analyze three quantum Reed-Muller (QRM) codes of different code lengths under code conversion schemes, and compare them with the 105-qubit concatenated code on optimized encoding circuits. The depolarizing error thresholds for the 7-, 15-, and 31-qubit QRM codes turn out to be 1.19 × 10 −3 , 5.40 × 10 −4 and 2.41 × 10 −6 respectively, all of three compared unfavorably with the improved result of 1.52 × 10 −3 for the 105-qubit code, which indicates a relatively small error-suppression capability and strict precision requirements for hardware equipment when using the code conversion scheme. While for resource requirements, code conversion schemes show obvious advantages. For the seven-qubit QRM code, the required qubit and gate overheads for level-3 gates to achieve the target logical error rate of 10 −15 are roughly 4 orders of magnitude smaller than those for the 105-qubit code.

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Universal fault-tolerant quantum computation using fault-tolerant conversion schemes

Cited by 2 publications

References 27 publications

Magic state distillation and cost analysis in fault-tolerant universal quantum computation

Magic state distillation and cost analysis in fault-tolerant universal quantum computation

Fault-tolerance thresholds for code conversion schemes with quantum Reed–Muller codes

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