Symmetry-Protected Self-Correcting Quantum Memories

Roberts, Susan L.; Bartlett, Stephen D.

doi:10.1103/physrevx.10.031041

Cited by 35 publications

(42 citation statements)

References 101 publications

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“…From a condensed matter perspective, the models we have constructed can be viewed as symmetry-protected topological phases [103][104][105][106][107][108][109]. Further study of these models may therefore lead to new phases of matter that are robust resources for quantum information processing tasks.…”

Section: Discussionmentioning

confidence: 99%

Universal fault-tolerant measurement-based quantum computation

Brown

Roberts

2020

Phys. Rev. Research

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Certain physical systems that one might consider for fault-tolerant quantum computing where qubits do not readily interact, for instance photons, are better suited for measurement-based quantum-computational protocols. Here we propose a measurement-based model for universal quantum computation that simulates the braiding and fusion of Majorana modes. To derive our model we develop a general framework that maps any scheme of fault-tolerant quantum computation with stabilizer codes into the measurement-based picture. As such, our framework gives an explicit way of producing fault-tolerant models of universal quantum computation with linear optics using any protocol developed using the stabilizer formalism. Given the remarkable fault-tolerant properties that Majorana modes promise, the main example we present offers a robust and resource-efficient proposal for photonic quantum computation.

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Section: Discussionmentioning

confidence: 99%

Universal fault-tolerant measurement-based quantum computation

Brown

Roberts

2020

Phys. Rev. Research

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“…the 2D cluster state) [63,64] or protected by higher-form symmetries (e.g. the 3D cluster state) [23,[65][66][67][68][69]. In our argument, we assumed that the protecting symmetry is a 0-form symmetry, i.e., it is supported on a codimension-0 manifold.…”

Section: Symmetry-protected Magic In Spt Statesmentioning

confidence: 99%

Symmetry-protected sign problem and magic in quantum phases of matter

Ellison

Kato

Liu

et al. 2021

Quantum

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We introduce the concepts of a symmetry-protected sign problem and symmetry-protected magic to study the complexity of symmetry-protected topological (SPT) phases of matter. In particular, we say a state has a symmetry-protected sign problem or symmetry-protected magic, if finite-depth quantum circuits composed of symmetric gates are unable to transform the state into a non-negative real wave function or stabilizer state, respectively. We prove that states belonging to certain SPT phases have these properties, as a result of their anomalous symmetry action at a boundary. For example, we find that one-dimensional Z2×Z2 SPT states (e.g. cluster state) have a symmetry-protected sign problem, and two-dimensional Z2 SPT states (e.g. Levin-Gu state) have symmetry-protected magic. Furthermore, we comment on the relation between a symmetry-protected sign problem and the computational wire property of one-dimensional SPT states. In an appendix, we also introduce explicit decorated domain wall models of SPT phases, which may be of independent interest.

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“…In particular, as the stability of topological order is closely connected to QEC [73][74][75][76], it is natural to expect interesting interplay between approximate symmetries and topological features especially in certain symmetry-protected topological (SPT) phases, for which our theory may be useful. Indeed, the QEC properties of SPT phases is under active study recently [76][77][78]. One potentially interesting subject that arises is to understand the "robustness" of topological or QEC features associated with "approximate SPT" order.…”

Section: Potential Physical Applicationsmentioning

confidence: 99%

Approximate symmetries and quantum error correction

Liu¹,

Zhou²

2021

Preprint

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It is known that continuous symmetries induce fundamental restrictions on the accuracy of quantum error correction (QEC). Here we systematically study the competition between continuous symmetries and QEC in a quantitative manner. We first define meaningful measures of approximate symmetries based on the degree of covariance and charge conservation violation, which induce corresponding notions of approximately covariant codes, and then derive a series of trade-off bounds between these different approximate symmetry measures and QEC accuracy by leveraging insights and techniques from approximate QEC, quantum metrology, and resource theory. From a quantum computation perspective, our results indicate general limits on the precision and density of transversal logical gates. For concrete examples, we showcase two explicit types of approximately covariant codes that nearly saturate certain bounds, respectively obtained from quantum Reed-Muller codes and thermodynamic codes. Finally, we discuss potential applications of our theory to several important topics in physics.

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Symmetry-Protected Self-Correcting Quantum Memories

Cited by 35 publications

References 101 publications

Universal fault-tolerant measurement-based quantum computation

Universal fault-tolerant measurement-based quantum computation

Symmetry-protected sign problem and magic in quantum phases of matter

Approximate symmetries and quantum error correction

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