It reminds me of Sean Carrols Hilbert Space Fundamentalism.
Sean M. Carroll: Reality as a Vector in Hilbert Space
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Looking at the date on that article, he isn't the first to propose the idea. I remember hearing about "The Church of the larger Hilbert space" many years ago.
Hilbert space https://en.wikipedia.org/wiki/Hilbert_space :
From sympy.physics.quantum.hilbert https://github.com/sympy/sympy/blob/master/sympy/physics/qua... :
__all__ = [
'HilbertSpaceError',
'HilbertSpace',
'TensorProductHilbertSpace',
'TensorPowerHilbertSpace',
'DirectSumHilbertSpace',
'ComplexSpace',
'L2',
'FockSpace'
]
__all__ = [
'Operator',
'HermitianOperator',
'UnitaryOperator',
'IdentityOperator',
'OuterProduct',
'DifferentialOperator'
]
""" A module for mapping operators to their corresponding eigenstates and vice versa
It contains a global dictionary with eigenstate-operator pairings.
If a new state-operator pair is created,
this dictionary should be updated as well.
It also contains functions operators_to_state and state_to_operators for mapping between the two. These can handle both classes and instances of operators and states.
See the individual function descriptions for details.
TODO List:
- Update the dictionary with a complete list of state-operator pairs
"""
"""Logic for representing operators in state in various bases.
TODO:
* Get represent working with continuous hilbert spaces.
* Document default basis functionality.
"""
# ...
__all__ = [
'represent',
'rep_innerproduct',
'rep_expectation',
'integrate_result',
'get_basis',
'enumerate_states'
]
# ...
def represent(expr, **options):
"""Represent the quantum expression in the given basis.
From tequila/simulators/simulator_cirq https://github.com/tequilahub/tequila/blob/master/src/tequil... :
from tequila.wavefunction.qubit_wavefunction import QubitWaveFunction
> """ Export QCircuits as qasm code OPENQASM version 2.0 specification from:
> A. W. Cross, L. S. Bishop, J. A. Smolin, and J. M. Gambetta, e-print arXiv:1707.03429v2 [quant-ph] (2017). https://arxiv.org/pdf/1707.03429v2.pdf
Why are you posting this?
Because there is a functional executable symbolic algebra implementation of such Hilbert spaces and their practical representations (and qubit applications) that's approachable because it's not ambiguous MathTeX without automated tests and test assertions.
Because it's easier to learn math things by preparing a notebook with MathTex and/or SymPy expressions with a MathTeX representation and then make test assertions about the symbolic expression and/or `assert np.allclose()` with real valued parameters after symbolic construction and derivation