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Related papers: Quantum Self-Correcting Stabilizer Codes

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To build a fault-tolerant quantum computer, it is necessary to implement a quantum error correcting code. Such codes rely on the ability to extract information about the quantum error syndrome while not destroying the quantum information…

It has been recently discovered that stabilization of two-dimensional (2D) solitons against the critical collapse in media with the cubic nonlinearity by means of nonlinear lattices (NLs) is a challenging problem. We address the 1D version…

Pattern Formation and Solitons · Physics 2015-06-03 Jianhua Zeng , Boris A. Malomed

Precise control of atom-light interactions is vital to many quantum information protocols. In particular, atomic systems can be used to slow and store light to form a quantum memory. Optical storage can be achieved via stopped light, where…

An important measure of utility for a quantum code is the identification of which logical operations can be implemented fault-tolerantly on its codespace. We introduce a framework which leverages the automorphism groups of associated…

Quantum Physics · Physics 2026-04-03 Aisling Mac Aree , Mark Howard

We give an introduction to the theory of quantum error correction using stabilizer codes that is geared towards the working computer scientists and mathematicians with an interest in exploring this area. To this end, we begin with an…

Quantum Physics · Physics 2026-02-03 Zachary P. Bradshaw , Jeffrey J. Dale , Ethan N. Evans

A self-stabilizing simulation of a single-writer multi-reader atomic register is presented. The simulation works in asynchronous message-passing systems, and allows processes to crash, as long as at least a majority of them remain working.…

Distributed, Parallel, and Cluster Computing · Computer Science 2010-08-03 Noga Alon , Hagit Attiya , Shlomi Dolev , Swan Dubois , Maria Gradinariu , Sebastien Tixeuil

We discuss real-space lattice models equivalent to gauge theories with a discrete non-Abelian gauge group. We construct the Hamiltonian formalism which is appropriate for their solid-state physics implementation and outline their basic…

Strongly Correlated Electrons · Physics 2010-05-11 B. Doucot , L. B. Ioffe , J. Vidal

Active quantum error correction is a central ingredient to achieve robust quantum processors. In this paper we investigate the potential of quantum machine learning for quantum error correction in a quantum memory. Specifically, we…

Quantum Physics · Physics 2023-03-15 David F. Locher , Lorenzo Cardarelli , Markus Müller

We present rigorous bounds on the thermalization time of the family of quantum mechanical spin systems known as stabilizer Hamiltonians. The thermalizing dynamics are modeled by a Davies master equation that arises from a weak local…

Quantum Physics · Physics 2015-05-29 Kristan Temme , Michael J. Kastoryano

In this paper we investigate stabilizer quantum error correction codes using controlled phase rotations of strong coherent probe states. We explicitly describe two methods to measure the Pauli operators which generate the stabilizer group…

Quantum Physics · Physics 2009-11-13 Casey R. Myers , Marcus Silva , Kae Nemoto , William J. Munro

We study the behaviour of continuous automorphism groups of quantum spin systems on the lattice. Whereas the shift is norm asymptotically abelian continuous automorphism groups can lead only to delocalization but not to norm asymptotic…

Mathematical Physics · Physics 2024-05-31 Heide Narnhofer

We introduce a purely graph-theoretical object, namely the coding clique, to construct quantum errorcorrecting codes. Almost all quantum codes constructed so far are stabilizer (additive) codes and the construction of nonadditive codes,…

Quantum Physics · Physics 2007-09-13 Sixia Yu , Qing Chen , C. H. Oh

A two-dimensional quantum system with anyonic excitations can be considered as a quantum computer. Unitary transformations can be performed by moving the excitations around each other. Measurements can be performed by joining excitations in…

Quantum Physics · Physics 2009-10-30 A. Yu. Kitaev

Sensitivity to noise makes most of the current quantum computing schemes prone to error and nonscalable, allowing only for small proof-of-principle devices. Topologically-protected quantum computing aims at solving this problem by encoding…

Disordered Systems and Neural Networks · Physics 2013-12-17 Helmut G. Katzgraber , Ruben S. Andrist

Simulating quantum dynamics on digital or analog quantum simulators often requires ``problem-to-simulator" mappings such as trotterization, floquet-magnus expansion or perturbative expansions. When the simulator is noiseless, it is well…

Quantum Physics · Physics 2025-09-23 Rahul Trivedi , J. Ignacio Cirac

Standard approaches to quantum error correction (QEC) require active maintenance using measurements and classical processing. Passive QEC, by contrast, has so far been established only in unphysical spatial dimensions. Here, we give an…

Quantum Physics · Physics 2026-05-22 Gesa Dünnweber , Georgios Styliaris , Rahul Trivedi

An important open question for the current generation of highly controllable quantum devices is understanding which phases can be realized as stable steady-states under local quantum dynamics. In this work, we show how robust steady-state…

Quantum Physics · Physics 2025-12-02 Sanket Chirame , Abhinav Prem , Sarang Gopalakrishnan , Fiona J. Burnell

We construct quantum error-correcting codes that embed a finite-dimensional code space in the infinite-dimensional Hilbert state space of rotational states of a rigid body. These codes, which protect against both drift in the body's…

Quantum Physics · Physics 2020-09-09 Victor V. Albert , Jacob P. Covey , John Preskill

We consider a two-dimensional spin system that exhibits abelian anyonic excitations. Manipulations of these excitations enable the construction of a quantum computational model. While the one-qubit gates are performed dynamically the model…

Quantum Physics · Physics 2007-08-28 Jiannis K. Pachos

A quantum thermodynamic system is described by a Hamiltonian and a list of conserved, non-commuting charges, and a fundamental goal is to determine the minimum energy of the system subject to constraints on the charges. Recently, [Liu et…