From bfc9b8d75a61a820cbe7f60a6262b4716b41550c Mon Sep 17 00:00:00 2001 From: "Victor V. Albert" Date: Thu, 19 Sep 2024 14:25:52 -0400 Subject: [PATCH] refs --- codes/quantum/oscillators/oscillators.yml | 3 +++ codes/quantum/properties/qecc.yml | 3 ++- codes/quantum/qubits/majorana/fermions.yml | 3 ++- .../icosahedral_permutation_invariant.yml | 4 ++++ codes/quantum/qubits/qubits_into_qubits.yml | 2 ++ .../color/2d_color/triangular_color/triangular_color.yml | 2 +- 6 files changed, 14 insertions(+), 3 deletions(-) diff --git a/codes/quantum/oscillators/oscillators.yml b/codes/quantum/oscillators/oscillators.yml index ee482f02b..ca038177b 100644 --- a/codes/quantum/oscillators/oscillators.yml +++ b/codes/quantum/oscillators/oscillators.yml @@ -24,6 +24,9 @@ description: | Alternatively, states can be represented as functions over the reals by expanding in a continuous "basis" (more technically, set of tempered distributions in the space dual to Schwartz space), such as the position "basis" \(|y\rangle\) with \(y\in\mathbb{R}\) or the momentum "basis" \(|p\rangle\) with \(p\in\mathbb{R}\). States can further be represented as functions over the joint position-momentum phase space in the Wigner function formalism \cite{doi:10.1103/PhysRev.40.749,doi:10.1103/PhysRevA.15.449}. + An important subset of states is formed by the \textit{Gaussian states}, which are in one-to-one correspondence with a (displacement) vector and covariance matrix \cite{arxiv:quant-ph/0410100,arxiv:0801.4604,arxiv:1110.3234,arxiv:2010.15518,arxiv:2409.11628}. + Pure Gaussian states can be obtained from the \textit{vacuum Fock state} \(|n=0\rangle\) via a Gaussian unitary transformation (defined below). + protection: | \subsection{Displacement error basis} diff --git a/codes/quantum/properties/qecc.yml b/codes/quantum/properties/qecc.yml index a1a8a3a8c..188d640c2 100644 --- a/codes/quantum/properties/qecc.yml +++ b/codes/quantum/properties/qecc.yml @@ -63,7 +63,8 @@ notes: - 'See Refs. \cite{doi:10.1017/CBO9781139034807,doi:10.1201/b15868,preset:GottesmanBook} for books on quantum error correction.' - 'See video tutorials by \href{https://www.youtube.com/watch?v=_ls3KczZL2c}{V. V. Albert}, \href{https://www.youtube.com/watch?v=uD69GCYF9Zg}{S. M. Girvin}, \href{https://www.youtube.com/watch?v=buIbd_aXAHw}{P. Shor}, \href{https://www.youtube.com/watch?v=Je7sVJGKMgU}{B. Terhal}, and \href{https://www.youtube.com/watch?v=mcwpe8iJ5uo}{J. Wright}.' - 'Quantum error correction was initially claimed not to be theoretically possible \cite{arxiv:hep-th/9406058,doi:10.1098/rsta.1995.0106}.' - - 'A resource theory of quantum error correction has been developed \cite{doi:10.1103/PhysRevA.110.032413}.' + - 'Resource-theoretic interpretations of quantum error correction have been developed, including those that think of codes together with recovery operations as superchannels (a.k.a. quantum combs or bipartite operations) \cite{arxiv:1210.4722,arxiv:1406.7142,arxiv:2405.17567,arxiv:2409.09416}.' + # 20240704 subsystem QECC, hybrid QECC, and QECC are three children of OAQECC relations: diff --git a/codes/quantum/qubits/majorana/fermions.yml b/codes/quantum/qubits/majorana/fermions.yml index f7b1d4dc0..d47511c41 100644 --- a/codes/quantum/qubits/majorana/fermions.yml +++ b/codes/quantum/qubits/majorana/fermions.yml @@ -14,10 +14,11 @@ description: | Finite-dimensional quantum error-correcting code encoding a logical (qudit or fermionic) Hilbert space into a physical Fock space of fermionic modes. Codes are typically described using Majorana operators, which are linear combinations of fermionic creation and annihilation operators \cite{arxiv:quant-ph/0003137}. + Admissible codewords are called fermionic states, a subset of which is the Gaussian fermionic states \cite{arxiv:quant-ph/0108033,arxiv:quant-ph/0108010,arxiv:quant-ph/0404180,arxiv:2010.15518,arxiv:2409.11628}. features: general_gates: - - 'Clifford operations on fermionic codes can often be formulated using \textit{Fermionic Linear Optics}, a classically simulable model of computation \cite{arxiv:quant-ph/0108033,arxiv:quant-ph/0108010,arxiv:quant-ph/0404180}. The structure of the Majorana Clifford group has been studied \cite{arxiv:2407.11319}.' + - 'Clifford operations on fermionic codes can often be formulated using \textit{Fermionic Linear Optics}, a classically simulable model of computation \cite{arxiv:quant-ph/0108033,arxiv:quant-ph/0108010,arxiv:quant-ph/0404180,arxiv:2010.15518,arxiv:2409.11628}. The structure of the Majorana Clifford group has been studied \cite{arxiv:2407.11319}.' notes: - 'See Ref. \cite{arxiv:1404.0897} for an introduction into Majorana-based qubits.' diff --git a/codes/quantum/qubits/permutation_invariant/icosahedral_permutation_invariant.yml b/codes/quantum/qubits/permutation_invariant/icosahedral_permutation_invariant.yml index 59782d5f1..defa703eb 100644 --- a/codes/quantum/qubits/permutation_invariant/icosahedral_permutation_invariant.yml +++ b/codes/quantum/qubits/permutation_invariant/icosahedral_permutation_invariant.yml @@ -10,6 +10,10 @@ logical: qubits name: '\(((7,2,3))\) Pollatsek-Ruskai code' introduced: '\cite{arxiv:quant-ph/0304153,arxiv:2005.10910,arxiv:2305.07023}' +alternative_names: + - '\(((7,2,3))\) icosahedral code' + + description: | Seven-qubit PI code that realizes gates from the binary icosahedral group transversally. Can also be interpreted as a spin-\(7/2\) single-spin code. diff --git a/codes/quantum/qubits/qubits_into_qubits.yml b/codes/quantum/qubits/qubits_into_qubits.yml index 598be25c2..91638003f 100644 --- a/codes/quantum/qubits/qubits_into_qubits.yml +++ b/codes/quantum/qubits/qubits_into_qubits.yml @@ -122,6 +122,7 @@ features: where \(P\) is any Pauli matrix, where \(C_1\) is the \hyperref[topic:pauli]{Pauli group}, and where \(C_2\) is the \hyperref[topic:clifford]{Clifford group}. \end{defterm}' - 'Arbitrary \(n\)-qubit circuits can be implemented fault-tolerantly in a 3D architecture using \(O(n^{3/2}\log^3 n)\) qubits, and in a 2D architecture using only \(O(n^2 \log^3 n)\) qubits \cite{arxiv:2402.13863}.' + - 'Fault-tolerant gates can be done for any code supporting a transversal implementation of Pauli gates using generalized gate teleportation \cite{arxiv:2409.11616}.' decoders: - 'Incorporating faulty syndrome measurements can be done using the \textit{phenomenological noise model}, which simulates errors during syndrome extraction by flipping some of the bits of the measured syndrome bitstring. In the more involved \textit{circuit-level noise model}, every component of the syndrome extraction circuit can be faulty.' - 'The decoder determining the most likely error given a noise channel is called the \textit{maximum probability error} (MPE) decoder. For few-qubit codes (\(n\) is small), MPE decoding can be based by creating a lookup table. For infinite code families, the size of such a table scales exponentially with \(n\), so approximate decoding algorithms scaling polynomially with \(n\) have to be used.' @@ -132,6 +133,7 @@ features: fault_tolerance: - 'There are lower bounds on the overhead of fault-tolerant QEC in terms of the capacity of the noise channel \cite{arxiv:2202.00119}. A more stringent bound applies to geometrically local QEC due to the fact that locality constrains the growth of the entanglement that is needed for protection \cite{arxiv:2302.04317}.' - 'Arbitrary \(n\)-qubit circuits can be implemented fault-tolerantly in a 3D architecture using \(O(n^{3/2}\log^3 n)\) qubits, and in a 2D architecture using only \(O(n^2 \log^3 n)\) qubits \cite{arxiv:2402.13863}.' + - 'Fault-tolerant gates can be done for any code supporting a transversal implementation of Pauli gates using generalized gate teleportation \cite{arxiv:2409.11616}.' threshold: - '\begin{defterm}{Computational threshold} \label{topic:computational-threshold} diff --git a/codes/quantum/qubits/stabilizer/topological/color/2d_color/triangular_color/triangular_color.yml b/codes/quantum/qubits/stabilizer/topological/color/2d_color/triangular_color/triangular_color.yml index d84ba6bed..490c31448 100644 --- a/codes/quantum/qubits/stabilizer/topological/color/2d_color/triangular_color/triangular_color.yml +++ b/codes/quantum/qubits/stabilizer/topological/color/2d_color/triangular_color/triangular_color.yml @@ -40,7 +40,7 @@ features: general_gates: - 'Lattice surgery scheme for a hybrid 6.6.6-4.8.8 layout yields lower resource overhead when compared to analogous surface code scheme \cite{arxiv:2201.07806}.' - - 'Low-overhead magic-state distillation circuit using flag qubits \cite{arxiv:2003.03049}.' + - 'Low-overhead magic-state distillation circuit using flag qubits \cite{arxiv:2003.03049} or lattice surgery \cite{arxiv:2409.07707}.' decoders: - 'Distance-three measurement schedule based on detector error models \cite{arxiv:2407.13826}.'