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Entanglement increases the error-correcting ability of quantum error-correcting codes

TLDR
This work shows how to optimize the minimum distance of an entanglement-assisted quantum error-correcting (EAQEC) code, obtained by adding ebits to a regular quantum stabilizer code, over different encoding operators.
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On statistically-secure quantum homomorphic encryption

TLDR
This work provides a limitation for the first question that an ITS quantum FHE necessarily incurs exponential overhead and proposes a QHE scheme for the instantaneous quantum polynomial-time (IQP) circuits.
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Duality in Entanglement-Assisted Quantum Error Correction

TLDR
A table of upper and lower bounds on the minimum distance of any maximal-entanglement EAQEC code with length up to 15 channel qubits is established.
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Linear Programming Bounds for Entanglement-Assisted Quantum Error-Correcting Codes by Split Weight Enumerators

  • C. LaiA. Ashikhmin
  • Computer Science
    IEEE Transactions on Information Theory
  • 1 February 2016
TLDR
The Singleton bound and Hamming bound are more general than the previous bounds for entanglement-assisted quantum stabilizer codes, and the first linear programming bound is shown to improve the linear programming bounds on the minimum distance of quantum codes of small length.
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Entanglement-assisted quantum error-correcting codes with imperfect ebits

TLDR
It is shown that any (nondegenerate) standard stabilizer code can be transformed into an EAQEC code that can correct errors on the qubits of both sender and receiver, and hence the decoding techniques of standard stabilizers codes can be applied.
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Dualities and identities for entanglement-assisted quantum codes

TLDR
The dual of an entanglement-assisted quantum error-correcting (EAQEC) code is the code resulting from exchanging the original code’s information qubits with its ebits, and an explicit, general quantum shift-register circuit is given that encodes both classes of codes.
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QuRE: The Quantum Resource Estimator toolbox

TLDR
The tradeoff between concatenated and surface error correction coding techniques is investigated, demonstrating the existence of a crossover point for the Ground State Estimation Algorithm.
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On the need for large Quantum depth

TLDR
The results show that relative to oracles, doubling the quantum circuit depth indeed gives the hybrid model more power, and this cannot be traded by classical computation.
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Estimating the Resources for Quantum Computation with the QuRE Toolbox

TLDR
This work, which provides these resource estimates for a cross product of seven quantum algorithms, six physical machine descriptions, several quantum control protocols, and four error-correcting codes, represents the most comprehensive resource estimation effort in the field of quantum computation to date.

Performance and error analysis of Knill's postselection scheme in a two-dimensional architecture

TLDR
This work shows how to use Knill's postselection scheme in a practical two-dimensional quantum architecture that was designed with the goal to optimize the error correction properties, while satisfying important architectural constraints.
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