improvements to the non-clifford functionality

CHANGELOG.md

@@ -5,6 +5,15 @@
 
 # News
 
+## v0.10.0 - dev
+
+- **(breaking)** `StabMixture` was renamed to `GeneralizedStabilizer`.
+- **(fix)** `rowdecompose` was not accounting for the phase of the input Pauli string, leading to potential errors in nonclifford functionality.
+- `expect` is now implemented for `GeneralizedStabilizer`.
+- Constructing a `Destabilizer` out of a full-rank `Stabilizer` does not require a canonicalization anymore, i.e. `stabilizerview(Destabilizer(s))==s` is guaranteed.
+- The `maximally_mixed` function is now available for creating maximally mixed multi-qubit states.
+- `projectrand!` is now implemented for `GeneralizedStabilizer`.
+
 ## unreleased
 
 - Much faster indexing and slicing of `PauliOperator`.

Project.toml

@@ -1,7 +1,7 @@
 name = "QuantumClifford"
 uuid = "0525e862-1e90-11e9-3e4d-1b39d7109de1"
 authors = ["Stefan Krastanov <[email protected]> and QuantumSavory community members"]
-version = "0.9.19"
+version = "0.10.0"
 
 [deps]
 Combinatorics = "861a8166-3701-5b0c-9a16-15d98fcdc6aa"

docs/src/references.bib

@@ -197,6 +197,15 @@ @article{nahum2017quantum
   year = {2017}
 }
 
+% non-Clifford formalism
+
+@inproceedings{Yoder2012AGO,
+  title={A generalization of the stabilizer formalism for simulating arbitrary quantum circuits},
+  author={Theodore J. Yoder},
+  year={2012},
+  url={https://api.semanticscholar.org/CorpusID:18406560}
+}
+
 % codes
 
 @article{mackay2004sparse,

docs/src/stab-algebra-manual.md

@@ -627,12 +627,12 @@ julia> s=S"-XXX
 julia> d = Destabilizer(s)
 𝒟ℯ𝓈𝓉𝒶𝒷
 + Z__
-+ _X_
++ _XX
 + __X
 𝒮𝓉𝒶𝒷━
 - XXX
 - ZZ_
-- Z_Z
++ _ZZ
 ```
 
 They have convenience methods to extract only the stabilizer and destabilizer
@@ -642,11 +642,11 @@ pieces:
 julia> stabilizerview(d)
 - XXX
 - ZZ_
-- Z_Z
++ _ZZ
 
 julia> destabilizerview(d)
 + Z__
-+ _X_
++ _XX
 + __X
 ```
 
@@ -672,12 +672,12 @@ Clifford operations can be applied the same way they are applied to stabilizers.
 julia> apply!(d,tCNOT⊗tHadamard)
 𝒟ℯ𝓈𝓉𝒶𝒷
 - X_Z
-+ XXZ
++ _XZ
 + X__
 𝒮𝓉𝒶𝒷━
 + _ZX
 - _Z_
-- Z_X
++ ZZX
 ```
 
 # Mixed States

ext/QuantumCliffordQOpticsExt/QuantumCliffordQOpticsExt.jl

@@ -72,7 +72,14 @@ Ket(dim=4)
 ```"""
 Ket(s::QuantumClifford.AbstractStabilizer) = stab_to_ket(s)
 
-function stabmix_to_densityop(s::StabMixture)
+"""
+$TYPEDSIGNATURES
+
+Convert a stabilizer tableau to a density matrix corresponding to the given state.
+"""
+Operator(s::QuantumClifford.AbstractStabilizer) = dm(Ket(s)) # TODO support mixed stabilizer states
+
+function genstab_to_densityop(s::GeneralizedStabilizer)
     ρ₀ = zero(dm(Ket(s.stab)))
     for ((Pₗᵇⁱᵗˢ,Pᵣᵇⁱᵗˢ), χ) in s.destabweights
         ρ̃ = dm(Ket(s.stab))
@@ -96,7 +103,7 @@ end
 $TYPEDSIGNATURES
 
 """
-Operator(s::StabMixture) = stabmix_to_densityop(s)
+Operator(s::GeneralizedStabilizer) = genstab_to_densityop(s)
 
 
 """

src/QuantumClifford.jl

@@ -77,7 +77,7 @@
     # Pauli frames
     PauliFrame, pftrajectories, pfmeasurements,
     # Useful States
-    bell, ghz,
+    bell, ghz, maximally_mixed,
     single_z, single_x, single_y,
     # Graphs
     graphstate, graphstate!, graph_gatesequence, graph_gate,
@@ -92,7 +92,7 @@
     # petrajectories
     petrajectories, applybranches,
     # nonclifford
-    StabMixture, UnitaryPauliChannel, PauliChannel, pcT,
+    GeneralizedStabilizer, UnitaryPauliChannel, PauliChannel, pcT,
     # makie plotting -- defined only when extension is loaded
     stabilizerplot, stabilizerplot_axis,
     # sum types
@@ -109,6 +109,22 @@
     BIG_INT_MINUS_ONE[] = BigInt(-1)
     BIG_INT_TWO[] = BigInt(2)
     BIG_INT_FOUR[] = BigInt(4)
+
+    # Register error hint for the `project!` method for GeneralizedStabilizer
+    if isdefined(Base.Experimental, :register_error_hint)
+        Base.Experimental.register_error_hint(MethodError) do io, exc, argtypes, kwargs
+            if exc.f === project! && argtypes[1] <: GeneralizedStabilizer
+                print(io, """
+                \nThe method `project!` is not appropriate for use with`GeneralizedStabilizer`.
+                You probably are looking for `projectrand!`.
+                `project!` in this library is a low-level "linear algebra" method to verify
+                whether a measurement operator commutes with a set of stabilizers, and to
+                potentially simplify the tableau and provide the index of the anticommuting
+                term in that tableau. This linear algebra operation is not defined for
+                `GeneralStabilizer` as there is no single tableau to provide an index into.""")
+            end
+        end
+    end
 end
 
 const NoZeroQubit = ArgumentError("Qubit indices have to be larger than zero, but you are attempting to create a gate acting on a qubit with a non-positive index. Ensure indexing always starts from 1.")
@@ -462,21 +478,54 @@
 
 """
 A tableau representation of a pure stabilizer state. The tableau tracks the
-destabilizers as well, for efficient projections. On initialization there are
+destabilizers as well, for efficient projections.
+
+For full-rank tableaux, the stabilizer part of the tableau is guaranteed to be kept the same as the input stabilizer tableau given to the constructor (a guarantee not kept by [`MixedDestabilizer`](@ref)).
+
+On initialization there are
 no checks that the provided state is indeed pure. This enables the use of this
-data structure for mixed stabilizer state, but a better choice would be to use
+data structure for mixed stabilizer state, but usually a better choice would be
 [`MixedDestabilizer`](@ref).
-""" # TODO clean up and document constructor
+
+```
+julia> Destabilizer(S"ZZI XXX")
+𝒟ℯ𝓈𝓉𝒶𝒷
++ Z__
++ _X_
+𝒮𝓉𝒶𝒷━
++ XXX
++ ZZ_
+
+julia> Destabilizer(S"ZZI XXX IZZ")
+𝒟ℯ𝓈𝓉𝒶𝒷
++ X__
++ _Z_
++ __X
+𝒮𝓉𝒶𝒷━
++ ZZ_
++ XXX
++ _ZZ
+```
+"""
 struct Destabilizer{T<:Tableau} <: AbstractStabilizer
     tab::T
 end
 
 function Destabilizer(s::Stabilizer)
     row, col = size(s)
-    row>col && error(DomainError("The input stabilizer has more rows than columns, making it inconsistent or overdetermined."))
-    mixed_destab = MixedDestabilizer(s)
-    t = vcat(tab(destabilizerview(mixed_destab)),tab(stabilizerview(mixed_destab)))
-    Destabilizer(t)
+    if row<col
+        mixed_destab = MixedDestabilizer(s)
+        t = vcat(tab(destabilizerview(mixed_destab)),tab(stabilizerview(mixed_destab)))
+        return Destabilizer(t)
+    elseif row==col
+        maxmix = maximally_mixed(col)
+        for row in s
+            project!(maxmix, row)
+        end
+        return Destabilizer(maxmix.tab)
+    else
+        error(DomainError("The input stabilizer has more rows than columns, making it inconsistent or overdetermined."))
+    end
 end
 
 Base.length(d::Destabilizer) = length(tab(d))÷2

src/dense_cliffords.jl

@@ -30,12 +30,12 @@ ERROR: DimensionMismatch: Input tableau should be of size 2n×n (top half is the
 ```jldoctest
 julia> d = Destabilizer(S"Y")
 𝒟ℯ𝓈𝓉𝒶𝒷
-+ Z
++ X
 𝒮𝓉𝒶𝒷
 + Y
 
 julia> CliffordOperator(d)
-X₁ ⟼ + Z
+X₁ ⟼ + X
 Z₁ ⟼ + Y
 ```
 """