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Loss-tolerant all-photonic quantum repeater with generalized Shor code

The all-photonic quantum repeater (APQR) is a promising repeater scheme to
realize long-distance quantum communication. For a practical APQR, an
indispensable requirement is the robustness of the repe

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Homomorphic Logical Measurements

Shor and Steane ancilla are two well-known methods for fault-tolerant logical
measurements, which are successful on small codes and their concatenations. On
large quantum low-density-parity-check (LDP

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Shor-Movassagh chain leads to unusual integrable model

The ground state of Shor-Movassagh chain can be analytically described by the
Motzkin paths. There is no analytical description of the excited states, the
model is not solvable. We prove the integrabi

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Between Shor and Steane: A unifying construction for measuring error syndromes

Fault-tolerant quantum error correction requires the measurement of error
syndromes in a way that minimizes correlated errors on the quantum data. Steane
and Shor ancilla are two well-known methods fo

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Disordered Systems and Neural Networks

Statistical Mechanics

Strongly Correlated Electrons

Quantum Physics

A 2D measurement-only random circuit motivated by the Bacon-Shor error correcting code

Subsystem symmetry, spin glass order, and criticality from random measurements in a 2D Bacon-Shor circuit

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The Algorithm of Shor for Prime Factorization

Continued Fractions and Probability Estimations in the Shor Algorithm -- A Detailed and Self-Contained Treatise

We present the relevant results and proofs from the theory of continued fractions in detail (even in more detail than in text books) filling the gap to allow a complete comprehension of the algorithm of shor for prime factorization.

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Universal fault-tolerant quantum computation with Bacon-Shor codes

We present a fault-tolerant universal gate set consisting of Hadamard and
controlled-controlled-Z (CCZ) on Bacon-Shor subsystem codes. Transversal
non-Clifford gates on these codes are intriguing in t

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Optimal Bacon-Shor codes

We study the performance of Bacon-Shor codes, quantum subsystem codes which
are well suited for applications to fault-tolerant quantum memory because the
error syndrome can be extracted by performing

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2-D Compass Codes

The compass model on a square lattice provides a natural template for
building subsystem stabilizer codes. The surface code and the Bacon-Shor code
represent two extremes of possible codes depending o

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Adaptive syndrome measurements for Shor-style error correction

The Shor fault-tolerant error correction (FTEC) scheme uses transversal gates
and ancilla qubits prepared in the cat state in syndrome extraction circuits to
prevent propagation of errors caused by ga

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Direct measurement of Bacon-Shor code stabilizers

A Bacon-Shor code is a subsystem quantum error-correcting code on an $L
\times L$ lattice where the $2(L-1)$ weight-$2L$ stabilizers are usually
inferred from the measurements of $(L-1)^2$ weight-2 ga

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Fault-Tolerant Preparation of Quantum Polar Codes Encoding One Logical Qubit

This paper explores a new approach to fault-tolerant quantum computing,
relying on quantum polar codes. We consider quantum polar codes of
Calderbank-Shor-Steane type, encoding one logical qubit, whic

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Demonstration of Shor encoding on a trapped-ion quantum computer

Fault-tolerant quantum error correction (QEC) is crucial for unlocking the
true power of quantum computers. QEC codes use multiple physical qubits to
encode a logical qubit, which is protected against

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Approximate Bacon-Shor Code and Holography

We construct an explicit and solvable toy model for the AdS/CFT
correspondence in the form of an approximate quantum error correction code with
a non-trivial center in the code subalgebra. Specificall

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Realization of a scalable Shor algorithm

Quantum computers are able to outperform classical algorithms. This was long
recognized by the visionary Richard Feynman who pointed out in the 1980s that
quantum mechanical problems were better solve

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Fault-Tolerant Operation of a Quantum Error-Correction Code

Quantum error correction protects fragile quantum information by encoding it
in a larger quantum system whose extra degrees of freedom enable the detection
and correction of errors. An encoded logical

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Bacon-Shor Quantum Error Correction Codes

From Generalization of Bacon-Shor Codes to High Performance Quantum LDPC Codes

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Quantum phase transition from bounded to extensive entanglement entropy in a frustration-free spin chain

We introduce a continuous family of frustration-free Hamiltonians with
exactly solvable ground states. We prove that the {ground state of our model is
non-degenerate and exhibits} a novel quantum phas

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Logical Performance of 9 Qubit Compass Codes in Ion Traps with Crosstalk Errors

We simulate four quantum error correcting codes under error models inspired
by realistic noise sources in near-term ion trap quantum computers: $T_2$
dephasing, gate overrotation, and crosstalk. We us

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Toric Varieties and Codes, Error-correcting Codes, Quantum Codes, Secret Sharing and Decoding

Toric varieties and their associated toric codes, as well as determination of
their parameters with intersection theory, are presented in the two dimensional
case.
Linear Secret Sharing Schemes with s

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