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Related papers: A Note on Clifford Stabilizer Codes for Ising Anyo…

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We perform an extended numerical search for practical fermion-to-qubit encodings with error correcting properties. Ideally, encodings should strike a balance between a number of the seemingly incompatible attributes, such as having a high…

Quantum Physics · Physics 2024-05-29 Fedor Simkovic , Martin Leib , Francisco Revson F. Pereira

We construct Narain conformal field theories (CFTs) from quantum subsystem codes, a more comprehensive class of quantum error-correcting codes than quantum stabilizer codes, for qudit systems of prime dimensions. The resulting code CFTs…

High Energy Physics - Theory · Physics 2024-11-26 Keiichi Ando , Kohki Kawabata , Tatsuma Nishioka

A non-Hermitian version of Rashba Hamiltonian has been introduced motivated from the Levy-leblond type linearisation of Schrodinger equation in a Galilean invariant frame-work. The said Hamiltonian is found to be pseudo-Hermitian under…

Mathematical Physics · Physics 2023-04-18 Arindam Chakraborty

We provide a detailed study of the general structure of two-dimensional topological stabilizer quantum error correcting codes, including subsystem codes. Under the sole assumption of translational invariance, we show that all such codes can…

Quantum Physics · Physics 2015-05-28 H. Bombin

In this article, we firstly introduce higher spin Clifford analysis, which are considered as generalizations of classical Clifford analysis by considering functions taking values in irreducible representations of the spin group. Then, we…

Mathematical Physics · Physics 2024-02-06 Chao Ding , John Ryan

Stabilizer circuits arise in almost every area of quantum computation and communication, so there is interest in studying them from an information-theoretic perspective, i.e. as quantum channels. We consider several natural approaches to…

Quantum Physics · Physics 2025-03-26 Vsevolod I. Yashin , Maria A. Elovenkova

The monograph offers a coherent and self-contained treatment of massless (ladder) representations of the conformal group U(2,2) and their restriction to the de Sitter group Sp(2,2), combining rigorous representation-theoretic analysis with…

Mathematical Physics · Physics 2026-04-07 Jean-Pierre Gazeau , Hamed Pejhan , Ivan Todorov

Chiral Majorana fermion is a massless self-conjugate fermion which can arise as the edge state of certain two-dimensonal topological matters. It has been theoretically predicted and experimentally observed in a hybrid device of quantum…

Mesoscale and Nanoscale Physics · Physics 2018-10-10 Biao Lian , Xiao-Qi Sun , Abolhassan Vaezi , Xiao-Liang Qi , Shou-Cheng Zhang

I present a new approach for designing quantum error-correcting codes that guarantees a physically natural implementation of Clifford operations. Inspired by the scheme put forward by Gottesman, Kitaev, and Preskill for encoding a qubit in…

Quantum Physics · Physics 2021-07-07 Jonathan A. Gross

This manuscript introduces various notions of k-locality of stabilizer codes inherited from the associated stabilizer groups. A choice of generators for the group leads to a Hamiltonian with the code in its groundspace, while a Hamiltonian…

Quantum Physics · Physics 2008-02-06 Stephen S. Bullock , Dianne P. O'Leary

We define and show how to construct nonbinary quantum stabilizer codes. Our approach is based on nonbinary error bases. It generalizes the relationship between selforthogonal codes over $GF_{4}$ and binary quantum codes to one between…

Quantum Physics · Physics 2007-05-23 Alexei Ashikhmin , Emanuel Knill

Quantum error correction is an essential ingredient for reliable quantum computation for theoretically provable quantum speedup. Topological color codes, one of the quantum error correction codes, have an advantage against the surface codes…

Quantum Physics · Physics 2024-02-02 Yugo Takada , Yusaku Takeuchi , Keisuke Fujii

We study the phase transition from two different topological phases to the ferromagnetic phase by focusing on points of the phase transition. To this end, we present a detailed mapping from such models to the Ising model in a transverse…

Quantum Physics · Physics 2015-06-23 Mohammad Hossein Zarei

We prove that the natural isomorphism between GF(2^h) and GF(2)^h induces a bijection between stabiliser codes on n quqits with local dimension q=2^h and binary stabiliser codes on hn qubits. This allows us to describe these codes…

Combinatorics · Mathematics 2024-09-10 Simeon Ball , Edgar Moreno , Robin Simoens

A number of new L$\acute{e}$vi-Leblond type equations admitting four component spinor solutions have been proposed. The pair of linearized equations thus obtained in each case lead to Hamiltonians with characteristic features like L-S…

Quantum Physics · Physics 2019-03-08 Arindam Chakraborty , Bhaskar Debnath , Ritaban Datta , Pratyay Banerjee

We describe a method to use measurements and correction operations in order to implement the Clifford group in a stabilizer code, generalising a result from [Bombin,2011] for topological subsystem colour codes. In subsystem stabilizer codes…

Quantum Physics · Physics 2025-02-10 Darren Banfield , Heather Leitch , Alastair Kay

We classify instances of quantum pseudo-telepathy in the graph isomorphism game, exploiting the recently discovered connection between quantum information and the theory of quantum automorphism groups. Specifically, we show that graphs…

Quantum Physics · Physics 2019-05-14 Benjamin Musto , David Reutter , Dominic Verdon

We show that all quantum gates which could be implemented by braiding of Ising anyons in the Ising topological quantum computer preserve the n-qubit Pauli group. Analyzing the structure of the Pauli group's centralizer, also known as the…

Mathematical Physics · Physics 2015-05-14 Andre Ahlbrecht , Lachezar S. Georgiev , Reinhard F. Werner

We revisit the Pauli-Clifford connection to introduce a real, grade-preserving algebraic framework for $n$-qubit quantum computation based on the tensor product $C\ell_{2,0}(\mathbb{R})^{\otimes n}$. In this setting, the bivector $J =…

Quantum Physics · Physics 2026-04-10 Kagwe A. Muchane

Linear combination of unitaries (LCU) decompositions have appeared as one of the main tools for encoding operators on quantum computers, allowing efficient implementations of arbitrary operators. In particular, LCU approaches present a way…

Quantum Physics · Physics 2024-10-16 Ignacio Loaiza , Aritra Sankar Brahmachari , Artur F. Izmaylov