Fermionic swap gate added

Author: Harsha Nagarajan

CHANGELOG.md

@@ -3,6 +3,7 @@ QuantumCircuitOpt.jl Change Log
 
 ### v0.6.0 
 - Minor clean up in global phase enforcing constraints 
+- Added 2-qubit Fermionic SWAP gate, that swaps adjacent fermionic modes
 - Added support for `unitary_complex_conjugate` constraints (for both with and without global phase), which significantly speeds up QCOpt’s decomposition methods.
 - Added `is_zero` function with a `tol` option
 - Added `QFT3Gate` to docs

docs/src/2_qubit_gates.md

@@ -116,6 +116,10 @@ CU3RevGate
 ```@docs
 SwapGate
 ```
+## fSwapGate
+```@docs
+fSwapGate
+```
 ## SSwapGate
 ```@docs
 SSwapGate

src/gates.jl

@@ -1369,6 +1369,31 @@ function SwapGate()
     return Array{Complex{Float64},2}([1 0 0 0; 0 0 1 0; 0 1 0 0; 0 0 0 1])
 end
 
+@doc raw"""
+    fSwapGate()
+
+Two-qubit, symmetric, Fermionic SWAP gate, that swaps adjacent fermionic modes 
+in the Jordan-Wigner representation. Because the qubits represent identical 
+fermions, swapping two particles applies a -1 phase to the state.
+
+Reference: https://doi.org/10.22331/q-2018-12-21-114
+
+**Matrix Representation**
+
+```math
+fSWAP = \begin{pmatrix}
+1 & 0 & 0 & 0 \\
+0 & 0 & 1 & 0 \\
+0 & 1 & 0 & 0 \\
+0 & 0 & 0 & -1
+\end{pmatrix}
+```
+"""
+function fSwapGate()
+    return Array{Complex{Float64},2}([1 0 0 0; 0 0 1 0; 0 1 0 0; 0 0 0 -1])
+end
+
+
 @doc raw"""
     SSwapGate()
 

test/gates_tests.jl

@@ -207,4 +207,7 @@
     M1 = QCO.multi_controlled_gate(QCO.HGate(), [1], 2, 3)
     M2 = kron(QCO.CHGate(), QCO.IGate(1))
     @test isapprox(M1, M2, atol=tol_0)
+
+    # Test Fermionic-Swap gate
+    @test isapprox(QCO.fSwapGate(), QCO.SwapGate()*QCO.CZGate(), atol=tol_0)
 end