Single-shot quantum error correction with the three-dimensional subsystem toric code

Kubica, Aleksander; Vasmer, Michael

doi:10.1038/s41467-022-33923-4

Cited by 24 publications

(2 citation statements)

References 94 publications

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“…These logical qubits are called gauge qubits. By fixing gauge qubits to some specific states, the same subsystem code may exhibit different properties, for instance, having different sets of transversal gates [7,44,45,51,67]. This provides a tool to circumvent restrictions on transversal gates such as the Eastin-Knill theorem [24].…”

Section: Css Subsystem Codesmentioning

confidence: 99%

Graphical CSS Code Transformation Using ZX Calculus

Huang,

Li,

Yeh

et al. 2023

Electron. Proc. Theor. Comput. Sci.

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In this work, we present a generic approach to transform CSS codes by building upon their equivalence to phase-free ZX diagrams. Using the ZX calculus, we demonstrate diagrammatic transformations between encoding maps associated with different codes. As a motivating example, we give explicit transformations between the Steane code and the quantum Reed-Muller code, since by switching between these two codes, one can obtain a fault-tolerant universal gate set. To this end, we propose a bidirectional rewrite rule to find a (not necessarily transversal) physical implementation for any logical ZX diagram in any CSS code.We then focus on two code transformation techniques: code morphing, a procedure that transforms a code while retaining its fault-tolerant gates, and gauge fixing, where complimentary codes can be obtained from a common subsystem code (e.g., the Steane and the quantum Reed-Muller codes from the 15, 1, 3, 3 code). We provide explicit graphical derivations for these techniques and show how ZX and graphical encoder maps relate several equivalent perspectives on these code transforming operations.

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Section: Css Subsystem Codesmentioning

confidence: 99%

Graphical CSS Code Transformation Using ZX Calculus

Huang,

Li,

Yeh

et al. 2023

Electron. Proc. Theor. Comput. Sci.

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“…Single-shot error correction is a different paradigm of decoding that uses only the results of a single round of QEC measurements, without any historical data. This type of decoding is only possible for certain quantum codes, such as higher-dimensional topological codes 16 – 19 and quantum low-density parity-check codes (qLDPC) 20 , 21 . To date, no such code has yet been able to reproduce the very high threshold of the surface code.…”

Section: Introductionmentioning

confidence: 99%

Parallel window decoding enables scalable fault tolerant quantum computation

Skoric,

Browne,

Barnes

et al. 2023

Nat Commun

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Large-scale quantum computers have the potential to hold computational capabilities beyond conventional computers. However, the physical qubits are prone to noise which must be corrected in order to perform fault-tolerant quantum computations. Quantum Error Correction (QEC) provides the path for realizing such computations. QEC generates a continuous stream of data that decoders must process at the rate it is received, which can be as fast as 1 μs per QEC round in superconducting quantum computers. If the decoder infrastructure cannot keep up, a data backlog problem is encountered and the computation runs exponentially slower. Today’s leading approaches to quantum error correction are not scalable as existing decoders typically run slower as the problem size is increased, inevitably hitting the backlog problem. Here, we show how to parallelize decoding to achieve almost arbitrary speed, removing this roadblock to scalability. Our parallelization requires some classical feed forward decisions to be delayed, slowing-down the logical clock speed. However, the slow-down is now only polynomial in the size of the QEC code, averting the exponential slowdown. We numerically demonstrate our parallel decoder for the surface code, showing no noticeable reduction in logical fidelity compared to previous decoders and demonstrating the predicted speedup.

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Single-Shot Decoding of Good Quantum LDPC Codes

Gu,

Tang,

Caha

et al. 2024

Commun. Math. Phys.

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Quantum Tanner codes constitute a family of quantum low-density parity-check codes with good parameters, i.e., constant encoding rate and relative distance. In this article, we prove that quantum Tanner codes also facilitate single-shot quantum error correction (QEC) of adversarial noise, where one measurement round (consisting of constant-weight parity checks) suffices to perform reliable QEC even in the presence of measurement errors. We establish this result for both the sequential and parallel decoding algorithms introduced by Leverrier and Zémor. Furthermore, we show that in order to suppress errors over multiple repeated rounds of QEC, it suffices to run the parallel decoding algorithm for constant time in each round. Combined with good code parameters, the resulting constant-time overhead of QEC and robustness to (possibly time-correlated) adversarial noise make quantum Tanner codes alluring from the perspective of quantum fault-tolerant protocols.

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Single-shot quantum error correction with the three-dimensional subsystem toric code

Cited by 24 publications

References 94 publications

Graphical CSS Code Transformation Using ZX Calculus

Graphical CSS Code Transformation Using ZX Calculus

Parallel window decoding enables scalable fault tolerant quantum computation

Single-Shot Decoding of Good Quantum LDPC Codes

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