Rewrite

[mtfishman]

To-do:

• Split off parts that are specific to ITensor, and rename the package to QuantumOperatorDefinitions.jl.
• Add tests.
• Generalize generic state constructors to accept domain sizes as an alternative to site types, i.e. Vector(StateName("1"), 3) == [0, 1, 0] as an alternative notation to Vector(StateName("1"), SiteType("Qudit"; length=3)).
• Bring back op/state definitions, with one layer that accepts integer sizes and site types, and another that accepts Index objects and constructs ITensors. That will allow the simpler notation op("X", 3) to make a 3x3 X operator.
• Bring back string parsing of operators, i.e. OpName("X * Y") == OpName("X") * OpName("Y") (implemented in a new function opexpr("X * Y") == OpName("X") * OpName("Y") but that isn't used in OpName/op constructors yet).

Future PRs:

• Generalize "Rn" gate to "Qudit" (see https://docs.quantum.ibm.com/api/qiskit/qiskit.circuit.library.UGate, https://en.wikipedia.org/wiki/Spin_(physics)#Rotations, https://en.wikipedia.org/wiki/Pauli_matrices#Exponential_of_a_Pauli_vector).
• Define clock and shift operators: https://en.wikipedia.org/wiki/Generalizations_of_Pauli_matrices#Construction:_The_clock_and_shift_matrices
• Generalize controlled gates to "Qudit" (see https://docs.quantum.ibm.com/api/qiskit/qiskit.circuit.library.UCGate).
• Create a QuantumOperatorDefinitionsITensorsExt package extension for constructing ITensor states and operators.
• Decide if we should have the behavior OpName("X * Y") == OpName("X") * OpName("Y"), op("X * Y") == op("X") * op("Y"), etc. using the function opexpr introduced in this PR.

[codecov]

Codecov Report

Attention: Patch coverage is 28.04233% with 272 lines in your changes missing coverage. Please review.

Project coverage is 24.65%. Comparing base (c04f2fc) to head (6cce957).

Files with missing lines	Patch %	Lines
src/op.jl	42.94%	97 Missing ⚠️
src/sitetypes/electron.jl	0.00%	83 Missing ⚠️
src/sitetypes/qubit.jl	6.06%	31 Missing ⚠️
src/state.jl	58.69%	19 Missing ⚠️
src/sitetypes/spinone.jl	0.00%	15 Missing ⚠️
src/sitetype.jl	30.76%	9 Missing ⚠️
src/sitetypes/fermion.jl	0.00%	9 Missing ⚠️
src/sitetypes/tj.jl	0.00%	7 Missing ⚠️
src/sitetypes/qudit.jl	0.00%	2 Missing ⚠️

Additional details and impacted files

@@             Coverage Diff             @@
##             main       #3       +/-   ##
===========================================
+ Coverage   12.73%   24.65%   +11.91%     
===========================================
  Files          21       10       -11     
  Lines         683      430      -253     
===========================================
+ Hits           87      106       +19     
+ Misses        596      324      -272     

Flag	Coverage Δ
docs	24.65% <28.04%> (+13.35%)	⬆️

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