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AngouriMath.Functions.Quantum

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Classes within the AngouriMath.Functions.Quantum namespace

• Factorization

  Summary

  Writing a state as a tensor product where its leading or trailing qubits are in a
  definite basis state.
  

  Remarks

  |001> + |011> is |0> (x) (|0> + |1>) (x) |1>: the first
  and last qubits agree across the whole superposition, so they factor out and only the
  middle carries it.
  **Which positions agree is not computed here.** It is
  FactorOutCommon(AngouriMath.Functions.Algebra.MonoidAlgebra.IBasisOps{`0}), the same call that takes the common
  monomial out of a polynomial -- the meet of the support. What is specific to states is
  only how the answer is written down, and that division is the whole point of the spine.
  **What this does not do.** Only a common *prefix or suffix* is factored, because a ket
  says which qubit it describes by its position in the product and there is no notation
  here for "the state of qubits 1 and 3". Nor does it find general separability:
  (|0> + |1>) (x) (|0> + |1>) has no qubit in a definite state at all,
  so the meet is empty and nothing is factored, yet it is a product state. Detecting that
  is a rank-one test on the amplitudes across a bipartition -- a different algorithm,
  belonging to this file rather than to the spine, and not written yet.
  

• Ket

  Summary

  A computational basis state: a fixed-width word over {0, 1}, with
  Free marking a position that has been factored out.
  

  Remarks

  Compared by value, which SparseTerms`1 requires -- keyed on a
  reference-equal basis it would silently stop collecting like terms.
  

• KetOps

  Summary

  The monoid and lattice structure on kets: the tensor product joins them, and the meet
  keeps a position only where both agree.
  

  Remarks

  The alphabet is unordered, so this is the meet in a product of *flat* lattices -- which
  is the only place it differs from a polynomial's exponent vector, where the meet is a
  componentwise minimum in a product of chains. Everything else about factoring is shared.
  

• QuantumState

  Summary

  Reading a quantum state out of an ordinary expression, and writing one back.
  

  Remarks

  **A state is not a new kind of node.** A ket is written apply(ket, 0, 1) -- an
  application of an undeclared name, which the library already understands -- so a state
  is an ordinary sum of products and everything that reads expressions reads it. That is
  not only tidy: it is why a|x> + b|x> = (a+b)|x> and 0|x> = 0 need no code here at all. Simplify collects like terms over an opaque
  application already, and it factors the amplitude out of a Bell state without being
  told what one is.
  The cost of the choice is that ket is a name rather than a type: nothing stops
  apply(ket, 5, 7), and a caller with their own variable called ket will
  collide with it. A dedicated node would close both and would forfeit everything in the
  paragraph above, so the loose reading is taken deliberately and is reversible.