ExpGate

The exponential of a generator: one variational gate, abstract over the family.

A single gate type serves every family; the generator must be an operator object (it carries the system size), and its type decides how it is normalized (mirroring how a single :class:Circuit dispatches on its gates):

• :class:~monoprop.majorana.MajoranaOperator -- a Majorana generator carrying the Hermitian operator (its coefficients follow the same convention as an observable: imaginary for a weight-2 monomial, real for weight-4); it is antihermitian-normalized -- the Hermitian phase :math:i^\{\binom\{w\}\{2\}\} divided out -- by :func:_gate_layers when the circuit is ingested. A coefficient that leaves a non-negligible imaginary residue after normalization is rejected as non-Hermitian.
• :class:~monoprop.pauli.PauliOperator -- a qubit generator; each Pauli term is Jordan-Wigner mapped and antihermitian-normalized by :func:expand_monomials when the circuit is ingested, using the propagator's qubit count.
• :class:~monoprop.fermi.FermiOperator -- a fermionic generator; converted to its (Hermitian) Majorana form by :meth:get_majorana_operator right here in __init__, so the gate is a "majorana" gate from then on. The fermionic-to-Majorana mapping already carries the factors of :math:\tfrac12 and the phases, so the resulting coefficients are exactly the Hermitian convention above -- no separate fermionic normalization is needed.

All three families thus take the Hermitian generator and normalize it identically; the only exception is the internal wire/dense format (:meth:Circuit.from_dense_arrays), whose coefficients are already the real structural g and are flagged so :func:_gate_layers passes them through unchanged.

Attributes

attribute__slots__

= ('_structural', 'family', 'generator', 'index')

attributegenerator

= generator

The generator operator (a MajoranaOperator or PauliOperator; a FermiOperator is stored in its converted MajoranaOperator form).

attributeindex

= None if index is None else int(index)

The variational-angle index driving this gate, or None for the identity mapping (see :class:Circuit).

attributefamily

= family

The generator family -- "pauli" or "majorana" -- inferred from the generator type at construction (a fermionic generator becomes "majorana").

attribute_structural

= _structural

attribute__hash__

= None

Functions

func__init__(self, generator, index=None, *, _structural=False) -> None

Wrap a generator operator; its type selects the family and normalization convention.

The generator must be an operator object -- a :class:~monoprop.majorana.MajoranaOperator, :class:~monoprop.pauli.PauliOperator, or :class:~monoprop.fermi.FermiOperator -- because those carry the system num_modes / num_qubits. A bare :class:~monoprop.majorana.Majorana / :class:~monoprop.pauli.Pauli term is not accepted; wrap it in the corresponding operator (e.g. MajoranaOperator(\{(0, 1): 1j\}, num_modes) -- a Majorana generator carries the Hermitian operator, so a weight-2 coefficient is imaginary).

_structural is internal: :meth:_structural_gate sets it when the generator already carries the real structural coefficients g (the wire/dense format), so :func:_gate_layers passes them through rather than antihermitian-normalizes them.

Source Code

paramself

paramgeneratorMajoranaOperator | PauliOperator | FermiOperator

paramindexint | None

= None

param_structuralbool

= False

Returns

None

func__eq__(self, other) -> bool

Equal when the generator, parameter index, family, and structural flag all match.

Source Code

paramself

paramotherobject

Returns

bool

func__repr__(self) -> str

Return a string representation such as ExpGate(\<generator>, index=0).

Source Code

paramself

Returns

str