seemps.analysis.integration.integrate_mps#

seemps.analysis.integration.integrate_mps(mps, domain, mps_order='A')[source]#

Returns the integral of a multivariate function represented as a MPS. Uses the ‘best possible’ quadrature rule according to the intervals that compose the mesh. Intervals of type RegularInterval employ high-order Newton-Côtes rules, while those of type ChebyshevInterval employ Clenshaw-Curtis rules.

Parameters:

mpsMPS: The MPS representation of the multivariate function to be integrated.
domainUnion[Interval, Mesh]: An object defining the discretization domain of the function. Can be either an Interval or a Mesh given by a collection of intervals. The quadrature rules are selected based on the properties of these intervals.
mps_orderstr, default=’A’: Specifies the ordering of the qubits in the quadrature. Possible values:. - ‘A’: Qubits are serially ordered (by variable). - ‘B’: Qubits are interleaved (by significance).

Returns:

Union[complex, float]: The integral of the MPS representation of the function discretized in the given Mesh.

Notes

This algorithm assumes that all function variables are in the standard MPS form, i.e.

quantized in base 2, and are discretized either on a RegularInterval or `ChebyshevInterval.

For more general structures, the quadrature MPS can be constructed

using the univariate quadrature rules and the mps_tensor_product routine, which can be subsequently contracted using the scprod routine.

Examples

# Integrate a given bivariate function using the Clenshaw-Curtis quadrature.
# Assuming that the MPS is already loaded (for example, using TT-Cross or Chebyshev).
mps_function_2d = ...

# Define a domain that matches the MPS to integrate.
start, stop = -1, 1
n_qubits = 10
interval = ChebyshevInterval(-1, 1, 2**n_qubits, endpoints=True)
mesh = Mesh([interval, interval])

# Integrate the MPS on the given discretization domain.
integral = integrate_mps(mps_function_2d, mesh)