2-designs and redundant syndrome extraction for quantum error correction

Premakumar, Vickram N.; Sha, Hele; Crow, Daniel; Bach, Eric; Joynt, Robert

doi:10.1007/s11128-021-03015-1

Cited by 5 publications

(3 citation statements)

References 11 publications

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“…This is due to stabilizer of different weights being measured in our SM scheme, resulting in a different number of total measurements being done. Ashikhmin et al [3] and Premakumar et al [26] sidestep this issue by choosing stabilizer code whose non-identity stabilizer elements are all of the same weight or of almost the same weights. While this is the case for the stabilizer group of the 9-qubit Bacon-Shor code, it is not true for the Shor code, which has Z-stabilizer generators that range from weight-2 to weight-6.…”

Section: Starting With Anmentioning

confidence: 99%

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Quantum Data-Syndrome Codes: Subsystem and Impure Code Constructions

Nemec¹

2023

Preprint

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Quantum error correction requires the use of error syndromes derived from measurements that may be unreliable. Recently, quantum data-syndrome (QDS) codes have been proposed as a possible approach to protect against both data and syndrome errors, in which a set of linearly dependent stabilizer measurements are performed to increase redundancy. Motivated by wanting to reduce the total number of measurements performed, we introduce QDS subsystem codes, and show that they can outperform similar QDS stabilizer codes derived from them. We also give a construction of single-error-correcting QDS stabilizer codes from impure stabilizer codes, and show that any such code must satisfy a variant of the quantum Hamming bound for QDS codes. Finally, we use this bound to prove a new bound that applies to impure, but not pure, stabilizer codes that may be of independent interest.

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Section: Starting With Anmentioning

confidence: 99%

“…More recent work on QDS codes has included more efficient decoding techniques [21], [28], connections to the theory of 2designs [26], and an extension to quantum convolutional codes [38]. Recently, Wagner et al [36] showed how QDS codes can be used to estimate a logical channel with a phenomenological Pauli noise model.…”

Section: Introductionmentioning

confidence: 99%

Quantum Data-Syndrome Codes: Subsystem and Impure Code Constructions

Nemec¹

2023

Preprint

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“…After an error stage represented by the circuit element E ∈ {I, X 1 , X 2 , X 3 }, we consistently observe that two stabilizer prompts exhibit errors, while one stabilizer prompt remains error-free. This strategy has been used in combination with 2-designs to improve the fault tolerance of error correction circuits [96]. In addition, its combination with our parity-controlled gate will yield even more unexpected results.…”

Section: B Distance-3 Repetition Codementioning

confidence: 99%

Quantum error rejection for faithful quantum communication over noise channels

Guo

Gao

et al. 2019

Sci. China Phys. Mech. Astron.

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Quantum error detection relies primarily on precise measurement of qubit parity, a fundamental operation in quantum information processing. Here, we introduce a resilient parity-controlled gate tailored for detecting quantum errors within a 2D Rydberg atom array. Our method enables the discrimination between even and odd parities of virtually excited control atoms by tracking the dynamic evolution of an auxiliary atom. Using spin-exchange dipolar interactions of Rydberg states and single-and two-photon driving between ground states and Rydberg states, our method speeds up Rydberg-parity measurements by a large amount compared to previous methods. In practical application, we explore three-qubit repetition codes, standard surface codes featuring stabilizers in the forms ZZZZ and XXXX, as well as rotated surface codes in the XZZX configuration, facilitating the measurement of stabilizers with a single-shot readout. We carry out thorough numerical simulations to evaluate the feasibility of our strategy, considering potential experimental imperfections such as undesired interactions between Rydberg states, fluctuations in atomic positions, dephasing noise, and laser amplitude inhomogeneities. Particular emphasis is placed on ensuring the reliability and advantages of the physical mechanisms of the parity meter. These results affirm the robustness and viability of our protocol, positioning it as a promising candidate for quantum error detection employing the Rydberg atom system in the foreseeable future.

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