A new take on permutation-invariant quantum codes

We construct a new family of permutationally invariant codes that correct t Pauli errors for any t≥1 . We also show that codes in the new family correct quantum deletion errors as well as spontaneous decay errors. Our construction contains some of the previously known permutationally invariant quantum codes as particular cases, which also admit transversal gates. In many cases, the codes in the new family are shorter than the best previously known explicit permutationally invariant codes for Pauli errors and deletions. Furthermore, our new code family includes a new ((4,2,2)) optimal single-deletion-correcting code. As a separate result, we generalize the conditions for permutationally invariant codes to correct t Pauli errors from the previously known results for t=1 to any number of errors. For small t , these conditions can be used to construct new examples of codes by computer.We construct a new family of permutationally invariant codes that correct t Pauli errors for any t≥1 . We also show that codes in the new family correct quantum deletion errors as well as spontaneous decay errors. Our construction contains some of the previously known permutationally invariant quantum codes as particular cases, which also admit transversal gates. In many cases, the codes in the new family are shorter than the best previously known explicit permutationally invariant codes for Pauli errors and deletions. Furthermore, our new code family includes a new ((4,2,2)) optimal single-deletion-correcting code. As a separate result, we generalize the conditions for permutationally invariant codes to correct t Pauli errors from the previously known results for t=1 to any number of errors. For small t , these conditions can be used to construct new examples of codes by computer.

arXiv:2310.05358QuantumApr 30, 202418 citations

A Family of Permutationally Invariant Quantum Codes

Arda Aydin, Max A. Alekseyev, Alexander Barg

We construct a new family of permutationally in-variant codes that correct $t$ Pauli errors for any $t\geqslant 1$ . We also show that codes in the new family correct quantum deletion errors as well as spontaneous decay errors. Our construction contains some of the previously known permutationally invariant quantum codes as particular cases. In many cases, the codes in the new family are shorter than the best previously known explicit permutationally invariant codes for Pauli errors and deletions. This is an extended abstract of the preprint [1].We construct a new family of permutationally in-variant codes that correct$t$Pauli errors for any$t\geqslant 1$. We also show that codes in the new family correct quantum deletion errors as well as spontaneous decay errors. Our construction contains some of the previously known permutationally invariant quantum codes as particular cases. In many cases, the codes in the new family are shorter than the best previously known explicit permutationally invariant codes for Pauli errors and deletions. This is an extended abstract of the preprint [1].

IEEE International Symposium on Information Theory (ISIT)Jul 7, 20240 citations

New Quantum Codes Derived from Cyclic Codes

Binbin Pang, Shixin Zhu, Jin Li +1 more

International Journal of Theoretical PhysicsJan 21, 20202 citations

Permutation-invariant codes encoding more than one qubit

Yingkai Ouyang, Joseph F. Fitzsimons

A permutation-invariant code on $m$ qubits is a subspace of the symmetric subspace of the $m$ qubits. We derive permutation-invariant codes that can encode an increasing amount of quantum information while suppressing leading-order spontaneous decay errors. To prove the result, we use elementary number theory with prior theory on permutation-invariant codes and quantum error correction.A permutation-invariant code on $m$ qubits is a subspace of the symmetric subspace of the $m$ qubits. We derive permutation-invariant codes that can encode an increasing amount of quantum information while suppressing leading-order spontaneous decay errors. To prove the result, we use elementary number theory with prior theory on permutation-invariant codes and quantum error correction.

arXiv:1512.02469Physical Review AApr 26, 201636 citations

We construct a new family of permutationally in-variant codes that correct

t

Pauli errors for any

t\geqslant 1

. We also show that codes in the new family correct quantum deletion errors as well as spontaneous decay errors. Our construction contains some of the previously known permutationally invariant quantum codes as particular cases. In many cases, the codes in the new family are shorter than the best previously known explicit permutationally invariant codes for Pauli errors and deletions. This is an extended abstract of the preprint [1].

A permutation-invariant code on

m

qubits is a subspace of the symmetric subspace of the

m

qubits. We derive permutation-invariant codes that can encode an increasing amount of quantum information while suppressing leading-order spontaneous decay errors. To prove the result, we use elementary number theory with prior theory on permutation-invariant codes and quantum error correction.