Fix some aliasing issues

Project.toml

@@ -1,7 +1,7 @@
 name = "QuantumOperatorDefinitions"
 uuid = "826dd319-6fd5-459a-a990-3a4f214664bf"
 authors = ["ITensor developers <[email protected]> and contributors"]
-version = "0.1.3"
+version = "0.1.4"
 
 [deps]
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"

src/op.jl

@@ -516,6 +516,17 @@ end
 
 @op_alias "CCCNOT" "Controlled" ncontrol = 3 op = OpName"X"()
 
+## # 1-qudit rotation around generic axis n̂.
+## # exp(-im * α / 2 * n̂ ⋅ σ⃗)
+## function (n::OpName"Rn")(domain)
+##   # TODO: Is this a good parametrization?
+##   n̂ = (sin(n.θ/2) * cos(n.ϕ), sin(n.θ/2) * sin(n.ϕ/2), cos(n.θ/2))
+##   σ⃗ = (OpName"X"(domain), OpName"Y"(domain), OpName"Z"(domain))
+##   n̂σ⃗ = mapreduce(*, +, n̂, σ⃗)
+##   return cis(-(n.λ/2) * n̂σ⃗)
+## end
+## @op_alias "Rn̂" "Rn"
+
 # Version of `sign` that returns one
 # if `x == 0`.
 function nonzero_sign(x)

src/sitetypes/qubit.jl

@@ -6,35 +6,39 @@ alias(::SiteType"SpinHalf=1/2") = SiteType"Qubit"()
 
 Base.length(::SiteType"Qubit") = 2
 
-(::StateName"↑")(::SiteType"Qubit") = StateName"0"()(2)
-(::StateName"Up")(::SiteType"Qubit") = StateName"0"()(2)
+# Avoid aliases since these aren't generic
+# to Qudits/higher spin.
 (::StateName"Z+")(::SiteType"Qubit") = StateName"0"()(2)
-(::StateName"Zp")(::SiteType"Qubit") = StateName"0"()(2)
-(::StateName"Emp")(::SiteType"Qubit") = StateName"0"()(2)
+(::StateName"Zp")(domain::SiteType"Qubit") = StateName"Z+"()(domain)
+(::StateName"↑")(domain::SiteType"Qubit") = StateName"Z+"()(domain)
+(::StateName"Up")(domain::SiteType"Qubit") = StateName"Z+"()(domain)
+(::StateName"Emp")(domain::SiteType"Qubit") = StateName"Z+"()(domain)
 
-(::StateName"↓")(::SiteType"Qubit") = StateName"1"()(2)
-(::StateName"Dn")(::SiteType"Qubit") = StateName"1"()(2)
+# Avoid aliases since these aren't generic
+# to Qudits/higher spin.
 (::StateName"Z-")(::SiteType"Qubit") = StateName"1"()(2)
-(::StateName"Zm")(::SiteType"Qubit") = StateName"1"()(2)
-(::StateName"Occ")(::SiteType"Qubit") = StateName"1"()(2)
+(::StateName"Zm")(domain::SiteType"Qubit") = StateName"Z-"()(domain)
+(::StateName"↓")(domain::SiteType"Qubit") = StateName"Z-"()(domain)
+(::StateName"Dn")(domain::SiteType"Qubit") = StateName"Z-"()(domain)
+(::StateName"Occ")(domain::SiteType"Qubit") = StateName"Z-"()(domain)
 
 # `eigvecs(X)`
-alias(::StateName"+") = (StateName"0"() + StateName"1"()) / √2
-@state_alias "X+" "+"
-@state_alias "Xp" "+"
+(::StateName"X+")(::SiteType"Qubit") = ((StateName"0"() + StateName"1"()) / √2)(2)
+(::StateName"Xp")(domain::SiteType"Qubit") = StateName"X+"()(domain)
+(::StateName"+")(domain::SiteType"Qubit") = StateName"X+"()(domain)
 
-alias(::StateName"-") = (StateName"0"() - StateName"1"()) / √2
-@state_alias "X-" "-"
-@state_alias "Xm" "-"
+(::StateName"X-")(::SiteType"Qubit") = ((StateName"0"() - StateName"1"()) / √2)(2)
+(::StateName"Xm")(domain::SiteType"Qubit") = StateName"X-"()(domain)
+(::StateName"-")(domain::SiteType"Qubit") = StateName"X-"()(domain)
 
 # `eigvecs(Y)`
-alias(::StateName"i") = (StateName"0"() + im * StateName"1"()) / √2
-@state_alias "Y+" "i"
-@state_alias "Yp" "i"
+(::StateName"Y+")(::SiteType"Qubit") = ((StateName"0"() + im * StateName"1"()) / √2)(2)
+(::StateName"Yp")(domain::SiteType"Qubit") = StateName"Y+"()(domain)
+(::StateName"i")(domain::SiteType"Qubit") = StateName"Y+"()(domain)
 
-alias(::StateName"-i") = (StateName"0"() - im * StateName"1"()) / √2
-@state_alias "Y-" "-i"
-@state_alias "Ym" "-i"
+(::StateName"Y-")(::SiteType"Qubit") = ((StateName"0"() - im * StateName"1"()) / √2)(2)
+(::StateName"Ym")(domain::SiteType"Qubit") = StateName"Y-"()(domain)
+(::StateName"-i")(domain::SiteType"Qubit") = StateName"Y-"()(domain)
 
 # SIC-POVMs
 (::StateName"Tetra0")(::SiteType"Qubit") = [
@@ -55,48 +59,51 @@ alias(::StateName"-i") = (StateName"0"() - im * StateName"1"()) / √2
 ]
 
 # TODO: Define as `(I + σᶻ) / 2`?
-alias(::OpName"ProjUp") = OpName"Proj"(; index=1)
-@op_alias "projUp" "ProjUp"
-@op_alias "Proj↑" "ProjUp"
-@op_alias "proj↑" "ProjUp"
-@op_alias "Proj0" "ProjUp"
-@op_alias "proj0" "ProjUp"
+(::OpName"ProjUp")(::SiteType"Qubit") = OpName"Proj"(; index=1)(2)
+(::OpName"projUp")(domain::SiteType"Qubit") = OpName"ProjUp"()(domain)
+(::OpName"Proj↑")(domain::SiteType"Qubit") = OpName"ProjUp"()(domain)
+(::OpName"proj↑")(domain::SiteType"Qubit") = OpName"ProjUp"()(domain)
+(::OpName"Proj0")(domain::SiteType"Qubit") = OpName"ProjUp"()(domain)
+(::OpName"proj0")(domain::SiteType"Qubit") = OpName"ProjUp"()(domain)
 
 # TODO: Define as `σ⁺ * σ⁻`?
 # TODO: Define as `(I - σᶻ) / 2`?
-alias(::OpName"ProjDn") = OpName"Proj"(; index=2)
-@op_alias "projDn" "ProjDn"
-@op_alias "Proj↓" "ProjDn"
-@op_alias "proj↓" "ProjDn"
-@op_alias "Proj1" "ProjDn"
-@op_alias "proj1" "ProjDn"
+(::OpName"ProjDn")(::SiteType"Qubit") = OpName"Proj"(; index=2)(2)
+(::OpName"projDn")(domain::SiteType"Qubit") = OpName"ProjDn"()(domain)
+(::OpName"Proj↓")(domain::SiteType"Qubit") = OpName"ProjDn"()(domain)
+(::OpName"proj↓")(domain::SiteType"Qubit") = OpName"ProjDn"()(domain)
+(::OpName"Proj1")(domain::SiteType"Qubit") = OpName"ProjDn"()(domain)
+(::OpName"proj1")(domain::SiteType"Qubit") = OpName"ProjDn"()(domain)
 
-# Rotation around generic axis n̂
-# exp(-im * n.θ / 2 * n̂ ⋅ σ⃗)
-#=
-TODO: Define R-gate when `λ == -ϕ`, i.e.:
-```julia
-function Base.AbstractArray(n::OpName"R", ::Tuple{SiteType"Qubit"})
-  return [
-    cos(n.θ / 2) -exp(-im * n.ϕ)*sin(n.θ / 2)
-    exp(im * n.ϕ)*sin(n.θ / 2) cos(n.θ / 2)
-  ]
-end
-```
-or:
-```julia
-alias(n::OpName"R") = OpName"Rn"(; θ=n.θ, ϕ=n.ϕ, λ=-n.ϕ)
-=#
-# https://docs.quantum.ibm.com/api/qiskit/qiskit.circuit.library.UGate
-# TODO: Generalize to `"Qudit"`, see:
-# https://quantumcomputing.stackexchange.com/questions/16251/how-does-a-general-rotation-r-hatn-theta-related-to-u-3-gate
-# https://quantumcomputing.stackexchange.com/questions/4249/decomposition-of-an-arbitrary-1-qubit-gate-into-a-specific-gateset
-# https://en.wikipedia.org/wiki/List_of_quantum_logic_gates#Other_named_gates
-# https://en.wikipedia.org/wiki/Spin_(physics)#Higher_spins
-function (n::OpName"Rn")(::SiteType"Qubit")
-  return [
-    cos(n.θ / 2) -exp(im * n.λ)*sin(n.θ / 2)
-    exp(im * n.ϕ)*sin(n.θ / 2) exp(im * (n.ϕ + n.λ))*cos(n.θ / 2)
-  ]
-end
-@op_alias "Rn̂" "Rn"
+## TODO: Bring this back, decide on names and angle conventions.
+## # Related to rotation `"Rn"` around generic axis n̂:
+## # exp(-im * n.θ / 2 * n̂ ⋅ σ⃗)
+## #=
+## TODO: Define R-gate when `λ == -ϕ`, i.e.:
+## ```julia
+## function Base.AbstractArray(n::OpName"R", ::Tuple{SiteType"Qubit"})
+##   return [
+##     cos(n.θ / 2) -exp(-im * n.ϕ)*sin(n.θ / 2)
+##     exp(im * n.ϕ)*sin(n.θ / 2) cos(n.θ / 2)
+##   ]
+## end
+## ```
+## or:
+## ```julia
+## alias(n::OpName"R") = OpName"Rn"(; θ=n.θ, ϕ=n.ϕ, λ=-n.ϕ)
+## =#
+## # https://docs.quantum.ibm.com/api/qiskit/qiskit.circuit.library.UGate
+## # TODO: Generalize to `"Qudit"`, see:
+## # https://quantumcomputing.stackexchange.com/questions/16251/how-does-a-general-rotation-r-hatn-theta-related-to-u-3-gate
+## # https://quantumcomputing.stackexchange.com/questions/4249/decomposition-of-an-arbitrary-1-qubit-gate-into-a-specific-gateset
+## # https://en.wikipedia.org/wiki/List_of_quantum_logic_gates#Other_named_gates
+## # https://en.wikipedia.org/wiki/Spin_(physics)#Higher_spins
+## # https://qudev.phys.ethz.ch/static/content/courses/QSIT07/presentations/Schmassmann.pdf
+## # http://theory.caltech.edu/~preskill/ph219/chap5_15.pdf
+## # https://almuhammadi.com/sultan/books_2020/Nielsen_Chuang.pdf (Chapter 4)
+## function (n::OpName"GeneralRotation")(::SiteType"Qubit")
+##   return [
+##     cos(n.θ / 2) -exp(im * n.λ)*sin(n.θ / 2)
+##     exp(im * n.ϕ)*sin(n.θ / 2) exp(im * (n.ϕ + n.λ))*cos(n.θ / 2)
+##   ]
+## end

src/sitetypes/spinone.jl

@@ -9,11 +9,11 @@ alias(::SiteType"SpinOne") = SiteType"S=1"()
 (::StateName"Z-")(::SiteType"S=1") = [0, 0, 1]
 
 ## TODO: Decide on these aliases.
-(::StateName"↑")(::SiteType"S=1") = StateName"Z+"()(domain)
-(::StateName"Up")(::SiteType"S=1") = StateName"Z+"()(domain)
-(::StateName"0")(::SiteType"S=1") = StateName"Z0"()(domain)
-(::StateName"↓")(::SiteType"S=1") = StateName"Z-"()(domain)
-(::StateName"Dn")(::SiteType"S=1") = StateName"Z-"()(domain)
+(::StateName"↑")(domain::SiteType"S=1") = StateName"Z+"()(domain)
+(::StateName"Up")(domain::SiteType"S=1") = StateName"Z+"()(domain)
+(::StateName"0")(domain::SiteType"S=1") = StateName"Z0"()(domain)
+(::StateName"↓")(domain::SiteType"S=1") = StateName"Z-"()(domain)
+(::StateName"Dn")(domain::SiteType"S=1") = StateName"Z-"()(domain)
 
 # TODO: Make these more general, define as something like:
 # `(n::StateName"X")(::SiteType"S=1") = eigvecs(OpName"X"())[n.eigval]`

src/state.jl

@@ -141,11 +141,16 @@ function (n::StateName"StandardBasis")(domain)
   a[n.index] = one(Bool)
   return a
 end
-function (n::StateName{N})(domain) where {N}
+function (n::StateName{N})(domain...) where {N}
+  # TODO: Try one alias at a time?
+  # TODO: First call `alias(n, domain...)`
+  # to allow for aliases specific to certain
+  # SiteTypes?
   n′ = alias(n)
-  if n == n′
+  domain′ = alias.(domain)
+  if n == n′ && domain′ == domain
     index = parse(Int, String(N)) + 1
-    return StateName"StandardBasis"(; index)(domain)
+    return StateName"StandardBasis"(; index)(domain...)
   end
-  return n′(domain)
+  return n′(domain′...)
 end

test/test_basics.jl

@@ -223,9 +223,31 @@ const elts = (real_elts..., complex_elts...)
     end
 
     for t in (SiteType("S=1"), SiteType("SpinOne"))
-      @test state("Z+", SiteType("S=1")) == [1, 0, 0]
-      @test state("Z0", SiteType("S=1")) == [0, 1, 0]
-      @test state("Z-", SiteType("S=1")) == [0, 0, 1]
+      for (ns, x) in (
+        (("Z+", "↑", "Up"), [1, 0, 0]),
+        (("Z0", "0"), [0, 1, 0]),
+        (("Z-", "↓", "Dn"), [0, 0, 1]),
+        (("X+",), [1 / 2, 1 / sqrt(2), 1 / 2]),
+        (("X0",), [-1 / sqrt(2), 0, 1 / sqrt(2)]),
+        (("X-",), [1 / 2, -1 / sqrt(2), 1 / 2]),
+        (("Y+",), [-1 / 2, -im / sqrt(2), 1 / 2]),
+        (("Y0",), [1 / sqrt(2), 0, 1 / sqrt(2)]),
+        (("Y-",), [-1 / 2, im / sqrt(2), 1 / 2]),
+      )
+        for n in ns
+          @test state(n, t) ≈ x
+        end
+      end
+    end
+
+    # Check they are eigenvalues
+    (λ⁺, λ⁰, λ⁻) = (2, 0, -2)
+    for t in (SiteType("S=1"), SiteType("SpinOne"))
+      for n in ("X", "Y", "Z")
+        @test op(n, t) * state("$(n)+", t) ≈ λ⁺ * state("$(n)+", t) atol = eps()
+        @test op(n, t) * state("$(n)0", t) ≈ λ⁰ * state("$(n)0", t) atol = eps()
+        @test op(n, t) * state("$(n)-", t) ≈ λ⁻ * state("$(n)-", t) atol = eps()
+      end
     end
   end
 end