netket.operator.ProductOperator

class netket.operator.ProductOperator

Bases: ABC

Base class for product of quantum operators.

This class represents a product of quantum operators with a coefficient, implementing the mathematical concept of \(c \prod_i \hat{H}_i\) where \(c\) is a scalar coefficient and \(\hat{H}_i\) are quantum operators.

The class uses a dispatch mechanism to automatically select the appropriate specialized subclass based on the types of operators being multiplied:

• ProductDiscreteJaxOperator for products of DiscreteJaxOperator instances

• ProductDiscreteOperator for products of DiscreteOperator instances

• ProductGenericOperator for mixed operator types or fallback cases.

Products can be constructed using the @ operator (matrix multiplication) or by directly instantiating this class with a list of operators.

Examples

Creating a product of Pauli operators:

>>> import netket as nk
>>> hi = nk.hilbert.Spin(s=1/2, N=4)
>>> sx0 = nk.operator.spin.sigmax(hi, 0)
>>> sz1 = nk.operator.spin.sigmaz(hi, 1)
>>> sy2 = nk.operator.spin.sigmay(hi, 2)
>>> # Using ProductOperator constructor
>>> product1 = nk.operator.ProductOperator(sx0, sz1, sy2)
>>> print(product1)
ProductDiscreteJaxOperator with terms:
 ∙ 1.0
 ∙ PauliStringsJax(n_sites=4, hilbert=Spin(s=1/2, N=4), n_strings=1)
 ∙ PauliStringsJax(n_sites=4, hilbert=Spin(s=1/2, N=4), n_strings=1)
 ∙ PauliStringsJax(n_sites=4, hilbert=Spin(s=1/2, N=4), n_strings=1)

Creating a product with explicit coefficient:

>>> # Direct instantiation
>>> product2 = nk.operator.ProductOperator(sx0, sz1, coefficient=2.0)
>>> print(product2.coefficient)
2.0

Products of products are automatically flattened:

>>> prod_a = nk.operator.ProductOperator(sx0, sz1)
>>> prod_b = nk.operator.ProductOperator(sy2, nk.operator.spin.sigmaz(hi, 3))
>>> combined = nk.operator.ProductOperator(prod_a, prod_b)
>>> print(len(combined.operators))  # All 4 operators are flattened
4

Scaling a product:

>>> scaled = 3.0 * product1
>>> print(scaled.coefficient)
(3+0j)

Inheritance

__init__(operators, *args, coefficient=1.0, dtype=None, **kwargs)

Constructs a Product of Operators.

Parameters:

• operators (Iterable[AbstractHilbert]) – An iterable of quantum operators to be multiplied. All operators must act on the same Hilbert space.

• coefficient (float) – Scalar coefficient for the product. Default is 1.0.

• dtype – Data type for the coefficient. If None, it will be inferred from the operators and coefficient.

Attributes

coefficient

The scalar coefficient multiplying the product of operators.

dtype

operators

The tuple of all operators in the terms of this product. All operators are multiplied together with the scalar coefficient.

Methods