From 4f541899e7e43e0280f696da5d5815028594ea12 Mon Sep 17 00:00:00 2001 From: VVA2024 Date: Tue, 7 Jan 2025 14:47:24 -0500 Subject: [PATCH] refs --- codes/quantum/qubits/qubits_into_qubits.yml | 5 ++++- .../qubits/small_distance/small/7/steane/steane.yml | 3 +++ codes/quantum/qubits/stabilizer/mbqc/rbh.yml | 1 + codes/quantum/qubits/stabilizer/mbqc/tree_cluster.yml | 7 +++++-- .../topological/color/2d_color/4612_color/4612_color.yml | 2 +- .../topological/color/2d_color/488_color/488_color.yml | 2 +- .../color/2d_color/488_color/union_jack_color.yml | 2 +- .../color/2d_color/triangular_color/triangular_color.yml | 7 +++---- codes/quantum/qudits/stabilizer/qudit_cluster_state.yml | 3 +++ 9 files changed, 22 insertions(+), 10 deletions(-) diff --git a/codes/quantum/qubits/qubits_into_qubits.yml b/codes/quantum/qubits/qubits_into_qubits.yml index 2d427960a..2a65d5f98 100644 --- a/codes/quantum/qubits/qubits_into_qubits.yml +++ b/codes/quantum/qubits/qubits_into_qubits.yml @@ -115,7 +115,8 @@ features: More generally, the \textit{Solovay-Kitaev} theorem \cite{doi:10.1070/rm1997v052n06abeh002155,doi:10.1090/gsm/047} states that any subset of gates the generates a dense subgroup of the full \(n\)-qubit gate group can be used to construct any gate to arbitrary accuracy (see \cite{arxiv:quant-ph/0505030}\cite[Appx. 3]{doi:10.1017/cbo9780511976667.019}). The task of approximating a desired gate by Clifford gates and a fixed set of non-Clifford gates is called \textit{gate compilation} or \textit{circuit synthesis}.' - 'Non-Clifford gates are typically more difficult to implement than Clifford gates and so are treated as a resource. Optimizing T-gate count in circuit synthesis is \(NP\)-hard \cite{arxiv:2310.05958} and can be done using various procedures \cite{arxiv:1303.2042,arxiv:1308.4134,arxiv:1601.07363,arxiv:1710.07345,arxiv:1712.01557,arxiv:2110.10292}, e.g., \textit{ZX calculus} (a.k.a. Penrose spin calculus) \cite{arxiv:1903.10477,arxiv:1911.09039,arxiv:2004.05164,arxiv:2109.01076} or reinforcement learning \cite{arxiv:2402.14396}. There is an optimal asymptotic scaling of the number of T gates needed to prepare an arbitrary state \cite{arxiv:1812.00954,arxiv:2411.04790}. - Decompositions in terms of Toffoli and Hadamard gates \cite{arxiv:quant-ph/0205115} as well as cosine-sine gates also exist \cite{arxiv:quant-ph/0404089}. Gate errors in circuit synthesis can sometimes add up destructively \cite{arxiv:1612.01011}.' + Decompositions in terms of Toffoli and Hadamard gates \cite{arxiv:quant-ph/0205115} as well as cosine-sine gates also exist \cite{arxiv:quant-ph/0404089}. Gate errors in circuit synthesis can sometimes add up destructively \cite{arxiv:1612.01011}. + There is a threshold against depolarizing noise for any single-qubit gate that determines if the gate enables universal quantum computation \cite{arxiv:0907.3189}.' - '\begin{defterm}{Clifford hierarchy} \label{topic:clifford-hierarchy} The Clifford hierarchy \cite{arxiv:quant-ph/9908010,arxiv:1608.06596,arxiv:1902.04022,arXiv:2212.05398,arxiv:2410.11818} is a tower of gate sets which includes Pauli and Clifford gates at its first two levels, and non-Clifford gates at higher levels. @@ -151,6 +152,7 @@ features: Subsequently, thresholds were determined for infinite families of lattice stabilizer codes, starting with the toric code \cite{arxiv:quant-ph/0110143}; such a threshold is colloquially called a \textit{topological threshold}. Fault-tolerant computations with no notion of locality can be made local on a 2D or 3D geometry with minimal overhead \cite{arxiv:2402.13863}. \end{defterm} + - 'There is a threshold against depolarizing noise for any single-qubit gate that determines if the gate enables universal quantum computation \cite{arxiv:0907.3189}.' - '\begin{defterm}{Measurement threshold} \label{topic:measurement-threshold} One can derive conditions quantifying how many random single-qubit measurements can be made without destroying the logical information \cite{arxiv:2402.00145}. @@ -159,6 +161,7 @@ features: \end{defterm}' - 'There is a dynamical phase transition between a bounded-error and an unbounded-error phase for a model of qubits weakly coupled to a refrigerator \cite{arxiv:2411.12805}.' + notes: - 'There is a relation between one-way entanglement distillation protocols and QECCs \cite{arxiv:quant-ph/9604024}.' - 'See \href{https://github.com/qiskit-community/qiskit-qec}{Qiskit QEC framework} for realizing protocols on IBM machines.' diff --git a/codes/quantum/qubits/small_distance/small/7/steane/steane.yml b/codes/quantum/qubits/small_distance/small/7/steane/steane.yml index 83d7c961e..0c090a8f7 100644 --- a/codes/quantum/qubits/small_distance/small/7/steane/steane.yml +++ b/codes/quantum/qubits/small_distance/small/7/steane/steane.yml @@ -93,6 +93,9 @@ realizations: Rains shadow enumerators have been measured \cite{arxiv:2408.16914}.' - 'Rydberg atom arrays: Lukin group \cite{arxiv:2112.03923}; ten logical qubits, transversal CNOT gate performed, logical ten-qubit GHZ state initialized with break-even fidelity, and fault-tolerant logical two-qubit GHZ state initialized \cite{arxiv:2312.03982}.' +notes: + - 'The Steane code can be used for entanglement purification \cite{arxiv:0811.2639}.' + relations: parents: diff --git a/codes/quantum/qubits/stabilizer/mbqc/rbh.yml b/codes/quantum/qubits/stabilizer/mbqc/rbh.yml index afef3b293..57224604a 100644 --- a/codes/quantum/qubits/stabilizer/mbqc/rbh.yml +++ b/codes/quantum/qubits/stabilizer/mbqc/rbh.yml @@ -41,6 +41,7 @@ features: threshold: - 'Various thresholds for optical quantum computing scheme with RBH codes \cite{arxiv:quant-ph/0509060,arxiv:1005.2915}.' - '\(0.75\%\) for preparation, gate, storage, and measurement errors \cite{arxiv:quant-ph/0610082}.' + - '\(24.9\%\) under erasure noise \cite{arxiv:1005.2456}.' - 'Concatenation of the RBH code with small codes such as the \([[2,1,1]]\) repetition code, \([[4,1,1,2]]\) subsystem code, or Steane code can improve thresholds \cite{arxiv:2209.09390}.' notes: diff --git a/codes/quantum/qubits/stabilizer/mbqc/tree_cluster.yml b/codes/quantum/qubits/stabilizer/mbqc/tree_cluster.yml index e73ecbdc0..94144c97d 100644 --- a/codes/quantum/qubits/stabilizer/mbqc/tree_cluster.yml +++ b/codes/quantum/qubits/stabilizer/mbqc/tree_cluster.yml @@ -8,14 +8,17 @@ physical: qubits logical: qubits name: 'Tree cluster-state code' -introduced: '\cite{arxiv:quant-ph/0507036,arxiv:1309.7207,arxiv:1603.01353}' +introduced: '\cite{arxiv:quant-ph/0507036,arxiv:1008.2048,arxiv:1008.3752,arxiv:1309.7207,arxiv:1603.01353}' description: | - Code obtained from a cluster state on a tree graph that has been proposed in the context of quantum repeater and MBQC architectures. + Code obtained from a cluster state on a tree graph (e.g., a star graph \cite{arxiv:1008.2048,arxiv:1008.3752}) that has been proposed in the context of quantum repeater and MBQC architectures. protection: | Some tree cluster-state codes have shown good performance over the depolarizing channel \cite{arxiv:1910.00471}. +features: + general_gates: + - 'Cluster states constructed from star clusters can be used to perform universal MBQC with probabilistic two-qubit gates \cite{arxiv:1008.3752}.' relations: parents: diff --git a/codes/quantum/qubits/stabilizer/topological/color/2d_color/4612_color/4612_color.yml b/codes/quantum/qubits/stabilizer/topological/color/2d_color/4612_color/4612_color.yml index 20e6acf93..0f311df3f 100644 --- a/codes/quantum/qubits/stabilizer/topological/color/2d_color/4612_color/4612_color.yml +++ b/codes/quantum/qubits/stabilizer/topological/color/2d_color/4612_color/4612_color.yml @@ -13,7 +13,7 @@ introduced: '\cite{arxiv:1108.5738}' description: | - Triangular color code defined on a patch of the 4.6.12 (truncated trihexagonal or square-hexagon-dodecagon) tiling. + 2D color code defined on a patch of the 4.6.12 (truncated trihexagonal or square-hexagon-dodecagon) tiling. Stabilizer generators are shown in \ref{figure:4.6.12-operators}. \begin{figure} diff --git a/codes/quantum/qubits/stabilizer/topological/color/2d_color/488_color/488_color.yml b/codes/quantum/qubits/stabilizer/topological/color/2d_color/488_color/488_color.yml index 2bf8da7b5..e1f99dfb4 100644 --- a/codes/quantum/qubits/stabilizer/topological/color/2d_color/488_color/488_color.yml +++ b/codes/quantum/qubits/stabilizer/topological/color/2d_color/488_color/488_color.yml @@ -13,7 +13,7 @@ introduced: '\cite{arxiv:quant-ph/0605138}' description: | - Triangular color code defined on a patch of the 4.8.8 (square-octagon) tiling, which itself is obtained by applying a fattening procedure to the square lattice \cite{arxiv:cond-mat/0607736}. + 2D color code defined on a patch of the 4.8.8 (square-octagon) tiling, which itself is obtained by applying a fattening procedure to the square lattice \cite{arxiv:cond-mat/0607736}. Stabilizer generators are shown in \ref{figure:4.8.8-operators}. \begin{figure} diff --git a/codes/quantum/qubits/stabilizer/topological/color/2d_color/488_color/union_jack_color.yml b/codes/quantum/qubits/stabilizer/topological/color/2d_color/488_color/union_jack_color.yml index a7ac5e5f2..b17b1e6ea 100644 --- a/codes/quantum/qubits/stabilizer/topological/color/2d_color/488_color/union_jack_color.yml +++ b/codes/quantum/qubits/stabilizer/topological/color/2d_color/488_color/union_jack_color.yml @@ -12,7 +12,7 @@ introduced: '\cite{arxiv:0910.0573}' description: | - Triangular color code defined on a patch of the Tetrakis square tiling (a.k.a. the Union Jack lattice). + 2D color code defined on a patch of the Tetrakis square tiling (a.k.a. the Union Jack lattice). features: 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 c7eb01a6c..4b2fd9b9d 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 @@ -12,7 +12,7 @@ short_name: '6.6.6 color' introduced: '\cite{arxiv:quant-ph/0605138}' description: | - Triangular color code defined on a patch of the 6.6.6 (honeycomb) tiling. + 2D color code defined on a patch of the 6.6.6 (honeycomb) tiling. Stabilizer generators are shown in \ref{figure:6.6.6-operators}. \begin{figure} @@ -64,10 +64,9 @@ features: - 'Depolarizing channel: \(12.6\%\) under the restriction decoder \cite{arxiv:1911.00355} and the projection decoder \cite{arxiv:1308.6207}, and \(\approx 14.5\%\) under AMBP4 decoding \cite[Fig. 12]{arxiv:2202.06612}.' -# First point is for this code threshold: - - 'Circuit-level noise: \(0.2\%\) using two flag qubits per stabilizer generator and the restriction decoder \cite{arxiv:1911.00355}, and - \(0.46\%\) under concatenated MWPM decoder \cite{arxiv:2404.07482}.' + - 'The threshold under ML decoding with measurement errors corresponds to the value of a critical point of a three-dimensional disordered Ising model, estimated to be \(4.8(2)\%\) \cite{arxiv:1005.0777}.' + - 'Circuit-level noise: \(0.2\%\) using two flag qubits per stabilizer generator and the restriction decoder \cite{arxiv:1911.00355}, and \(0.46\%\) under concatenated MWPM decoder \cite{arxiv:2404.07482}.' - 'A \hyperref[topic:measurement-threshold]{measurement threshold} of one \cite{arxiv:2402.00145}.' diff --git a/codes/quantum/qudits/stabilizer/qudit_cluster_state.yml b/codes/quantum/qudits/stabilizer/qudit_cluster_state.yml index be8692ce6..0b9dba96d 100644 --- a/codes/quantum/qudits/stabilizer/qudit_cluster_state.yml +++ b/codes/quantum/qudits/stabilizer/qudit_cluster_state.yml @@ -24,6 +24,9 @@ description: | where the neighborhood \(N(v)\) is the set of vertices which share an edge with \(v\).' features: + encoders: + - 'Operators forming the information group can be used to track how logical information is encoded \cite{arxiv:0912.2017}.' + general_gates: - '1D modular-qudit cluster states \cite{arxiv:quant-ph/0304054,arxiv:quant-ph/0512155} are resources for universal MBQC.'