diff --git a/src/PEPSKit.jl b/src/PEPSKit.jl
index a0317a6b1..f1c537ee6 100644
--- a/src/PEPSKit.jl
+++ b/src/PEPSKit.jl
@@ -61,6 +61,7 @@ include("utility/symmetrization.jl")
 include("operators/infinitepepo.jl")
 include("operators/transfermatrix.jl")
 include("operators/localoperator.jl")
+include("operators/localcircuit.jl")
 include("operators/lattices/squarelattice.jl")
 include("operators/models.jl")
 
diff --git a/src/algorithms/time_evolution/trotter_gate.jl b/src/algorithms/time_evolution/trotter_gate.jl
index 84a4882b5..24248ad9c 100644
--- a/src/algorithms/time_evolution/trotter_gate.jl
+++ b/src/algorithms/time_evolution/trotter_gate.jl
@@ -1,116 +1,3 @@
-"""
-$(TYPEDEF)
-
-Circuit consisting of local gates and MPOs.
-
-## Fields
-
-$(TYPEDFIELDS)
-"""
-struct LocalCircuit{O, S}
-    "lattice of physical spaces on which the gates act"
-    lattice::Matrix{S}
-
-    "list of `sites => gate` pairs that make up the circuit"
-    gates::Vector{Pair{Vector{CartesianIndex{2}}, O}}
-
-    LocalCircuit{O, S}(lattice::Matrix{S}) where {O, S} =
-        new{O, S}(lattice, Vector{Pair{Vector{CartesianIndex{2}}, O}}())
-end
-
-LocalCircuit{O}(lattice::Matrix{<:ElementarySpace}) where {O} =
-    LocalCircuit{O, eltype(lattice)}(lattice)
-LocalCircuit{O}(lattice, gates::Pair...) where {O} = LocalCircuit{O}(lattice, gates)
-
-function LocalCircuit{O}(lattice, terms) where {O}
-    operator = LocalCircuit{O}(lattice)
-    for (inds, term) in terms
-        add_factor!(operator, inds, term)
-    end
-    return operator
-end
-
-# Default to Any for eltype: needs to be abstract anyways so not that much to gain
-LocalCircuit(lattice, terms) = LocalCircuit{Any}(lattice, terms)
-LocalCircuit(lattice, terms::Pair...) = LocalCircuit(lattice, terms)
-
-add_factor!(operator::LocalCircuit, inds::Tuple, term::AbstractTensorMap) = add_factor!(operator, collect(inds), term)
-add_factor!(operator::LocalCircuit, inds::Vector, term::AbstractTensorMap) = add_factor!(operator, map(CartesianIndex{2}, inds), term)
-function add_factor!(operator::LocalCircuit, inds::Vector{CartesianIndex{2}}, term::AbstractTensorMap)
-    # input checks
-    length(inds) == numin(term) == numout(term) || throw(ArgumentError("Incompatible number of indices and tensor legs"))
-    for (i, ind) in enumerate(inds)
-        ind_translated = CartesianIndex(mod1.(Tuple(ind), size(operator)))
-        physicalspace(operator, ind_translated) == domain(term)[i] == codomain(term)[i] ||
-            throw(SpaceMismatch("Incompatible physical spaces at $(ind)."))
-    end
-
-    # permute input
-    if !issorted(inds)
-        I = sortperm(inds)
-        inds = inds[I]
-        term = permute(term, (Tuple(I), Tuple(I) .+ numout(term)))
-    end
-
-    # translate coordinates
-    I1 = first(inds)
-    I1_mod = CartesianIndex(mod1.(Tuple(I1), size(operator)))
-    inds .-= (I1 - I1_mod)
-
-    push!(operator.gates, inds => term)
-
-    return operator
-end
-# for MPO term
-# TODO: consider directly use MPSKit.FiniteMPO
-function add_factor!(
-        operator::LocalCircuit, inds::Vector{CartesianIndex{2}}, term::Vector{M}
-    ) where {M <: AbstractTensorMap}
-    # input checks
-    length(inds) >= 2 || throw(ArgumentError("Gate MPO must act on 2 or more sites."))
-    length(inds) == length(term) || throw(ArgumentError("Incompatible number of indices and length of gate MPO."))
-    allunique(inds) || throw(ArgumentError("`inds` should not contain repeated coordinates."))
-    for (i, (ind, t)) in enumerate(zip(inds, term))
-        ind_translated = CartesianIndex(mod1.(Tuple(ind), size(operator)))
-        out_ax = (i == 1) ? 1 : 2
-        in_ax = (i == 1) ? 2 : 3
-        physicalspace(operator, ind_translated) == space(t, out_ax) == space(t, in_ax)' ||
-            throw(SpaceMismatch("Incompatible physical spaces at $(ind)."))
-        if i >= 2
-            ind_prev = inds[i - 1]
-            sum(Tuple(ind - ind_prev) .^ 2) == 1 || throw(ArgumentError("Two consecutive sites in `inds` must be nearest neighbours for MPO terms."))
-        end
-    end
-    # for MPO term, `inds` should not be sorted
-    push!(operator.gates, inds => term)
-    return operator
-end
-
-function checklattice(::Type{Bool}, H1::LocalCircuit, H2::LocalCircuit)
-    return physicalspace(H1) == physicalspace(H2)
-end
-function checklattice(::Type{Bool}, peps::InfinitePEPS, O::LocalCircuit)
-    return physicalspace(peps) == physicalspace(O)
-end
-function checklattice(::Type{Bool}, H::LocalCircuit, peps::InfinitePEPS)
-    return checklattice(Bool, peps, H)
-end
-function checklattice(::Type{Bool}, pepo::InfinitePEPO, O::LocalCircuit)
-    return size(pepo, 3) == 1 && physicalspace(pepo) == physicalspace(O)
-end
-function checklattice(::Type{Bool}, O::LocalCircuit, pepo::InfinitePEPO)
-    return checklattice(Bool, pepo, O)
-end
-
-"""
-    physicalspace(gates::LocalCircuit)
-
-Return lattice of physical spaces on which the `LocalCircuit` is defined.
-"""
-physicalspace(gates::LocalCircuit) = gates.lattice
-physicalspace(gates::LocalCircuit, args...) = physicalspace(gates)[args...]
-Base.size(gates::LocalCircuit) = size(physicalspace(gates))
-
 const NNGate{T, S} = AbstractTensorMap{T, S, 2, 2}
 
 """
diff --git a/src/operators/lattices/squarelattice.jl b/src/operators/lattices/squarelattice.jl
index 005c0bdad..102546594 100644
--- a/src/operators/lattices/squarelattice.jl
+++ b/src/operators/lattices/squarelattice.jl
@@ -29,19 +29,19 @@ function vertices(lattice::InfiniteSquare)
 end
 
 function nearest_neighbours(lattice::InfiniteSquare)
-    neighbors = Tuple{CartesianIndex, CartesianIndex}[]
+    neighbors = Vector{CartesianIndex{2}}[]
     for idx in vertices(lattice)
-        push!(neighbors, (idx, idx + CartesianIndex(0, 1)))
-        push!(neighbors, (idx, idx + CartesianIndex(1, 0)))
+        push!(neighbors, [idx, idx + CartesianIndex(0, 1)])
+        push!(neighbors, [idx, idx + CartesianIndex(1, 0)])
     end
     return neighbors
 end
 
 function next_nearest_neighbours(lattice::InfiniteSquare)
-    neighbors = Tuple{CartesianIndex, CartesianIndex}[]
+    neighbors = Vector{CartesianIndex{2}}[]
     for idx in vertices(lattice)
-        push!(neighbors, (idx, idx + CartesianIndex(1, 1)))
-        push!(neighbors, (idx + CartesianIndex(0, 1), idx + CartesianIndex(1, 0)))
+        push!(neighbors, [idx, idx + CartesianIndex(1, 1)])
+        push!(neighbors, [idx + CartesianIndex(0, 1), idx + CartesianIndex(1, 0)])
     end
     return neighbors
 end
diff --git a/src/operators/localcircuit.jl b/src/operators/localcircuit.jl
new file mode 100644
index 000000000..f60a17ad2
--- /dev/null
+++ b/src/operators/localcircuit.jl
@@ -0,0 +1,137 @@
+"""
+$(TYPEDEF)
+
+Circuit consisting of local gates and MPOs.
+
+## Fields
+
+$(TYPEDFIELDS)
+"""
+struct LocalCircuit{O, S}
+    "lattice of physical spaces on which the gates act"
+    lattice::Matrix{S}
+
+    "list of `sites => gate` pairs that make up the circuit"
+    gates::Vector{Pair{Vector{CartesianIndex{2}}, O}}
+
+    LocalCircuit{O, S}(lattice::Matrix{S}) where {O, S} =
+        new{O, S}(lattice, Vector{Pair{Vector{CartesianIndex{2}}, O}}())
+end
+
+LocalCircuit{O}(lattice::Matrix{<:ElementarySpace}) where {O} =
+    LocalCircuit{O, eltype(lattice)}(lattice)
+LocalCircuit{O}(lattice, gates::Pair...) where {O} = LocalCircuit{O}(lattice, gates)
+
+function LocalCircuit{O}(lattice, terms) where {O}
+    operator = LocalCircuit{O}(lattice)
+    for (inds, term) in terms
+        add_factor!(operator, inds, term)
+    end
+    return operator
+end
+
+# Default to Any for eltype: needs to be abstract anyways so not that much to gain
+LocalCircuit(lattice, terms) = LocalCircuit{Any}(lattice, terms)
+LocalCircuit(lattice, terms::Pair...) = LocalCircuit(lattice, terms)
+
+add_factor!(operator::LocalCircuit, inds::Tuple, term::AbstractTensorMap) = add_factor!(operator, collect(inds), term)
+add_factor!(operator::LocalCircuit, inds::Vector, term::AbstractTensorMap) = add_factor!(operator, map(CartesianIndex{2}, inds), term)
+# for AbstractTensorMap term
+function add_factor!(operator::LocalCircuit, inds::Vector{CartesianIndex{2}}, term::AbstractTensorMap)
+    # input checks
+    length(inds) == numin(term) == numout(term) || throw(ArgumentError("Incompatible number of indices and tensor legs"))
+    for (i, ind) in enumerate(inds)
+        ind_translated = CartesianIndex(mod1.(Tuple(ind), size(operator)))
+        physicalspace(operator, ind_translated) == domain(term)[i] == codomain(term)[i] ||
+            throw(SpaceMismatch("Incompatible physical spaces at $(ind)."))
+    end
+    # permute input
+    if !issorted(inds)
+        I = sortperm(inds)
+        inds = inds[I]
+        term = permute(term, (Tuple(I), Tuple(I) .+ numout(term)))
+    end
+    # translate coordinates
+    I1 = first(inds)
+    I1_mod = CartesianIndex(mod1.(Tuple(I1), size(operator)))
+    inds .-= (I1 - I1_mod)
+    push!(operator.gates, inds => term)
+    return operator
+end
+# for MPO term
+# TODO: consider directly use MPSKit.FiniteMPO
+function add_factor!(
+        operator::LocalCircuit, inds::Vector{CartesianIndex{2}}, term::Vector{M}
+    ) where {M <: AbstractTensorMap}
+    # input checks
+    length(inds) >= 2 || throw(ArgumentError("Gate MPO must act on 2 or more sites."))
+    length(inds) == length(term) || throw(ArgumentError("Incompatible number of indices and length of gate MPO."))
+    allunique(inds) || throw(ArgumentError("`inds` should not contain repeated coordinates."))
+    for (i, (ind, t)) in enumerate(zip(inds, term))
+        ind_translated = CartesianIndex(mod1.(Tuple(ind), size(operator)))
+        out_ax = (i == 1) ? 1 : 2
+        in_ax = (i == 1) ? 2 : 3
+        physicalspace(operator, ind_translated) == space(t, out_ax) == space(t, in_ax)' ||
+            throw(SpaceMismatch("Incompatible physical spaces at $(ind)."))
+        if i >= 2
+            ind_prev = inds[i - 1]
+            sum(Tuple(ind - ind_prev) .^ 2) == 1 || throw(ArgumentError("Two consecutive sites in `inds` must be nearest neighbours for MPO terms."))
+        end
+    end
+    # for MPO term, `inds` should not be sorted
+    push!(operator.gates, inds => term)
+    return operator
+end
+
+function checklattice(::Type{Bool}, H1::LocalCircuit, H2::LocalCircuit)
+    return physicalspace(H1) == physicalspace(H2)
+end
+function checklattice(::Type{Bool}, peps::InfinitePEPS, O::LocalCircuit)
+    return physicalspace(peps) == physicalspace(O)
+end
+function checklattice(::Type{Bool}, H::LocalCircuit, peps::InfinitePEPS)
+    return checklattice(Bool, peps, H)
+end
+function checklattice(::Type{Bool}, pepo::InfinitePEPO, O::LocalCircuit)
+    return size(pepo, 3) == 1 && physicalspace(pepo) == physicalspace(O)
+end
+function checklattice(::Type{Bool}, O::LocalCircuit, pepo::InfinitePEPO)
+    return checklattice(Bool, pepo, O)
+end
+
+"""
+    physicalspace(gates::LocalCircuit)
+
+Return lattice of physical spaces on which the `LocalCircuit` is defined.
+"""
+physicalspace(gates::LocalCircuit) = gates.lattice
+physicalspace(gates::LocalCircuit, args...) = physicalspace(gates)[args...]
+Base.size(gates::LocalCircuit) = size(physicalspace(gates))
+
+# Equality
+# -----------
+
+Base.:(==)(O₁::LocalCircuit, O₂::LocalCircuit) =
+    physicalspace(O₁) == physicalspace(O₂) && O₁.gates == O₂.gates
+
+# Rotation
+# ----------------------
+
+function Base.rotr90(H::LocalCircuit)
+    Hsize = size(H)
+    lattice2 = rotr90(physicalspace(H))
+    terms2 = (siterotr90.(inds, Ref(Hsize)) => term for (inds, term) in H.gates)
+    return LocalCircuit(lattice2, terms2)
+end
+function Base.rotl90(H::LocalCircuit)
+    Hsize = size(H)
+    lattice2 = rotl90(physicalspace(H))
+    terms2 = (siterotl90.(inds, Ref(Hsize)) => term for (inds, term) in H.gates)
+    return LocalCircuit(lattice2, terms2)
+end
+function Base.rot180(H::LocalCircuit)
+    Hsize = size(H)
+    lattice2 = rot180(physicalspace(H))
+    terms2 = (siterot180.(inds, Ref(Hsize)) => term for (inds, term) in H.gates)
+    return LocalCircuit(lattice2, terms2)
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index f59691b93..24bc65bb9 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -23,6 +23,9 @@ end
         @time @safetestset "LocalOperator" begin
             include("types/localoperator.jl")
         end
+        @time @safetestset "LocalCircuit" begin
+            include("types/localcircuit.jl")
+        end
     end
     if GROUP == "ALL" || GROUP == "CTMRG"
         @time @safetestset "Gauge Fixing" begin
diff --git a/test/types/localcircuit.jl b/test/types/localcircuit.jl
new file mode 100644
index 000000000..16d96597c
--- /dev/null
+++ b/test/types/localcircuit.jl
@@ -0,0 +1,21 @@
+using TensorKit
+using PEPSKit
+using PEPSKit: LocalCircuit
+using Test
+
+@testset "Rotation" begin
+    op = LocalCircuit(
+        [ℂ^1 ℂ^2 ℂ^3; ℂ^4 ℂ^5 ℂ^6],
+        (
+            ((1, 1), (1, 2)) => randn(ℂ^1, ℂ^1) ⊗ randn(ℂ^2, ℂ^2),
+            ((2, 1), (1, 1)) => randn(ℂ^4, ℂ^4) ⊗ randn(ℂ^1, ℂ^1),
+            ((1, 2), (2, 3)) => randn(ℂ^2, ℂ^2) ⊗ randn(ℂ^6, ℂ^6),
+            ((1, 3), (2, 2)) => randn(ℂ^3, ℂ^3) ⊗ randn(ℂ^5, ℂ^5),
+        )...
+    )
+    @test rot180(rot180(op)) == op
+    @test rotl90(rotl90(op)) == rot180(op) == rotr90(rotr90(op))
+    @test physicalspace(rotl90(op)) == rotl90(physicalspace(op))
+    @test physicalspace(rotr90(op)) == rotr90(physicalspace(op))
+    @test physicalspace(rot180(op)) == rot180(physicalspace(op))
+end