Low-overhead quantum computing with the color code

Thomsen, Felix Sebastian Leo; Kesselring, Markus S.; Bartlett, Stephen D.; Brown, B. R.

doi:10.48550/arxiv.2201.07806

Cited by 4 publications

(6 citation statements)

References 53 publications

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“…Remarkably, we find that the operation is sufficiently rapid that its execution came at only a small cost in output state fidelity on the superconducting device. These dynamic circuits are essential to future quantum-computing architectures as they will be needed, for example, to perform magic-state distillation circuits [9][10][11] and gate teleportation 35,36 , as well as many other measurement-based methods 13,[17][18][19][37][38][39][40][41][42][43][44][45][46][47][48] that have been proposed to complete a universal set of logic gates.…”

Section: Discussionmentioning

confidence: 99%

“…Given there are known methods for distilling Toffoli states 11 , let us review how the Toffoli state is produced from the copies of the CZ state. In the following sections, we show how to inject the CZ state into larger quantum error-correcting codes that are capable of performing fault-tolerant Clifford operations 17,18,45 to complete these circuits.…”

Section: Using Cz States In Large-scale Quantum-computing Architecturesmentioning

confidence: 99%

“…We distil magic states to complete a universal set of fault-tolerant logic gates that is needed for large-scale quantum computing with low-density parity-check code architectures [13][14][15][16][17][18] . High-fidelity magic states are produced [9][10][11] by processing noisy input magic states with fault-tolerant distillation circuits; experimental progress in preparing input magic states using trapped-ion architectures is described in refs.…”

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confidence: 99%

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Encoding a magic state with beyond break-even fidelity

Gupta,

Sundaresan,

Alexander

et al. 2024

Nature

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To run large-scale algorithms on a quantum computer, error-correcting codes must be able to perform a fundamental set of operations, called logic gates, while isolating the encoded information from noise1–8. We can complete a universal set of logic gates by producing special resources called magic states9–11. It is therefore important to produce high-fidelity magic states to conduct algorithms while introducing a minimal amount of noise to the computation. Here we propose and implement a scheme to prepare a magic state on a superconducting qubit array using error correction. We find that our scheme produces better magic states than those that can be prepared using the individual qubits of the device. This demonstrates a fundamental principle of fault-tolerant quantum computing12, namely, that we can use error correction to improve the quality of logic gates with noisy qubits. Moreover, we show that the yield of magic states can be increased using adaptive circuits, in which the circuit elements are changed depending on the outcome of mid-circuit measurements. This demonstrates an essential capability needed for many error-correction subroutines. We believe that our prototype will be invaluable in the future as it can reduce the number of physical qubits needed to produce high-fidelity magic states in large-scale quantum-computing architectures.

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Section: Discussionmentioning

confidence: 99%

Section: Using Cz States In Large-scale Quantum-computing Architecturesmentioning

confidence: 99%

mentioning

confidence: 99%

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Encoding a magic state with beyond break-even fidelity

Gupta,

Sundaresan,

Alexander

et al. 2024

Nature

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“…For example, the logical operators of a topological code on a manifold with boundary are associated to ribbon operators [17] of anyons which connect different boundary segments through the bulk. Moreover, any lattice-surgery-based computation scheme ultimately relies on deforming non-transparent domain walls between code patches into (partly-)transparent ones in a systematic way [18][19][20]. Understanding how the anyon ribbon operators precisely behave close to these domain walls is therefore essential in the design of novel computational protocols in topological codes.…”

mentioning

confidence: 99%

“…This induces a local ordering of the faces around any vertex by the number of flags pointing into the faces. Analogously, one can think of such a framing as a branching structure on the dual triangulation, see for example(19).…”

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confidence: 99%

Bulk-to-boundary anyon fusion from microscopic models

Fuente¹,

Eisert²,

Bauer³

2023

Preprint

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Topological quantum error correction based on the manipulation of the anyonic defects constitutes one of the most promising frameworks towards realizing fault-tolerant quantum devices. Hence, it is crucial to understand how these defects interact with external defects such as boundaries or domain walls. Motivated by this line of thought, in this work, we study the fusion events between anyons in the bulk and at the boundary in fixed-point models of 2+1-dimensional nonchiral topological order defined by arbitrary fusion categories. Our construction uses generalized tube algebra techniques to construct a bi-representation of bulk and boundary defects. We explicitly derive a formula to calculate the fusion multiplicities of a bulk-to-boundary fusion event for twisted quantum double models and calculate some exemplary fusion events for Abelian models and the (twisted) quantum double model of S 3 , the simplest non-Abelian group-theoretical model. Moreover, we use the folding trick to study the anyonic behavior at non-trivial domain walls between twisted S 3 and twisted Z 2 as well as Z 3 models. A recurring theme in our construction is an isomorphism relating twisted cohomology groups to untwisted ones. The results of this work can directly be applied to study logical operators in two-dimensional topological error correcting codes with boundaries described by a twisted gauge theory of a finite group.

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Decoding quantum color codes with MaxSAT

Berent,

Burgholzer,

Derks

et al. 2024

Quantum

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In classical computing, error-correcting codes are well established and are ubiquitous both in theory and practical applications. For quantum computing, error-correction is essential as well, but harder to realize, coming along with substantial resource overheads and being concomitant with needs for substantial classical computing. Quantum error-correcting codes play a central role on the avenue towards fault-tolerant quantum computation beyond presumed near-term applications. Among those, color codes constitute a particularly important class of quantum codes that have gained interest in recent years due to favourable properties over other codes. As in classical computing, decoding is the problem of inferring an operation to restore an uncorrupted state from a corrupted one and is central in the development of fault-tolerant quantum devices. In this work, we show how the decoding problem for color codes can be reduced to a slight variation of the well-known LightsOut puzzle. We propose a novel decoder for quantum color codes using a formulation as a MaxSAT problem based on this analogy. Furthermore, we optimize the MaxSAT construction and show numerically that the decoding performance of the proposed decoder achieves state-of-the-art decoding performance on color codes. The implementation of the decoder as well as tools to automatically conduct numerical experiments are publicly available as part of the Munich Quantum Toolkit (MQT) on GitHub.

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Low-overhead quantum computing with the color code

Cited by 4 publications

References 53 publications

Encoding a magic state with beyond break-even fidelity

Encoding a magic state with beyond break-even fidelity

Bulk-to-boundary anyon fusion from microscopic models

Decoding quantum color codes with MaxSAT

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