refs

codes/quantum/oscillators/fock_state/rotation/binomial.yml

@@ -38,6 +38,7 @@ features:
   general_gates:
     - 'Error-detecting \(CCZ\) and \(cSWAP\) gates for "0-2-4" code using three-level ancilla \cite{arxiv:2212.11196}.'
     - 'Single logical-qubit rotations \cite{arxiv:2408.12968}.'
+    - 'Amplitude-mixing error-transparent gates \cite{arxiv:2412.08870}.'
 
   decoders:
     - 'Photon loss and dephasing errors can be detected by measuring the phase-space rotation \(\exp\left(2\pi\mathrm{i} \hat{n} / (S+1)\right)\) and the check operator \(J_x/J\) in the spin-coherent state language, where \(J\) is the total angular momentum and \(J_x\) is the angular momentum in the \(x\) direction \cite{arxiv:1708.05010}. This type of error correction fails for errors that are products of photon loss/gain and dephasing errors. However, for certain \((N,S)\) instances of the binomial code, detection of these types of errors can be done.'

codes/quantum/properties/hamiltonian/commuting_projector.yml

@@ -17,7 +17,8 @@ protection: |
 
   2D topological order on qubit manifolds requires weight-four (four-body) Hamiltonian terms, i.e., it cannot be stabilized via weight-two (two-body) or weight-three (three-body) terms on nearly Euclidean geometries of qubits or qutrits \cite{arxiv:quant-ph/0308021,arxiv:1102.0770,arxiv:1803.02213}.
 
-  Commuting-projector Hamiltonians with weight-two (two-body) terms cannot be used to suppress errors in adiabatic quantum computation \cite{arxiv:1410.5487}, but this can be circumvented with subsystem code Hamiltonians, e.g., using BBS codes \cite{arxiv:1511.01997,arxiv:1606.03795}.
+  Ground-state spaces of commuting-projector Hamiltonians with weight-two (two-body) terms cannot be used to suppress errors in adiabatic quantum computation \cite{arxiv:1410.5487}, but this can be circumvented with excited-state subspaces \cite{arxiv:2412.07764} or ground-state subspaces of subsystem code Hamiltonians, e.g., using BBS codes \cite{arxiv:1511.01997,arxiv:1606.03795}.
+  No eigenspace of a weight-two commuting-projector Hamiltonian can simultaneously have \(d > 2\) and dimension greater than 1 \cite{arxiv:2412.07764}.
 
 
 relations:
@@ -30,9 +31,9 @@ relations:
       detail: 'Geometrically local commuting-projector code Hamiltonians on Euclidean manifolds are stable with respect to small perturbations when they satisfy the \hyperref[topic:tqo]{TQO conditions}, meaning that a notion of a phase can be defined \cite{arxiv:1001.4363,arxiv:1001.0344,arxiv:1109.1588,arxiv:1810.02428,arxiv:2010.15337}.
       This notion can be extended to semi-hyperbolic manifolds \cite{arxiv:2405.19412} and non-geometrically local QLDPC codes exhibiting check soundness \cite{arxiv:2411.01002} (see also \cite{arxiv:2411.02384}).'
     - code_id: subsystem_stabilizer
-      detail: 'Commuting-projector Hamiltonians with weight-two (two-body) terms cannot be used to suppress errors in adiabatic quantum computation \cite{arxiv:1410.5487}, but this can be circumvented with subsystem code Hamiltonians, e.g., using BBS codes \cite{arxiv:1511.01997,arxiv:1606.03795}.'
+      detail: 'Ground-state spaces of commuting-projector Hamiltonians with weight-two (two-body) terms cannot be used to suppress errors in adiabatic quantum computation \cite{arxiv:1410.5487}, but this can be circumvented with excited-state subspaces \cite{arxiv:2412.07764} or ground-state subspaces of subsystem code Hamiltonians, e.g., using BBS codes \cite{arxiv:1511.01997,arxiv:1606.03795}.'
     - code_id: bravyi_bacon_shor
-      detail: 'Commuting-projector Hamiltonians with weight-two (two-body) terms cannot be used to suppress errors in adiabatic quantum computation \cite{arxiv:1410.5487}, but this can be circumvented with subsystem code Hamiltonians, e.g., using BBS codes \cite{arxiv:1511.01997,arxiv:1606.03795}.'
+      detail: 'Ground-state spaces of commuting-projector Hamiltonians with weight-two (two-body) terms cannot be used to suppress errors in adiabatic quantum computation \cite{arxiv:1410.5487}, but this can be circumvented with excited-state subspaces \cite{arxiv:2412.07764} or ground-state subspaces of subsystem code Hamiltonians, e.g., using BBS codes \cite{arxiv:1511.01997,arxiv:1606.03795}.'
 
 
 # Begin Entry Meta Information

codes/quantum/qubits/small_distance/small/4/stab_4_2_2.yml

@@ -36,13 +36,13 @@ description: |
   This code can be thought of as a concatenation of a two-qubit bit-flip with a two-qubit phase-flip code.
 
 
-
 protection: |
   Detects a single-qubit error \cite{arxiv:quant-ph/9603031} or single erasure \cite{arxiv:quant-ph/9610042}.
   Not able to correct arbitrary single-qubit errors because \( \lfloor \frac{d-1}{2} \rfloor =0 \).
 
   The \([[4,1,2]]\) subcodes \(\{|\overline{00}\rangle,|\overline{10}\rangle\}\) \cite{arxiv:quant-ph/9704002} and \(\{|\overline{01}\rangle,|\overline{11}\rangle\}\) \cite{arxiv:quant-ph/0103042} approximately correct a single \hyperref[topic:ad]{AD} error, with the latter being a constant excitation code.
 
+  An equivalent version of this code can suppress errors in adiabatic quantum computation by being used as an excited-state space of a particular Hamiltonian \cite{arxiv:2412.07764}.
 
 features:
   magic_scaling_exponent: 'Various magic-state distillation protocols exist for the \([[4,2,2]]\) qubit code and the \([[6,2,2]]\) \(C_6\) code in what are known as Meier-Eastin-Knill (MEK) protocols \cite{arxiv:1204.4221}.
@@ -53,6 +53,9 @@ features:
     - 'A transversal \(CZ\) gate is realized by the rotation \(\sqrt{Z}\otimes\sqrt{Z}^{\dagger}\otimes\sqrt{Z}^{\dagger}\otimes\sqrt{Z}\).'
     - 'Adding \(XYZI\) to the stabilizer group produces a \([[4,1,2]]\) subcode that admits weight-two transversal logical Pauli operations \cite{arxiv:quant-ph/0512170}.'
 
+  general_gates:
+    - 'Some inter-block gates can be weight-two (two-body) with the help of perturbative gadgets, making it possible to suppress errors in adiabatic quantum computation \cite{arxiv:2412.07764}.'
+
   fault_tolerance:
     - 'Preparation of certain states, both magic and non-magic, along with transversal gates can be performed fault-tolerantly, but requires post-selection because the code cannot correct errors \cite{arxiv:1610.03507}.
     Magic states can be injected into surface and color codes since the code is a small instance of both \cite{arxiv:2305.13581}.'