Struct HilbertState 

pub struct HilbertState<R: RealField> { /* private fields */ }

A strong type representing a Quantum State Vector (Ket) |ψ>.

This represents a Minimal Left Ideal of the algebra Cl(10) (or others), acting as the Hilbert Space.

Invariants

• The coefficients are Complex<R> for any R: RealField chosen by the caller (f32, f64, Float106, …). The type parameter has no default — call sites must spell the precision explicitly (e.g. HilbertState::<f64>::new(...)).
• The Metric is fixed at construction time (preventing mixed-algebra operations).

Implementations

impl<R: RealField> HilbertState<R>

pub fn new_spin10(data: Vec<Complex<R>>) -> Result<Self, CausalMultiVectorError>

Creates a new Hilbert State for the Grand Unified Algebra (Spin(10)). This enforces the metric Cl(10) (NonEuclidean, 10D).

pub fn new( data: Vec<Complex<R>>, metric: Metric, ) -> Result<Self, CausalMultiVectorError>

Generic constructor for other quantum systems (e.g. Qubits / Cl(2)).

pub fn new_unchecked(data: Vec<Complex<R>>, metric: Metric) -> Self

pub fn from_multivector(mv: CausalMultiVector<Complex<R>>) -> Self

pub fn into_inner(self) -> CausalMultiVector<Complex<R>>

Unwraps the state to access the underlying algebraic object. Useful when you need to perform raw geometric operations.

pub fn as_inner(&self) -> &CausalMultiVector<Complex<R>>

Borrows the underlying algebraic object.

pub fn mv(&self) -> &CausalMultiVector<Complex<R>>

impl<R: RealField + Default> HilbertState<R>

pub fn to_ket(&self) -> Result<CausalTensor<Complex<R>>, CausalMultiVectorError>

The d-dimensional complex column of this ket in the matrix representation: column KET_COLUMN of to_matrix(), scaled by 1/√D so that the raw column inner product k(φ)ᴴ · k(ψ) equals the metric-correct Dirac product ⟨φ|ψ⟩ on the minimal left ideal (and a Dirac-normalized ket yields a unit-trace ρ = k·kᴴ).

Defined only for even-dimensional metrics, where to_matrix() is a bijection (D² = 2ⁿ) — including Cl(0,10) (D = 32).

Errors

Returns a DimensionMismatch for an odd-dimensional metric (the expected field carries the next even dimension).

pub fn from_ket( ket: &CausalTensor<Complex<R>>, metric: Metric, ) -> Result<Self, CausalMultiVectorError>

Embeds a d-dimensional complex column as a minimal-left-ideal ket: the column is placed (scaled by √D, the inverse of the Self::to_ket gain) at column KET_COLUMN of a D×D matrix and mapped back via from_matrix, so to_ket(from_ket(v)) == v exactly.

Accepts a ket of shape [D] or [D, 1] with D = 2^(n/2); defined only for even-dimensional metrics.

Errors

Returns a DimensionMismatch for an odd-dimensional metric, or a DataLengthMismatch if the ket is not a D-vector / D×1 column.

Trait Implementations

impl<R: RealField> Add for HilbertState<R>

type Output = HilbertState<R>

The resulting type after applying the + operator.

fn add(self, rhs: Self) -> Self::Output

Performs the + operation.

impl<R: Clone + RealField> Clone for HilbertState<R>

fn clone(&self) -> HilbertState<R>

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<R: Debug + RealField> Debug for HilbertState<R>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<R: RealField> Default for HilbertState<R>

fn default() -> Self

Returns the “default value” for a type.

impl<R: RealField + Debug> Display for HilbertState<R>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<R: RealField> Mul<Complex<R>> for HilbertState<R>

type Output = HilbertState<R>

The resulting type after applying the * operator.

fn mul(self, rhs: Complex<R>) -> Self::Output

Performs the * operation.

impl<R: PartialEq + RealField> PartialEq for HilbertState<R>

fn eq(&self, other: &HilbertState<R>) -> bool

Equality operator ==.

fn ne(&self, other: &Rhs) -> bool

Inequality operator !=.

impl<R: PartialEq + RealField> StructuralPartialEq for HilbertState<R>

impl<R: RealField> TryFrom<&HilbertState<R>> for HopfState<R>

Conversion: Quantum State (Spinor) -> Topological Rotor (Hopf).

type Error = CausalMultiVectorError

The type returned in the event of a conversion error.

fn try_from(quantum_state: &HilbertState<R>) -> Result<Self, Self::Error>

Performs the conversion.

impl<R: RealField> TryFrom<HopfState<R>> for HilbertState<R>

Conversion: Topological Rotor (Hopf) -> Quantum State (Spinor).

type Error = CausalMultiVectorError

The type returned in the event of a conversion error.

fn try_from(hopf: HopfState<R>) -> Result<Self, Self::Error>

Performs the conversion.